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Evolving efficiency of spot and futures energy markets: A rolling sample approach
Journal of Behavioral and Experimental Finance 6 (2015) 67–79
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Evolving efficiency of spot and futures energy markets: A rolling sample approach Karim Ben Khediri a,b,c , Lanouar Charfeddine d,∗ a
CEROS, Université Paris Ouest Nanterre La Défense, France
b
FSEG Nabeul, University of Carthage, Tunisia
c
College of Administrative Sciences, Najran University, Saudi Arabia
d
Department of Finance and Economics, College of Business and Economics, Qatar University, P.O. Box 2713, Doha, Qatar
article
info
Article history: Received 8 November 2014 Received in revised form 14 March 2015 Accepted 23 March 2015 Available online 23 April 2015 Keywords: Market efficiency Energy market Rolling approach Variance Ratio Run test Modified R/S and DFA
abstract In this paper, we examine the weak-form efficient market hypothesis of energy markets by testing the random walk behavior of spot and futures prices. We contribute to the financial market efficiency literature by investigating the time varying markets efficiency using a ‘‘rolling sample’’ approach instead of an analysis of different time periods. For this end, we use the wild bootstrap Variance Ratio (VR) tests and the Detrended Fluctuation Analysis (DFA) technique. Empirical results show strong evidence of time varying markets efficiency with rapid mean reversion towards markets efficiency. The evolving efficiency of spot and futures markets depends on the prevailing economic and political conditions. Among the energy markets examined in this study, the spot and futures crude oil and the RBOB regular gasoline markets show the highest degree of market efficiency, while spot and future propane market is at the end of the ranking. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The Efficient Market Hypothesis (EMH) is one of the most important concepts in the modern finance literature. Formulated by Fama (1970), the EMH suggests that at any given time, prices fully reflect all available information. Since markets are efficient and current prices reflect all information then it is impossible to outperform the market. According to the EMH, no investor has an advantage in predicting a return on a stock price because no one has access to information not already available to everyone else. The EMH exists in various degrees: weak, semi-strong and strong, which addresses the inclusion of non-public information in market prices. The weak form
∗ Corresponding author. Tel.: +974 4403 7763 (Office); fax: +974 4403 5081. E-mail addresses: [email protected] (K.B. Khediri), [email protected] (L. Charfeddine). http://dx.doi.org/10.1016/j.jbef.2015.03.006 2214-6350/© 2015 Elsevier B.V. All rights reserved.
efficiency indicates that the information of all past prices is reflected in today’s prices. The semi-strong efficiency implies that all public information is calculated into current prices. The strong form efficiency indicates that all information in a market, whether public or private, is accounted for in prices. This study empirically analyzes the weak form efficiency for the energy spot and futures markets. Hereafter, ‘‘the efficiency’’ refers to the weak form efficiency in this study. The EMH has important implications for both monetary authorities and investors regarding market regulation, asset pricing, and portfolio allocation issues. The informational efficiency matters in two main ways. First, if a particular market is inefficient, investors may build up various trading strategies that lead to earn abnormal returns. Second, if all relevant information is incorporated in financial securities’ prices as soon as they appear, new capital will go to the most productive investments. These features thus highlight the necessity of research on the efficiency of markets.
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Understanding the efficiency of energy markets is of great importance for policy makers because energy plays an essential role in the world economy. Energy price movements have an impact on the performance of most economic sectors in both oil-importing and oil-exporting countries (Lescaroux and Mignon, 2008). The level of market efficiency will determine the trading and other strategies of market participants, and profitable opportunities may be available in an inefficient market. Moreover, energy markets have been considered as important markets for international portfolio diversification because of their different volatile returns and low correlations with stocks markets (Arouri and Nguyen, 2010; Daskalaki and Skiadopoulos, 2011; among others). In addition, the futures markets have two important functions. The first one is the hedging of risks. The other is the mechanism of price discovery, enabling to forecast spot prices at specified future dates. These two functions are based on the theory that the futures prices can reflect the expectation of investors which is one of the important determinants of price mechanism. In weak-form efficiency, future prices cannot be predicted based on the analysis of their past performance. This is consistent with the random walk model which assumes that the price changes are homogeneously distributed random variables. The examination of weakform efficiency can be performed by empirically testing the random walk model. The existence of long-range dependence in return series can reject the random walk model, thereby indicating that the market is not efficient in weak-form. The specificity of the energy market in comparison to other markets is it slightly nonlinear serial dependence in the return series (Alvarez-Ramirez et al., 2008, 2010; Tabak and Cajueiro, 2007; Serletis and Andreadis, 2004; Charfeddine, 2014). Thus, testing for market efficiency remains a challenging and interesting task especially in spot and futures energy markets. Although many studies to date have addressed the issue of energy markets efficiency, only a few researches have focused on the time-varying of market efficiency. Therefore, unlike traditional methods for testing market efficiency, this paper examines the time-varying efficiency of the spot and futures energy markets using the rolling sample approach. As tests of markets efficiency, we employ two variants of the VR tests statistics (Lo and MacKinlay, 1988; Chow and Denning, 1993), the wild bootstrapping technique of Kim (2006), and the Detrended Fluctuation Analysis (DFA) technique of Peng et al. (1994). Further, we provide a ranking of markets efficiency based on the percentage of time window that market departs from efficiency. In this paper, we further extend the works in existing literatures on the weak form of the EMH in the energy markets in four ways. First, in this study we pay more attention to energy market dynamics than to the average behavior of spot and futures energy prices. The classical test of market efficiency of Fama (1970) leads to a rejection or not of the null hypothesis of random walk for the sample period, which is highly unrealistic. However, according to the adaptive markets hypothesis of Lo (2004, 2005), the
market efficiency is not an all-or-none condition but is a characteristic that varies continuously over time, with periods of inefficiency alternate with those of efficiency. The evolving market efficiency over time is due by and large to changing market condition (cycles, bubbles, crashes, crises,..) and institutional factors. Hence, Instead of relying on a single measure of market efficiency for the whole sample period, we employ time-varying or rolling sample approach rather than focusing on time-invariant regressions or some different sub-periods. Therefore, there is no need to identify an event date, which is often subject to criticism. Moreover, the application of a rolling window essentially captures the persistence of energy prices departures from a random walk benchmark over time and so allows us to propose some relevant policy recommendations according to the degree of market efficiency. Second, in addition to the VR tests, we use the DFA method. Comparing with classical statistics, the DFA permits the detection of long term memory embedded in seemingly non-stationary time series, and also avoids the spurious detection of apparent long term memory that is an artifact of non-stationarity. In addition, the advantages of DFA in computation of H are that inherent trends are avoided at all timescales and local correlations can be easily probed. Third, this study is based on a more extensive sample. We use daily prices of spot and futures energy from the New Mercantile Exchange (NYMEX) with the one month maturity contracts over the period spanning from 1983 to 2014. Such period covers major events such as the Gulf war, the North American Free Trade Agreement (NAFTA), the US’ invasion of Iraq, the Asian and Russian crises, the subprime crisis and the Spring Arab. Fourth, we provide a ranking of the spot and futures markets efficiency of the crude oil (Light-Sweet, Cushing, Oklahoma), rBOB Regular Gasoline (New York Harbor), No. 2 Heating Oil (New York Harbor), and Propane (Mont Belvieu, Texas)based on different ranking criteria. In fact, ranking the efficiency of energy markets has evolved as an important information tool for policy makers and regulators to improve the efficiency channeling effective resource allocation to reduce distortions in the economy. To the best of our knowledge, this is the first work that ranks the efficiency of spot and futures energy markets. The main finding of the paper is that all four energy spot and futures markets show weak-form efficiency changing over time, depending on the prevailing economic and political conditions, which is in line with the predictions of the adaptive markets hypothesis. Moreover, it is found that the crude oil market is the most efficient, while the propane market is at the end of the ranking. The remaining of the paper is organized as follows. Section 2 presents a literature review. Section 3 presents the data and methodology. Section 4 discusses the empirical results. Finally, Section 5 concludes the paper. 2. Literature review There is a plethora of researches on the efficiency of energy markets. Previous studies have focused on different countries and markets(spot and/or futures markets), and have adopted various estimators, methodologies, sample periods and time frequencies. Overall, empirical evidences
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suggest controversial conclusions. That is, the random walk behavior in energy prices is still unresolved in the existing research. Based on monthly prices on the spot and official OPEC prices of crude oils over the period 1978–1985 and using the generalized method of moments (GMM), Green and Mork (1991) reject the weak-form efficiency for the sample as a whole but with an improvement over time. Using the unit root test allowing for a structural break, Serletis (1992) reject the hypothesis of random walk behavior in energy prices from the New York Mercantile Exchange (NYMEX) on spot-month futures prices for crude oil, heating oil and unleaded gasoline over the period 1983–1990. Using the detrending moving average technique over the period 1990–2006, Serletis and Rosenberg (2007) show that energy futures prices display long memory and that the particular form of long memory is anti-persistence. Using a semi-parametric wavelet-based estimator over the period 1994–2005, Elder and Serletis (2008) find new evidence that energy prices display long memory and that the particular form of long memory is anti-persistence,1 characterized by the variance of each series being dominated by high frequency (low wavelet scale) components. Maslyuk and Smyth (2008) examine the behavior of crude oil spot and futures prices for both West Texas Intermediate (WTI) and Brent crude oil prices over the period 1991–2004. They employ Lagrange multiplier unit root tests allowing for one and two endogenous structural breaks and show that the process of oil prices follows a random walk. Charles and Darné (2009) test the weak-form efficient market hypothesis for two crude oil markets(UK Brent and US West Texas Intermediate) over the period 1982–2008 with nonparametric variance ratio tests. They find that the Brent crude oil market exhibits weak-form efficiency, whereas the WTI crude oil market appears to be inefficient during the 1994–2008 sub-period, which suggests that the deregulation did not improve the efficiency of the WTI crude oil market with respect to less predictable returns. Wang and Yang (2010) use high-frequency (intraday) data on crude oil (along with heating oil, gasoline, and natural gas) futures markets, and find evidence of weak-form market inefficiency, but succeed only with respect to heating oil and natural gas, not crude oil. Gu et al. (2010) use the multifractal detrended fluctuation analysis to investigate the WTI and Brent crude oil prices over the period 1987–2008, and find that the two markets become more and more efficient for long-term and the two Gulf Wars cannot change time scale behavior of crude oil return series. Using parametric, semi-parametric and non-parametric methods to estimate the fractional integration parameter d of WTI crude oil prices over the period 1983–2008, Cunado et al. (2010) conclude that energy futures prices are always not long-range dependent. Wang et al. (2011) examine the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series over the period 1990–2010, employing detrended fluctuation analysis (DFA) and detrended cross-correlation
1 Anti-persistence would be indicative of an overreaction of asset prices to incoming information.
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analysis (DCCA). They identify three scaling regimes and show that, for time scales smaller than a month, the autocorrelations and cross correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Using three local Whittle methods and a modified rescaled range analysis, Wang and Wu (2012) show that returns in oil prices display no long-range dependence. More recently, Wang and Wu (2013) examine the efficiency of crude oil futures markets and find that crude oil price display weak persistent behavior for time scales smaller than a year. For time scales larger than a year, strong mean-reversion behaviors can be found. They conclude that crude oil futures markets are not efficient in the short-term or in the long-term. By quantifying the market inefficiency using a multifractality degree, they find that the futures markets are more inefficient in the longterm than in the short-term. Ozdemir et al. (2013) use the monthly crude oil spot and futures prices and show that the Brent market is weak-form efficient. Although there have been many works on the efficiency of energy markets, very few of them have focused on the time varying efficiency. So in order to analyze the dynamics of weak-form market efficiency, some studies have examined recently the evolving efficiency in some energy markets. Tabak and Cajueiro (2007) investigate the timevarying degrees of long-range dependence in the Brent and WTI crude-oil daily returns over the period 1983–2004 by means of estimating Lo (1991)’s modified Hurst exponent by a rescaled range analysis. They find that crude oil markets have become more efficient over time as evidenced by the decline in the long memory intensity. They explain their results by the fact that the crude oil market has been deregulated in the 1980s. Alvarez-Ramirez et al. (2008) apply the detrended fluctuation analysis (DFA) method on WTI and Brent oil prices over the period 1981–2002, and find that the oil market exhibits time varying shortterm(size of window of 175 business days) inefficient behavior that becomes efficient in the long term (size of window of 300 business days). Wang and Liu (2010) examine the efficiency of WTI crude oil market over the period 1990–2009 through observing the dynamic of local Hurst exponents employing the method of rolling window based on multiscale detrended fluctuation analysis. They find that short-term, medium-term and long-term behaviors were generally turning into efficient behavior over time. Arouri and Nguyen (2010) use average weekly spot prices to study time-varying predictability in crude oil markets of Gulf Cooperation Council (GCC) countries over the period 1997–2010, and they reject the hypothesis of convergence towards weak-form efficiency for all markets. Using daily data over the period 1986–2011, Ortiz-Cruz et al. (2012) analyze the evolution of the informational complexity and efficiency of the WTI crude oil market through a multiscale entropy analysis. They show that the crude oil market is informationally efficient over the study period, except for two periods that correspond to the early 1990s and late 2000 US recessions. More recently, Zhang et al. (2014) argue that using average weekly prices is inappropriate for
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Table 1 Data description. Data
Start date
End date
Number of observations
Crude oil Spot Future (1 month)
02/01/1986 04/04/1983
14/01/2014 14/01/2014
7169 7726
RBOB regular Gasoline Spot Future (1 month)
11/03/2003 03/11/2005
14/01/2014 14/01/2014
2726 2084
No. 2 Heating oil Spot Future (1 month)
02/06/1986 02/01/1980
14/01/2014 14/01/2014
6949 8543
Propane Spot Future (1 month)
09/07/1992 17/12/1993
14/01/2014 18/09/2009
5397 3942
autocorrelation tests and may lead to less reliable conclusions. They argue that the weekly Friday series fit the data better than the average series in autocorrelation tests. Using a time-varying GAR(1)-TGARCH(1,1) model with different frequency data for the crude oil spot markets in Europe, the US, the UAE and China over the period 2001–2013, they find that all four markets have reached efficiency with few brief inefficient periods during the past decade. Using the detrended fluctuation analysis (DFA) and the detrending moving average analysis (DMA) to estimate the Hurst index of the return time series of the daily prices of WTI crude oil futures at long and short-time periods over the period 1983–2012, Jiang et al. (2014) find that the market is efficient in long run and inefficient in some short turmoil periods (the oil crashes in 1985 and 2008, and the Gulf War). The results are statistically significant based on bootstrapping tests. These findings are consistent with the predictability of oil prices. Sensoy and Hacihasanoglu (2014) investigate the presence of long-range dependence in energy futures markets. Using a daily data set over the period 1990–2013, they find that efficiency of energy futures markets is time-varying and changes drastically over the sample period. 3. Empirical methodology In this paper we employ a rolling sample approach to investigate time varying market efficiency of spot and futures energy, instead of analyzing different sub-periods based on a cutoff date which is subject to criticism. Moreover, as argued by Sensoy and Hacihasanoglu (2014), arbitrary chosen sub-periods or non-overlapping intervals could not capture possible structural breaks in financial time series. Using a rolling sample approach, the parameters of interest. Is computed for the first window for a specified length n, and then we estimate again the parameter of interest by rolling the window forward by removing the first observation of the series and adding a new observation at the end. This process continues until the last observation is used. As tests statistics for weak form market efficiency we employ two variants of the Variance Ratio test (VR). The first is the Lo and MacKinlay (1988) test by assuming heteroscedasticity and the Chow and Denning (1993) multiple VR test. Moreover, we consider the Detrended Fluctuation Analysis (DFA) of Peng et al. (1994) method by computing the long memory parameter d. The rolling sample technique consists of 3 steps:
1– We set the length of the window equal to 500 observations (about two years).2 2– We calculate the p-values of the variance ratio tests and the parameter of long memory. 3– We roll forward the window and we re-estimate the parameters of interest for each time series. This provides us with a T − n estimates of these parameters. The use of this approach allows us to examine the evolution of market efficiency over time and to provide a useful indicator to rank the efficiency of spot and futures energy markets. 3.1. Data The data consist of the daily closing price of spot and futures energy from the New Mercantile Exchange (NYMEX) with the 1 month maturity contracts.3 The data set includes crude oil (Light-Sweet, Cushing, Oklahoma), rBOB Regular Gasoline (New York Harbor), No. 2 Heating Oil (New York Harbor), and Propane (Mont Belvieu, Texas). The data set is obtained from the Energy Information Administration (EIA) in the US Department of Energy. The sample period and the number of observations are reported in Table 1. The daily return rt is obtained by using the following transformation, rt = 100 ∗ (log (Pt ) − log (Pt −1 )), where (Pt ) is the price of the spot or futures energy at day t. 3.2. Variance ratio tests and wild bootstrapping We use two variants of the VR test statistic and the wild bootstrapping of Kim (2006) to test the weak-form
2 Note that only for the DFA method that we set the length of the window equal to 2168, 1725, 1226, 1084, 1946, 2542, 2397 and 1939 observations respectively for the spot crude oil, the futures crude oil, spot RBOB, futures RBOB, spot No. 2 heating oil, futures No. 2 heating oil, time series. As noted by many authors a time series with length higher than 2000 is need to obtain a consistent estimate of the long memory parameter d. 3 The NYMEX provides price data of energy futures with four maturity contracts C1, C2, C3 and C4. Contract 1 denotes a futures contract with the earliest delivery date. C2–C4 represent the successive delivery months following Contract 1. For more information about energy futures definition, we refer to http://www.eia.gov/dnav/pet/TblDefs/pet_pri_ fut_tbldef2.asp.
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efficiency. The first variant is the Lo and MacKinlay (1988) VR test by assuming heteroscedasticity. The VR test is one of the most popular test employed in the empirical finance literature to test the random walk hypothesis for financial data. Literally, the VR statistic stipulates that if stock returns follow an uncorrelated increment model (random walk under the null hypothesis), then the sample variance of k-period returns, rt + · · · + rt +k−1 is the same as k times the sample variance of the one period returns rt . The decision rule of this test is as follows. The null hypothesis is rejected when the ratio variance statistic differs statistically from unity. Otherwise we cannot reject the alternative hypothesis stating that the time series is not following a random walk. As in many papers, in the empirical part we use different values of holding period k set to 2, 5, 10 and 20 (k = 2, 5, 10, 20) and we report the time varying p-values of the wild bootstrapping technique. Following Wright (2000), the VR statistic can be written as follow,
VR (Y ; k) =
T 1
Tk t =k
(Yt + Yt −1 + . . .
+ Yt −k+1 − kµ ˆ
2
T 1
T t =1
Yt − µ ˆ
2
,
T
M (Y , k) = (VR (Y ; k) − 1)
2 k−1 2 (k − j) j=1
where δj
T
t =1
T t =j +1
= Yt − µ ˆ
2 2
The wild bootstrap is conducted in four steps as follows, 1– Form a bootstrap sample of T observations of Yt∗ = ϑt Yt (t = 1, . . . , T ) where ϑt is a random sequence with mean 0 and Variance 1. 2– Calculate M ∗ ≡ M (Y ∗ , k) and MV ∗ ≡ MV (Y ∗ , ki ) of the M (Y , k) and MV (Y ; ki ) statistics obtained from the bootstrap sample. 3– We repeat steps (1) and (2) for boot times, this allows us to form a bootstrap distribution of the test statistics
boot
MV Y ∗ , kj ; j
j =1
and {M (Y ; k; j)}boot j =1 .
4– Calculate the proportion of {M (Y ∗ ; k; j)}boot j=1 greater than M (Y , k) the sample value of the sample value
boot
and the proportion of MV Y ∗ , kj ; j j=1 greater than MV (Y , ki ). The calculated proportion corresponds to the p-values that we use to investigate the evolution of the time varying efficiency hypothesis.
The M ∗ and MV ∗ have the same asymptotic distributions as M (Y , k) and MV (Y , ki ), respectively. 3.3. Detrended Fluctuation Analysis (DFA) method
where µ ˆ = T −1 t =1 Yt . VR (Y ; k) is the estimator for the population VR, denoted as V (k). Lo and MacKinlay (1988) show under some assumptions that the M (X , k) statistic given below follows the normal distribution asymptotically under the null hypothesis that V (k) = 1,
71
k
Yt − µ ˆ
2
−1/2 δj
Yt −j − µ ˆ
2
/
.
The second test is the Chow and Denning (1993) multiple VR test which is designed to detect autocorrelation and heteroscedasticity in returns. The Chow and Denning test tests the joint null hypothesis that V (ki ) = 1 for i = 1, . . . , l The statistic of this test is given by, MV (Y ; ki ) = max |M (Y ; ki )| . 1≤i≤l
Chow and Denning (1993) show that the MV (Y ; ki ) statistic follows asymptotically the studentized maximum modulus distribution with l and T degrees of freedom. The main advantage of this test is that it control for a joint size issue in the original Lo and MacKinlay (1988). In this paper we apply the Kim (2006) wild bootstrapping procedure to approximate the sampling distribution of the M (Y , k) statistic of Lo and MacKinlay (1988) and the MV (Y ; ki ) statistic of Chow and Denning (1993). Precisely, this approach consists on resampling the original data by weighting it using random variables that have mean zero and unit variance.4 4 The wild bootstrap is a resampling method that approximates the sampling distribution of the VR test statistic, and is applicable to data with
In recent empirical literature, several research’s studies in finance and economics have employed the detrended fluctuation analysis (DFA) methods with linear polynomial local fit. The DFA method was firstly proposed by Peng et al. (1994) while examining series of DNA nucleotides. In recent year, this method have been widely used when detecting long-range correlations embedded in a seemingly non-stationary time series (see for instance Charfeddine and Ajmi, 2013, Charfeddine and Guegan, 2012 and Chen et al., 2005). The procedure to calculate the DFA long memory parameter consists of 4 steps, Step 1: We integrate the time series x (t ) (of length T ), y(t ) =
T
x(i).
i=1
Step 2: We divide the integrated time series into N adjacent sub-periods of length m while N ∗ m = T . For each sub-period, we fit a polynomial of order l = 1, see Hu et al. (2001). Step 3: We detrend the integrated time series by subtracting the local trend in each sub-period and then we define the fluctuation F (m) as,
F (m) =
T 1
T t =1
1/2 [y(t ) − ym (t )]
2
.
Scales as, F (m) = c mα where c is a constant independent of m. An ordinary least squares regression on logarithms of the previous relation will be run in order to estimate the correlation exponent.
unknown forms of conditional and unconditional heteroscedasticity. This approach has been used recently by Charles and Darné (2009) to examine the random walk hypothesis for the spot crude oil markets, and Enninful and Dowling (2013) to examine the market efficiency in European equity indices.
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Table 2 Descriptive statistics, ARCH LM and unit roots tests.
Mean (%) Std. Dev.(%) Skewness Kurtosis J–B Q(12) Q2 (12) LM(6) ADF PP ERS (OP) KPSS N. Obs
Futures oil
Futures heating oil
Futures RBOB
Futures propane
Spot oil
Spot heating oil
Spot RBOB
Spot propane
0.0148 2.3792 −0.827 18.933 82 573 73.970 935.36 444.68 −42.257 −89.062 0.0040 0.1141 7726
0.0148 2.266 −1.4492 22.958 144 752 47.918 528.72 221.572 −93.47 −93.96 0.0081 0.1456 8541
0.0157 2.4176 −0.1596 6.7178 1208.5 23.393 528.68 169.51 −45.158 −45.157 0.0476 0.0438 2083
0.0349 2.0847 −1.0960 15.459 26 271 44.900 485.82 196.983 −57.594 −57.687 0.0129 0.0435 3941
0.0112 2.5972 −0.755 16.874 58 170 65.015 795.16 344.41 −41.03 −85.92 0.0089 0.0615 7168
0.0287 2.5207 −1.6295 41.704 436 696 71.129 1940.8 1017.3 −45.054 −82.107 0.0076 0.0369 6947
0.0185 3.0755 0.1414 7.4843 2291.4 16.304 472.66 166.81 −51.043 −51.056 0.0499 0.0258 2725
0.0255 2.3869 −2.1363 65.422 879 854 44.435 216.92 155.43 −36.608 −72.215 0.0111 0.0308 5394
Note: The sample period is as described in Table 1. Jarque–Bera test of normality follows under the null hypothesis of normality the χ 2 (2) distribution with 2 degrees of freedom. The 5% critical value is equal to 5.99. The ARCH LM(6) statistic is the ARCH test up to the sixth lag and under the null hypothesis of no ARCH effect it follows a χ 2(q) distribution, where q is the number of lags. The Q(12) and Q2 (12) statistics denote the Ljung–Box test on the residuals and squared residuals of the conditional mean regression up to twelfth order. Under the null hypothesis of no serial correlation, the test is distributed as a χ 2 (12) = 21.026. ADF, PP, ERS, and KPSS denote the statistics of Augmented Dickey—Fuller (1979), Phillips—Perron (1988), Point Optimal Elliott— Rothenberg—Stock (1996) and Kwiatkowski, Phillips, Schmidt and Shin (1992) unit root test, respectively. Critical values of the ADF, PP, KPSS and ERS test, at the 5% level of significance, are equal to −1.941, −1.941, 0.463, and 3.26 respectively.
Then, three possible behavior can characterize the time series under study, 1. if the initial process is characterized by short-term correlations then α do not significantly differ from 0.5. 2. If the value of the exponent α lies in (0.5,1) then it indicates persistent long-range power-law correlations. 3. A value of α = 1.5 indicates Brown noise, the integration of white noise. To get a consistent estimate of the fractional long memory parameter, we set in this paper m = T 0.5 and m = T 0.6 . We consider also a value of l = 1. Then, the estimated value of the fractional long memory parameter is given by dˆ DFA = αˆ − 0.5. 4. Empirical results 4.1. Descriptive statistics Table 2 reports descriptive statistics for the spot and futures energy return series calculated as the first logarithmic difference of the daily closing prices. The results reveal that the mean is quite small, ranging from 0.0112% for spot crude oil to 0.0349% for futures propane. In terms of standard deviation, futures propane exhibits the least volatility (2.0847%), while spot RBOB displays the highest volatility (3.0755%). The kurtosis is significantly higher than the normal value of 3 indicating that the distribution of all return time series is fat-tailed. All return series display significant skewness, with negative skewness for all series except for spot RBOB, indicating that the empirical distributions of the spot and futures energy returns are asymmetric shape. The Jarque–Bera test statistic is significant at the 1% level of significance for all series, indicating that the spot and futures energy returns are highly non-normal distributed. Table 2 also reports the Ljung–Box LB statistics for the return and squared return series. For all return series, these
two statistics show the presence of high dependence in the returns series and squared returns series. The presence of high dependence in the squared return series indicates the presence of ARCH effects which is confirmed by the ARCH LM(12) statistic. In Table 2, we also report the results of the Augmented Dickey–Fuller (ADF), Phillips and Perron (PP), Point Optimal Elliott–Rothenberg–Stock (ERS) and Kwiatkowski, Phillips, Schmidt and Shin (KPSS) unit roots tests. For all return series, the hypothesis of unit root is rejected and the alternative hypothesis is accepted. 4.2. Time-varying efficiency of the spot and futures energy markets We examine the weak-form efficiency market hypothesis by testing the random walk hypothesis using wild bootstrapping VR and DFA tests. Fig. 1 through 6 report the evolution of the p-values of the Kim (2006) wild bootstrapping variance ratios statistics of Lo and MacKinlay (1988) and Chow and Denning (1993), as well as the evolution of the estimated fractional long memory parameter using the DFA approach. All figures clearly show that the estimated statistics are time-varying in nature. In particular, empirical results show that the spot and futures energy markets have enjoyed a long periods of market efficiency where returns series clearly follow pure white noise. Nevertheless, energy markets sometimes show departure from market efficiency depending on the prevailing economic and political conditions, which is consistent with the implication of the adaptive markets hypothesis. These empirical findings confirm the hypothesis of evolving efficiency of the energy markets. Moreover, empirical results seem to depend on the nature of the energy time series (sport or futures), and on the statistical methods employed for testing markets efficiency. Overall, the results are consistent with the random walk hypothesis in the four energy prices, and therefore with the weak-form efficiency of the four energy markets. More details analyzes of these empirical results are reported in the following Subsections 4.2.1 and 4.2.2.
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Fig. 1. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 2 and 5 for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
4.2.1. Wild bootstrapping of variance ratio results Estimation results of the p-values of the wild bootstrapping variance ratio statistic for both Lo and MacKinlay (1988) and Chow and Denning (1993) are plotted in Figures 1 to 6 for the spot and futures energy time series. We also report the VR statistic empirical results for the different values of k = 2 (two days), k = 5 (one week), k = 10 (two weeks), k = 20 (one month). In these figures, the horizontal line (in green color) indicates the critical threshold level for the p-value, which is set at 5%. Thus, a p-value less than 5% indicates the rejection of the null hypothesis of weak-form efficiency of the market. As shown in Figs. 1–6, the energy returns series are efficient for all different values of the parameter k, except for some time periods associated with some economic, political, weather events or supply shock. For the crude oil returns series, the VR tests reject the null hypothesis of market efficiency only around the years 1990, 1996, and 2005. The year 1990 correspond to the period of spikes in prices with the lower production, uncertainty associated with the Iraqi invasion of Kuwait and the ensuing Gulf War. In 1996, the Russian crude oil production reached its minimum level. The declining in Russian production contributed to the price recovery between 1990 and 1996. The year 2005 coincides with the hurricanes Katrina and Rita and US refinery problems. With regard to the RBOB regular gasoline time series, the null hypothesis of market efficiency is rejected around the year 2006 by the two VR tests and for different values of k. This date corresponds to Asian demand soars and refinery problems from hurricanes and MTBE/ethanol switch. For the futures series, the VR tests reject the null
hypothesis of weak-form efficiency around the end 2008 and around 2013. The deviation from a random walk in 2008 corresponds to the recent subprime financial crisis. The period around 2013 corresponds to the loss of Libyan exports in the face of the Libyan civil war. The VR tests for the spot series of the heating oil returns show that these series have experienced a several periods of markets inefficiency. The periods of inefficiency are 1990–1991, 1996–1998, and 2007–2008. These dates coincide with the Gulf war, the Asian financial crisis, and the subprime financial crisis. For the futures series of the heating oil returns, the null hypothesis of market efficiency is rejected only in 1986, 1993 and 1996. The deviation from a random walk in 1986 was caused by the large fluctuation of oil supply production (e.g., in early 1986 Saudi Arabia increased production of oil from two million barrels per day to five million). The timing 1996 corresponds to the OPEC announcement to reduce oil production in response to slack world oil demand, rising non-OPEC oil production, and weak oil prices. Finally, regarding the Propane, the VR tests for the spot series returns indicate that these series have experienced a several periods of markets inefficiency. The null hypothesis of weak-form efficiency is rejected over the periods 1995–1996, 2007–2009, and 2011–2014. As mentioned earlier, the first two periods coincide with the OPEC announcement regarding the reduction of oil production, and the increasing uncertainties caused by the recent global financial crisis, whereas the third period coincides with the Spring Arab. For the futures returns series, the obtained results are quite different than the spot series. The futures series have enjoyed a long periods of markets inefficiency mainly between 2006 and 2010.
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Fig. 2. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 10 and 20 for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
Fig. 3. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 2 and 5 for the future crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
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Fig. 4. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 10 and 20 for the future crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
Fig. 5. These figures report the trajectories of the p-value of the wild bootstrapping Chow and Denning (1993) Variance Ratio (VR) using k = 2, 5, 10 and 20 for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
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Fig. 6. These figures report the trajectories of the p-value of the wild bootstrapping Chow and Denning (1993) Variance Ratio (VR) using k = 2, 5, 10 and 20 for the future crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
4.2.2. DFA statistic Empirical results of the DFA method are reported in Figs. 7 and 8 for the spot and futures crude oil, RBOB regular gasoline, No.2 heating oil and the propane returns series. For consistency of the estimated fractionally parameter d employing DFA, we use a different values of the window length.5 Empirical results show that the estimated long memory parameter is significantly different from zero and negative in the majority of cases which means the presence of anti-persistence behavior. Concerning the market efficiency hypothesis, we find that for the crude oil returns series the null hypothesis of market efficiency has been rejected during the 1995–2000 and 2008–2010 periods for the spot series and during the 1992–2001 and 2008–2010 periods for the futures returns series. Regarding the RBOB regular gasoline, the null hypothesis of market efficiency has been rejected for the periods 2008–2009 and 2012–2014 for the spot returns series and 2011–2014 for the futures series. For the spot No.2 heating oil and propane time series, the periods of markets inefficiency correspond to the 1994–2001 and 2008–2010 periods for the No.2 heating oil and to the 2009–2012 periods for the propane time series. With regard to the futures returns series, empirical results show that the periods of market inefficiency are the 1999–2000, 2002–2003 and 2007–2010 periods the for crude oil series, the 2011–2014 period for the RBOB regular gasoline series, the 1990–2001 and 2009–2011 periods for
5 See footnote 2.
the No.2 heating oil series, and the 2002–end of 2005 and 2007–2010 periods for the propane returns series. 4.3. Ranking of the spot and futures energy markets In Tables 3 and 4, we report the ranking of the spot and futures energy markets based on the percentage of insignificant estimated values at the 5% level of the two variants of VR tests (Lo and MacKinlay, 1988 for the different values of k, and Chow and Denning, 1993), and the Detrended Fluctuation Analysis (DFA). As argued by Lim (2007), the use of the popular median measure of Cajueiro and Tabak (2004) would give a biased view of the degree of market efficiency for the whole sample period, and hence defeat the fundamental objective of using a rolling sample approach. Hence, in this study, we employ the percentage of insignificant H statistic for each time window as an indicator for assessing the relative efficiency of energy markets. Specifically, a window is defined as significant if the statistic rejects the null hypothesis of pure white noise at the specified threshold level for the p-value, which is set at 5%. As we can see, the different statistics used in this paper provide mixed results, mainly for the first rank. Regarding the spot market, the crude oil seems to be the most efficient market, based on the VR test of Lo and MacKinlay (1988) for all values of k except k = 20, and the VR test of Chow and Denning (1993). On the contrary, based on the DFA test, the most efficient spot market is heating oil. At the other end of the spectrum, the Propane market experienced the most frequent departure from efficiency, according to all tests.
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Fig. 7. (a), (b), (c) and (d) represent the trajectories of the estimated long memory parameter using the DFA method for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively using the rolling sample approach.
Fig. 8. (a), (b), (c) and (d) represent the trajectories of the estimated long memory parameter using the DFA method for the futures crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively using the rolling sample approach.
With regard to the futures energy markets, although there is a clear consensus for the most efficient market
(futures crude oil) based on the DFA and the VR test of Chow and Denning (1993), empirical results do not
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Table 3 Ranking of spot energy markets based on the percentage of energy markets efficiency. Percentage
Spot crude oil Spot RBOB regular gasoline Spot heating oil Spot propane
Ranking
VR (k = 2 )
VR (k = 5)
VR (k = 10)
VR (k = 20)
VR ( k = 2)
(k = 5)
(k = 10)
(k = 20)
97.0% 96.5% 83.3% 75.8%
98.4% 94.9% 93.0% 79.2%
98.1% 97.4% 96.5% 96.7%
99.2% 99.7% 98.8% 97.1%
1 2 3 4
1 2 3 4
1 2 4 3
2 1 3 4
Percentage
Spot crude oil Spot RBOB regular gasoline Spot heating oil Spot propane
VR
VR
VR
Ranking
DFA (m = 50)
DFA (m = 100)
CD Test
DFA (m = 50)
DFA (m = 100)
CD Test
50.84% 47.84% 52.11% 51.12%
49.16% 45.38% 54.59% 43.58%
99.1% 96.9% 91.2% 75.8%
2 3 1 4
2 3 1 4
1 2 3 4
Table 4 Ranking of futures energy markets based on the percentage of energy markets efficiency. Percentage
Futures crude oil Futures RBOB regular gasoline Futures heating oil Futures propane
Ranking
VR (k = 2)
VR (k = 5)
VR (k = 10)
VR (k = 20)
VR (k = 2)
VR (k = 5)
VR (k = 10)
VR (k = 20)
99.5% 100%. 99.8% 75.9%
99.7% 89.9% 99.1% 72.2%
98.5% 99.0% 96.9% 89.9%
98.9% 99.8% 99.6% 88.4%
2 1 3 4
1 3 2 4
2 1 3 4
3 1 2 4
Percentage
Futures crude oil Futures RBOB regular gasoline Futures heating oil Futures propane
Ranking
DFA (m = 50)
DFA (m = 100)
CD Test
DFA (m = 50)
DFA (m = 100)
CD Test
49.35% 23.80% 39.77% 22.42%
43.95% 29.10% 35.40% 17.23%
99.8% 99.5% 99.7% 70.6%
1 3 2 4
1 3 2 4
1 3 2 4
converge on the first rank (either crude oil or RBOB) based on the VR test of Lo and MacKinlay (1988) for different values of k. At the other end of the spectrum, futures propane market experienced the most frequent departure from efficiency, based on all tests. Finally, it is noteworthy that contrasting the Kim wild bootstrapping VR tests with the DFA indicates that the latter is more likely to reject the null hypothesis of random walk over longer time windows. 5. Conclusion This paper examines the weak-form efficiency of four energy markets (crude oil, RBOB regular gasoline, No. 2 heating oil, and propane), in close association with the adaptive market hypothesis. Instead of static approaches, we use a time-varying approach to see the dynamics efficiency of the four energy markets. This approach allows us to detect periods of efficiency/inefficiency and so the changing degree of energy market efficiency over time. Thus, the relative efficiency of energy markets can easily be assessed by comparing the total time periods these markets exhibit significant nonlinear serial dependence. As tests of market efficiency, we use the wild bootstrapping variance ratio tests, and the detrended fluctuation analysis (DFA) long memory parameters. Our empirical results reveal that the efficiency of energy markets is not uniform over time, which is consistent with the adaptive market
hypothesis. Specifically, results show strong evidence of time varying market efficiency of the spot and futures energy returns series. Empirical results also show that nonlinear dependence in energy returns is quite localized in time. This finding implies that time-varying parameter models might be superior to constant parameter models in capturing energy market dynamics. Furthermore, our research provides insights into the ranking of spot and futures energy markets. Overall, we find that the spot and futures crude oil and RBOB regular gasoline are among the most efficient markets while the spot and futures propane time series are at the end of the ranking. However, it should be noted that for the spot market, the result is controversial using the DFA. Specifically, we find that the spot propane is ranked first while the spot RBOB and the spot heating oil are among the less efficient markets. Overall, the findings of this paper provide evidence of the importance of the rolling approach in explaining the behavior of energy returns and thus contribute to better understanding the dynamics of spot and futures energy markets. They also provide important information for the regulators and investors and have implications for investment strategies. Specifically, the evidence of long range serial dependence implies the potential of returns predictability in some energy markets especially during those identified time periods of inefficiency. Further, market inefficiency implies that there exist yet markets
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imperfections and behavioral biases. To enhance the efficiency of spot and futures energy market, regulators should improve transparency by insuring the availability of high quality and timely information on fundamental supply and demand relationship. Future researches to examine the underlying factors that were responsible for energy market inefficiency during those identified time periods will certainly enhance our understanding of energy prices behavior. References Alvarez-Ramirez, J., Alvarez, J., Rodriguez, E., 2008. Short-term predictability of crude oil markets: a detrended fluctuation analysis approach. Energy Econ. 30 (5), 2645–2656. Alvarez-Ramirez, J., Alvarez, J., Solis, R., 2010. Crude oil market efficiency and modeling: Insights from the multiscaling autocorrelation pattern. Energy Econ. 32, 993–1000. Arouri, M.H., Nguyen, D., 2010. Oil prices, stock markets and portfolio investment: evidence from sector analysis in Europe over the last decade. Energy Policy 38, 4528–4539. Cajueiro, D.O., Tabak, B.M., 2004. Evidence of long range dependence in Asian equity markets: the role of liquidity and market restrictions. Physica A 342, 656–664. Charfeddine, L., 2014. True or spurious long memory: further evidence in futures energy markets. Energy policy 71, 76–93. Charfeddine, L., Ajmi, A.N., 2013. The Tunisian stock market index volatility: Long memory vs switching regime. Emerg. Mark. Rev. 16, 170–182. Charfeddine, L., Guegan, D., 2012. Breaks or long memory behaviour: an empirical investigation. Physica A 391 (22), 5712–5726. Charles, A., Darné, O., 2009. The efficiency of the crude oil markets: evidence from variance ratio tests. Energy Policy 37 (11), 4267–4272. Chen, Z., Hu, K., Carpena, P., Bernaola-Galvan, P., Stanley, H.E., Ivanov, P.Ch., 2005. Effect of nonlinear filters on detrended fluctuation analysis. Phys. Rev. E 71, 011104. Chow, K.V., Denning, K.C., 1993. A simple multiplevariance ratio test. J. Econometrics 58, 385–401. Cunado, J., Gil-Alana, L.A., Perez de Gracia, F., 2010. Persistence in some energy futures markets. J. Futures Mark. 30, 490–507. Daskalaki, C., Skiadopoulos, G., 2011. Should investors include commodities in their portfolios after all? New evidence. J. Bank. Finance 35, 2606–2626. Dickey, D.A., Fuller, W.A., 1979. Distribution of the estimators for autoregressive time series with a unit root. J. Amer. Statist. Assoc. 74, 427–431. Elder, J., Serletis, A., 2008. Long memory in energy futures prices. Rev. Financ. Econ. 17, 146–155. Elliot, G., Rothenberg, T.J., Stock, J.H., 1996. Efficient tests for an autoregressive unitroot. Econometrica 64, 813–836. Enninful, K., Dowling, M.M., 2013. Robust weak-form efficiency tests in volatile Europeanequity indices. Appl. Econ. Lett. 20 (9), 863–868. Fama, E.F., 1970. Efficient capital markets: A review of theory and empirical work. J. Finance 25, 383–417. Green, S.L., Mork, K.A., 1991. Toward efficiency in the crude-oil market. J. Appl. Econ. 6, 45–66. Gu, R., Chen, H., Wang, Y., 2010. Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis. Physica A 389, 2805–2815. Hu, K., Chen, Z., Ivanov, P.Ch., Carpena, P., Stanley, H.E., 2001. Effect of trends detrended fluctuation analysis. Phys. Rev. E 64, 011114. Jiang, Z,-Q, Xie, W,-J., Zhou, W,-X., 2014. Testing the weak-form efficiency of the WTI crude oil futures market. Physica A 405, 235–244.
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Journal of Behavioral and Experimental Finance journal homepage: www.elsevier.com/locate/jbef
Full length article
Evolving efficiency of spot and futures energy markets: A rolling sample approach Karim Ben Khediri a,b,c , Lanouar Charfeddine d,∗ a
CEROS, Université Paris Ouest Nanterre La Défense, France
b
FSEG Nabeul, University of Carthage, Tunisia
c
College of Administrative Sciences, Najran University, Saudi Arabia
d
Department of Finance and Economics, College of Business and Economics, Qatar University, P.O. Box 2713, Doha, Qatar
article
info
Article history: Received 8 November 2014 Received in revised form 14 March 2015 Accepted 23 March 2015 Available online 23 April 2015 Keywords: Market efficiency Energy market Rolling approach Variance Ratio Run test Modified R/S and DFA
abstract In this paper, we examine the weak-form efficient market hypothesis of energy markets by testing the random walk behavior of spot and futures prices. We contribute to the financial market efficiency literature by investigating the time varying markets efficiency using a ‘‘rolling sample’’ approach instead of an analysis of different time periods. For this end, we use the wild bootstrap Variance Ratio (VR) tests and the Detrended Fluctuation Analysis (DFA) technique. Empirical results show strong evidence of time varying markets efficiency with rapid mean reversion towards markets efficiency. The evolving efficiency of spot and futures markets depends on the prevailing economic and political conditions. Among the energy markets examined in this study, the spot and futures crude oil and the RBOB regular gasoline markets show the highest degree of market efficiency, while spot and future propane market is at the end of the ranking. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The Efficient Market Hypothesis (EMH) is one of the most important concepts in the modern finance literature. Formulated by Fama (1970), the EMH suggests that at any given time, prices fully reflect all available information. Since markets are efficient and current prices reflect all information then it is impossible to outperform the market. According to the EMH, no investor has an advantage in predicting a return on a stock price because no one has access to information not already available to everyone else. The EMH exists in various degrees: weak, semi-strong and strong, which addresses the inclusion of non-public information in market prices. The weak form
∗ Corresponding author. Tel.: +974 4403 7763 (Office); fax: +974 4403 5081. E-mail addresses: [email protected] (K.B. Khediri), [email protected] (L. Charfeddine). http://dx.doi.org/10.1016/j.jbef.2015.03.006 2214-6350/© 2015 Elsevier B.V. All rights reserved.
efficiency indicates that the information of all past prices is reflected in today’s prices. The semi-strong efficiency implies that all public information is calculated into current prices. The strong form efficiency indicates that all information in a market, whether public or private, is accounted for in prices. This study empirically analyzes the weak form efficiency for the energy spot and futures markets. Hereafter, ‘‘the efficiency’’ refers to the weak form efficiency in this study. The EMH has important implications for both monetary authorities and investors regarding market regulation, asset pricing, and portfolio allocation issues. The informational efficiency matters in two main ways. First, if a particular market is inefficient, investors may build up various trading strategies that lead to earn abnormal returns. Second, if all relevant information is incorporated in financial securities’ prices as soon as they appear, new capital will go to the most productive investments. These features thus highlight the necessity of research on the efficiency of markets.
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Understanding the efficiency of energy markets is of great importance for policy makers because energy plays an essential role in the world economy. Energy price movements have an impact on the performance of most economic sectors in both oil-importing and oil-exporting countries (Lescaroux and Mignon, 2008). The level of market efficiency will determine the trading and other strategies of market participants, and profitable opportunities may be available in an inefficient market. Moreover, energy markets have been considered as important markets for international portfolio diversification because of their different volatile returns and low correlations with stocks markets (Arouri and Nguyen, 2010; Daskalaki and Skiadopoulos, 2011; among others). In addition, the futures markets have two important functions. The first one is the hedging of risks. The other is the mechanism of price discovery, enabling to forecast spot prices at specified future dates. These two functions are based on the theory that the futures prices can reflect the expectation of investors which is one of the important determinants of price mechanism. In weak-form efficiency, future prices cannot be predicted based on the analysis of their past performance. This is consistent with the random walk model which assumes that the price changes are homogeneously distributed random variables. The examination of weakform efficiency can be performed by empirically testing the random walk model. The existence of long-range dependence in return series can reject the random walk model, thereby indicating that the market is not efficient in weak-form. The specificity of the energy market in comparison to other markets is it slightly nonlinear serial dependence in the return series (Alvarez-Ramirez et al., 2008, 2010; Tabak and Cajueiro, 2007; Serletis and Andreadis, 2004; Charfeddine, 2014). Thus, testing for market efficiency remains a challenging and interesting task especially in spot and futures energy markets. Although many studies to date have addressed the issue of energy markets efficiency, only a few researches have focused on the time-varying of market efficiency. Therefore, unlike traditional methods for testing market efficiency, this paper examines the time-varying efficiency of the spot and futures energy markets using the rolling sample approach. As tests of markets efficiency, we employ two variants of the VR tests statistics (Lo and MacKinlay, 1988; Chow and Denning, 1993), the wild bootstrapping technique of Kim (2006), and the Detrended Fluctuation Analysis (DFA) technique of Peng et al. (1994). Further, we provide a ranking of markets efficiency based on the percentage of time window that market departs from efficiency. In this paper, we further extend the works in existing literatures on the weak form of the EMH in the energy markets in four ways. First, in this study we pay more attention to energy market dynamics than to the average behavior of spot and futures energy prices. The classical test of market efficiency of Fama (1970) leads to a rejection or not of the null hypothesis of random walk for the sample period, which is highly unrealistic. However, according to the adaptive markets hypothesis of Lo (2004, 2005), the
market efficiency is not an all-or-none condition but is a characteristic that varies continuously over time, with periods of inefficiency alternate with those of efficiency. The evolving market efficiency over time is due by and large to changing market condition (cycles, bubbles, crashes, crises,..) and institutional factors. Hence, Instead of relying on a single measure of market efficiency for the whole sample period, we employ time-varying or rolling sample approach rather than focusing on time-invariant regressions or some different sub-periods. Therefore, there is no need to identify an event date, which is often subject to criticism. Moreover, the application of a rolling window essentially captures the persistence of energy prices departures from a random walk benchmark over time and so allows us to propose some relevant policy recommendations according to the degree of market efficiency. Second, in addition to the VR tests, we use the DFA method. Comparing with classical statistics, the DFA permits the detection of long term memory embedded in seemingly non-stationary time series, and also avoids the spurious detection of apparent long term memory that is an artifact of non-stationarity. In addition, the advantages of DFA in computation of H are that inherent trends are avoided at all timescales and local correlations can be easily probed. Third, this study is based on a more extensive sample. We use daily prices of spot and futures energy from the New Mercantile Exchange (NYMEX) with the one month maturity contracts over the period spanning from 1983 to 2014. Such period covers major events such as the Gulf war, the North American Free Trade Agreement (NAFTA), the US’ invasion of Iraq, the Asian and Russian crises, the subprime crisis and the Spring Arab. Fourth, we provide a ranking of the spot and futures markets efficiency of the crude oil (Light-Sweet, Cushing, Oklahoma), rBOB Regular Gasoline (New York Harbor), No. 2 Heating Oil (New York Harbor), and Propane (Mont Belvieu, Texas)based on different ranking criteria. In fact, ranking the efficiency of energy markets has evolved as an important information tool for policy makers and regulators to improve the efficiency channeling effective resource allocation to reduce distortions in the economy. To the best of our knowledge, this is the first work that ranks the efficiency of spot and futures energy markets. The main finding of the paper is that all four energy spot and futures markets show weak-form efficiency changing over time, depending on the prevailing economic and political conditions, which is in line with the predictions of the adaptive markets hypothesis. Moreover, it is found that the crude oil market is the most efficient, while the propane market is at the end of the ranking. The remaining of the paper is organized as follows. Section 2 presents a literature review. Section 3 presents the data and methodology. Section 4 discusses the empirical results. Finally, Section 5 concludes the paper. 2. Literature review There is a plethora of researches on the efficiency of energy markets. Previous studies have focused on different countries and markets(spot and/or futures markets), and have adopted various estimators, methodologies, sample periods and time frequencies. Overall, empirical evidences
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suggest controversial conclusions. That is, the random walk behavior in energy prices is still unresolved in the existing research. Based on monthly prices on the spot and official OPEC prices of crude oils over the period 1978–1985 and using the generalized method of moments (GMM), Green and Mork (1991) reject the weak-form efficiency for the sample as a whole but with an improvement over time. Using the unit root test allowing for a structural break, Serletis (1992) reject the hypothesis of random walk behavior in energy prices from the New York Mercantile Exchange (NYMEX) on spot-month futures prices for crude oil, heating oil and unleaded gasoline over the period 1983–1990. Using the detrending moving average technique over the period 1990–2006, Serletis and Rosenberg (2007) show that energy futures prices display long memory and that the particular form of long memory is anti-persistence. Using a semi-parametric wavelet-based estimator over the period 1994–2005, Elder and Serletis (2008) find new evidence that energy prices display long memory and that the particular form of long memory is anti-persistence,1 characterized by the variance of each series being dominated by high frequency (low wavelet scale) components. Maslyuk and Smyth (2008) examine the behavior of crude oil spot and futures prices for both West Texas Intermediate (WTI) and Brent crude oil prices over the period 1991–2004. They employ Lagrange multiplier unit root tests allowing for one and two endogenous structural breaks and show that the process of oil prices follows a random walk. Charles and Darné (2009) test the weak-form efficient market hypothesis for two crude oil markets(UK Brent and US West Texas Intermediate) over the period 1982–2008 with nonparametric variance ratio tests. They find that the Brent crude oil market exhibits weak-form efficiency, whereas the WTI crude oil market appears to be inefficient during the 1994–2008 sub-period, which suggests that the deregulation did not improve the efficiency of the WTI crude oil market with respect to less predictable returns. Wang and Yang (2010) use high-frequency (intraday) data on crude oil (along with heating oil, gasoline, and natural gas) futures markets, and find evidence of weak-form market inefficiency, but succeed only with respect to heating oil and natural gas, not crude oil. Gu et al. (2010) use the multifractal detrended fluctuation analysis to investigate the WTI and Brent crude oil prices over the period 1987–2008, and find that the two markets become more and more efficient for long-term and the two Gulf Wars cannot change time scale behavior of crude oil return series. Using parametric, semi-parametric and non-parametric methods to estimate the fractional integration parameter d of WTI crude oil prices over the period 1983–2008, Cunado et al. (2010) conclude that energy futures prices are always not long-range dependent. Wang et al. (2011) examine the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series over the period 1990–2010, employing detrended fluctuation analysis (DFA) and detrended cross-correlation
1 Anti-persistence would be indicative of an overreaction of asset prices to incoming information.
69
analysis (DCCA). They identify three scaling regimes and show that, for time scales smaller than a month, the autocorrelations and cross correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Using three local Whittle methods and a modified rescaled range analysis, Wang and Wu (2012) show that returns in oil prices display no long-range dependence. More recently, Wang and Wu (2013) examine the efficiency of crude oil futures markets and find that crude oil price display weak persistent behavior for time scales smaller than a year. For time scales larger than a year, strong mean-reversion behaviors can be found. They conclude that crude oil futures markets are not efficient in the short-term or in the long-term. By quantifying the market inefficiency using a multifractality degree, they find that the futures markets are more inefficient in the longterm than in the short-term. Ozdemir et al. (2013) use the monthly crude oil spot and futures prices and show that the Brent market is weak-form efficient. Although there have been many works on the efficiency of energy markets, very few of them have focused on the time varying efficiency. So in order to analyze the dynamics of weak-form market efficiency, some studies have examined recently the evolving efficiency in some energy markets. Tabak and Cajueiro (2007) investigate the timevarying degrees of long-range dependence in the Brent and WTI crude-oil daily returns over the period 1983–2004 by means of estimating Lo (1991)’s modified Hurst exponent by a rescaled range analysis. They find that crude oil markets have become more efficient over time as evidenced by the decline in the long memory intensity. They explain their results by the fact that the crude oil market has been deregulated in the 1980s. Alvarez-Ramirez et al. (2008) apply the detrended fluctuation analysis (DFA) method on WTI and Brent oil prices over the period 1981–2002, and find that the oil market exhibits time varying shortterm(size of window of 175 business days) inefficient behavior that becomes efficient in the long term (size of window of 300 business days). Wang and Liu (2010) examine the efficiency of WTI crude oil market over the period 1990–2009 through observing the dynamic of local Hurst exponents employing the method of rolling window based on multiscale detrended fluctuation analysis. They find that short-term, medium-term and long-term behaviors were generally turning into efficient behavior over time. Arouri and Nguyen (2010) use average weekly spot prices to study time-varying predictability in crude oil markets of Gulf Cooperation Council (GCC) countries over the period 1997–2010, and they reject the hypothesis of convergence towards weak-form efficiency for all markets. Using daily data over the period 1986–2011, Ortiz-Cruz et al. (2012) analyze the evolution of the informational complexity and efficiency of the WTI crude oil market through a multiscale entropy analysis. They show that the crude oil market is informationally efficient over the study period, except for two periods that correspond to the early 1990s and late 2000 US recessions. More recently, Zhang et al. (2014) argue that using average weekly prices is inappropriate for
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Table 1 Data description. Data
Start date
End date
Number of observations
Crude oil Spot Future (1 month)
02/01/1986 04/04/1983
14/01/2014 14/01/2014
7169 7726
RBOB regular Gasoline Spot Future (1 month)
11/03/2003 03/11/2005
14/01/2014 14/01/2014
2726 2084
No. 2 Heating oil Spot Future (1 month)
02/06/1986 02/01/1980
14/01/2014 14/01/2014
6949 8543
Propane Spot Future (1 month)
09/07/1992 17/12/1993
14/01/2014 18/09/2009
5397 3942
autocorrelation tests and may lead to less reliable conclusions. They argue that the weekly Friday series fit the data better than the average series in autocorrelation tests. Using a time-varying GAR(1)-TGARCH(1,1) model with different frequency data for the crude oil spot markets in Europe, the US, the UAE and China over the period 2001–2013, they find that all four markets have reached efficiency with few brief inefficient periods during the past decade. Using the detrended fluctuation analysis (DFA) and the detrending moving average analysis (DMA) to estimate the Hurst index of the return time series of the daily prices of WTI crude oil futures at long and short-time periods over the period 1983–2012, Jiang et al. (2014) find that the market is efficient in long run and inefficient in some short turmoil periods (the oil crashes in 1985 and 2008, and the Gulf War). The results are statistically significant based on bootstrapping tests. These findings are consistent with the predictability of oil prices. Sensoy and Hacihasanoglu (2014) investigate the presence of long-range dependence in energy futures markets. Using a daily data set over the period 1990–2013, they find that efficiency of energy futures markets is time-varying and changes drastically over the sample period. 3. Empirical methodology In this paper we employ a rolling sample approach to investigate time varying market efficiency of spot and futures energy, instead of analyzing different sub-periods based on a cutoff date which is subject to criticism. Moreover, as argued by Sensoy and Hacihasanoglu (2014), arbitrary chosen sub-periods or non-overlapping intervals could not capture possible structural breaks in financial time series. Using a rolling sample approach, the parameters of interest. Is computed for the first window for a specified length n, and then we estimate again the parameter of interest by rolling the window forward by removing the first observation of the series and adding a new observation at the end. This process continues until the last observation is used. As tests statistics for weak form market efficiency we employ two variants of the Variance Ratio test (VR). The first is the Lo and MacKinlay (1988) test by assuming heteroscedasticity and the Chow and Denning (1993) multiple VR test. Moreover, we consider the Detrended Fluctuation Analysis (DFA) of Peng et al. (1994) method by computing the long memory parameter d. The rolling sample technique consists of 3 steps:
1– We set the length of the window equal to 500 observations (about two years).2 2– We calculate the p-values of the variance ratio tests and the parameter of long memory. 3– We roll forward the window and we re-estimate the parameters of interest for each time series. This provides us with a T − n estimates of these parameters. The use of this approach allows us to examine the evolution of market efficiency over time and to provide a useful indicator to rank the efficiency of spot and futures energy markets. 3.1. Data The data consist of the daily closing price of spot and futures energy from the New Mercantile Exchange (NYMEX) with the 1 month maturity contracts.3 The data set includes crude oil (Light-Sweet, Cushing, Oklahoma), rBOB Regular Gasoline (New York Harbor), No. 2 Heating Oil (New York Harbor), and Propane (Mont Belvieu, Texas). The data set is obtained from the Energy Information Administration (EIA) in the US Department of Energy. The sample period and the number of observations are reported in Table 1. The daily return rt is obtained by using the following transformation, rt = 100 ∗ (log (Pt ) − log (Pt −1 )), where (Pt ) is the price of the spot or futures energy at day t. 3.2. Variance ratio tests and wild bootstrapping We use two variants of the VR test statistic and the wild bootstrapping of Kim (2006) to test the weak-form
2 Note that only for the DFA method that we set the length of the window equal to 2168, 1725, 1226, 1084, 1946, 2542, 2397 and 1939 observations respectively for the spot crude oil, the futures crude oil, spot RBOB, futures RBOB, spot No. 2 heating oil, futures No. 2 heating oil, time series. As noted by many authors a time series with length higher than 2000 is need to obtain a consistent estimate of the long memory parameter d. 3 The NYMEX provides price data of energy futures with four maturity contracts C1, C2, C3 and C4. Contract 1 denotes a futures contract with the earliest delivery date. C2–C4 represent the successive delivery months following Contract 1. For more information about energy futures definition, we refer to http://www.eia.gov/dnav/pet/TblDefs/pet_pri_ fut_tbldef2.asp.
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efficiency. The first variant is the Lo and MacKinlay (1988) VR test by assuming heteroscedasticity. The VR test is one of the most popular test employed in the empirical finance literature to test the random walk hypothesis for financial data. Literally, the VR statistic stipulates that if stock returns follow an uncorrelated increment model (random walk under the null hypothesis), then the sample variance of k-period returns, rt + · · · + rt +k−1 is the same as k times the sample variance of the one period returns rt . The decision rule of this test is as follows. The null hypothesis is rejected when the ratio variance statistic differs statistically from unity. Otherwise we cannot reject the alternative hypothesis stating that the time series is not following a random walk. As in many papers, in the empirical part we use different values of holding period k set to 2, 5, 10 and 20 (k = 2, 5, 10, 20) and we report the time varying p-values of the wild bootstrapping technique. Following Wright (2000), the VR statistic can be written as follow,
VR (Y ; k) =
T 1
Tk t =k
(Yt + Yt −1 + . . .
+ Yt −k+1 − kµ ˆ
2
T 1
T t =1
Yt − µ ˆ
2
,
T
M (Y , k) = (VR (Y ; k) − 1)
2 k−1 2 (k − j) j=1
where δj
T
t =1
T t =j +1
= Yt − µ ˆ
2 2
The wild bootstrap is conducted in four steps as follows, 1– Form a bootstrap sample of T observations of Yt∗ = ϑt Yt (t = 1, . . . , T ) where ϑt is a random sequence with mean 0 and Variance 1. 2– Calculate M ∗ ≡ M (Y ∗ , k) and MV ∗ ≡ MV (Y ∗ , ki ) of the M (Y , k) and MV (Y ; ki ) statistics obtained from the bootstrap sample. 3– We repeat steps (1) and (2) for boot times, this allows us to form a bootstrap distribution of the test statistics
boot
MV Y ∗ , kj ; j
j =1
and {M (Y ; k; j)}boot j =1 .
4– Calculate the proportion of {M (Y ∗ ; k; j)}boot j=1 greater than M (Y , k) the sample value of the sample value
boot
and the proportion of MV Y ∗ , kj ; j j=1 greater than MV (Y , ki ). The calculated proportion corresponds to the p-values that we use to investigate the evolution of the time varying efficiency hypothesis.
The M ∗ and MV ∗ have the same asymptotic distributions as M (Y , k) and MV (Y , ki ), respectively. 3.3. Detrended Fluctuation Analysis (DFA) method
where µ ˆ = T −1 t =1 Yt . VR (Y ; k) is the estimator for the population VR, denoted as V (k). Lo and MacKinlay (1988) show under some assumptions that the M (X , k) statistic given below follows the normal distribution asymptotically under the null hypothesis that V (k) = 1,
71
k
Yt − µ ˆ
2
−1/2 δj
Yt −j − µ ˆ
2
/
.
The second test is the Chow and Denning (1993) multiple VR test which is designed to detect autocorrelation and heteroscedasticity in returns. The Chow and Denning test tests the joint null hypothesis that V (ki ) = 1 for i = 1, . . . , l The statistic of this test is given by, MV (Y ; ki ) = max |M (Y ; ki )| . 1≤i≤l
Chow and Denning (1993) show that the MV (Y ; ki ) statistic follows asymptotically the studentized maximum modulus distribution with l and T degrees of freedom. The main advantage of this test is that it control for a joint size issue in the original Lo and MacKinlay (1988). In this paper we apply the Kim (2006) wild bootstrapping procedure to approximate the sampling distribution of the M (Y , k) statistic of Lo and MacKinlay (1988) and the MV (Y ; ki ) statistic of Chow and Denning (1993). Precisely, this approach consists on resampling the original data by weighting it using random variables that have mean zero and unit variance.4 4 The wild bootstrap is a resampling method that approximates the sampling distribution of the VR test statistic, and is applicable to data with
In recent empirical literature, several research’s studies in finance and economics have employed the detrended fluctuation analysis (DFA) methods with linear polynomial local fit. The DFA method was firstly proposed by Peng et al. (1994) while examining series of DNA nucleotides. In recent year, this method have been widely used when detecting long-range correlations embedded in a seemingly non-stationary time series (see for instance Charfeddine and Ajmi, 2013, Charfeddine and Guegan, 2012 and Chen et al., 2005). The procedure to calculate the DFA long memory parameter consists of 4 steps, Step 1: We integrate the time series x (t ) (of length T ), y(t ) =
T
x(i).
i=1
Step 2: We divide the integrated time series into N adjacent sub-periods of length m while N ∗ m = T . For each sub-period, we fit a polynomial of order l = 1, see Hu et al. (2001). Step 3: We detrend the integrated time series by subtracting the local trend in each sub-period and then we define the fluctuation F (m) as,
F (m) =
T 1
T t =1
1/2 [y(t ) − ym (t )]
2
.
Scales as, F (m) = c mα where c is a constant independent of m. An ordinary least squares regression on logarithms of the previous relation will be run in order to estimate the correlation exponent.
unknown forms of conditional and unconditional heteroscedasticity. This approach has been used recently by Charles and Darné (2009) to examine the random walk hypothesis for the spot crude oil markets, and Enninful and Dowling (2013) to examine the market efficiency in European equity indices.
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Table 2 Descriptive statistics, ARCH LM and unit roots tests.
Mean (%) Std. Dev.(%) Skewness Kurtosis J–B Q(12) Q2 (12) LM(6) ADF PP ERS (OP) KPSS N. Obs
Futures oil
Futures heating oil
Futures RBOB
Futures propane
Spot oil
Spot heating oil
Spot RBOB
Spot propane
0.0148 2.3792 −0.827 18.933 82 573 73.970 935.36 444.68 −42.257 −89.062 0.0040 0.1141 7726
0.0148 2.266 −1.4492 22.958 144 752 47.918 528.72 221.572 −93.47 −93.96 0.0081 0.1456 8541
0.0157 2.4176 −0.1596 6.7178 1208.5 23.393 528.68 169.51 −45.158 −45.157 0.0476 0.0438 2083
0.0349 2.0847 −1.0960 15.459 26 271 44.900 485.82 196.983 −57.594 −57.687 0.0129 0.0435 3941
0.0112 2.5972 −0.755 16.874 58 170 65.015 795.16 344.41 −41.03 −85.92 0.0089 0.0615 7168
0.0287 2.5207 −1.6295 41.704 436 696 71.129 1940.8 1017.3 −45.054 −82.107 0.0076 0.0369 6947
0.0185 3.0755 0.1414 7.4843 2291.4 16.304 472.66 166.81 −51.043 −51.056 0.0499 0.0258 2725
0.0255 2.3869 −2.1363 65.422 879 854 44.435 216.92 155.43 −36.608 −72.215 0.0111 0.0308 5394
Note: The sample period is as described in Table 1. Jarque–Bera test of normality follows under the null hypothesis of normality the χ 2 (2) distribution with 2 degrees of freedom. The 5% critical value is equal to 5.99. The ARCH LM(6) statistic is the ARCH test up to the sixth lag and under the null hypothesis of no ARCH effect it follows a χ 2(q) distribution, where q is the number of lags. The Q(12) and Q2 (12) statistics denote the Ljung–Box test on the residuals and squared residuals of the conditional mean regression up to twelfth order. Under the null hypothesis of no serial correlation, the test is distributed as a χ 2 (12) = 21.026. ADF, PP, ERS, and KPSS denote the statistics of Augmented Dickey—Fuller (1979), Phillips—Perron (1988), Point Optimal Elliott— Rothenberg—Stock (1996) and Kwiatkowski, Phillips, Schmidt and Shin (1992) unit root test, respectively. Critical values of the ADF, PP, KPSS and ERS test, at the 5% level of significance, are equal to −1.941, −1.941, 0.463, and 3.26 respectively.
Then, three possible behavior can characterize the time series under study, 1. if the initial process is characterized by short-term correlations then α do not significantly differ from 0.5. 2. If the value of the exponent α lies in (0.5,1) then it indicates persistent long-range power-law correlations. 3. A value of α = 1.5 indicates Brown noise, the integration of white noise. To get a consistent estimate of the fractional long memory parameter, we set in this paper m = T 0.5 and m = T 0.6 . We consider also a value of l = 1. Then, the estimated value of the fractional long memory parameter is given by dˆ DFA = αˆ − 0.5. 4. Empirical results 4.1. Descriptive statistics Table 2 reports descriptive statistics for the spot and futures energy return series calculated as the first logarithmic difference of the daily closing prices. The results reveal that the mean is quite small, ranging from 0.0112% for spot crude oil to 0.0349% for futures propane. In terms of standard deviation, futures propane exhibits the least volatility (2.0847%), while spot RBOB displays the highest volatility (3.0755%). The kurtosis is significantly higher than the normal value of 3 indicating that the distribution of all return time series is fat-tailed. All return series display significant skewness, with negative skewness for all series except for spot RBOB, indicating that the empirical distributions of the spot and futures energy returns are asymmetric shape. The Jarque–Bera test statistic is significant at the 1% level of significance for all series, indicating that the spot and futures energy returns are highly non-normal distributed. Table 2 also reports the Ljung–Box LB statistics for the return and squared return series. For all return series, these
two statistics show the presence of high dependence in the returns series and squared returns series. The presence of high dependence in the squared return series indicates the presence of ARCH effects which is confirmed by the ARCH LM(12) statistic. In Table 2, we also report the results of the Augmented Dickey–Fuller (ADF), Phillips and Perron (PP), Point Optimal Elliott–Rothenberg–Stock (ERS) and Kwiatkowski, Phillips, Schmidt and Shin (KPSS) unit roots tests. For all return series, the hypothesis of unit root is rejected and the alternative hypothesis is accepted. 4.2. Time-varying efficiency of the spot and futures energy markets We examine the weak-form efficiency market hypothesis by testing the random walk hypothesis using wild bootstrapping VR and DFA tests. Fig. 1 through 6 report the evolution of the p-values of the Kim (2006) wild bootstrapping variance ratios statistics of Lo and MacKinlay (1988) and Chow and Denning (1993), as well as the evolution of the estimated fractional long memory parameter using the DFA approach. All figures clearly show that the estimated statistics are time-varying in nature. In particular, empirical results show that the spot and futures energy markets have enjoyed a long periods of market efficiency where returns series clearly follow pure white noise. Nevertheless, energy markets sometimes show departure from market efficiency depending on the prevailing economic and political conditions, which is consistent with the implication of the adaptive markets hypothesis. These empirical findings confirm the hypothesis of evolving efficiency of the energy markets. Moreover, empirical results seem to depend on the nature of the energy time series (sport or futures), and on the statistical methods employed for testing markets efficiency. Overall, the results are consistent with the random walk hypothesis in the four energy prices, and therefore with the weak-form efficiency of the four energy markets. More details analyzes of these empirical results are reported in the following Subsections 4.2.1 and 4.2.2.
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Fig. 1. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 2 and 5 for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
4.2.1. Wild bootstrapping of variance ratio results Estimation results of the p-values of the wild bootstrapping variance ratio statistic for both Lo and MacKinlay (1988) and Chow and Denning (1993) are plotted in Figures 1 to 6 for the spot and futures energy time series. We also report the VR statistic empirical results for the different values of k = 2 (two days), k = 5 (one week), k = 10 (two weeks), k = 20 (one month). In these figures, the horizontal line (in green color) indicates the critical threshold level for the p-value, which is set at 5%. Thus, a p-value less than 5% indicates the rejection of the null hypothesis of weak-form efficiency of the market. As shown in Figs. 1–6, the energy returns series are efficient for all different values of the parameter k, except for some time periods associated with some economic, political, weather events or supply shock. For the crude oil returns series, the VR tests reject the null hypothesis of market efficiency only around the years 1990, 1996, and 2005. The year 1990 correspond to the period of spikes in prices with the lower production, uncertainty associated with the Iraqi invasion of Kuwait and the ensuing Gulf War. In 1996, the Russian crude oil production reached its minimum level. The declining in Russian production contributed to the price recovery between 1990 and 1996. The year 2005 coincides with the hurricanes Katrina and Rita and US refinery problems. With regard to the RBOB regular gasoline time series, the null hypothesis of market efficiency is rejected around the year 2006 by the two VR tests and for different values of k. This date corresponds to Asian demand soars and refinery problems from hurricanes and MTBE/ethanol switch. For the futures series, the VR tests reject the null
hypothesis of weak-form efficiency around the end 2008 and around 2013. The deviation from a random walk in 2008 corresponds to the recent subprime financial crisis. The period around 2013 corresponds to the loss of Libyan exports in the face of the Libyan civil war. The VR tests for the spot series of the heating oil returns show that these series have experienced a several periods of markets inefficiency. The periods of inefficiency are 1990–1991, 1996–1998, and 2007–2008. These dates coincide with the Gulf war, the Asian financial crisis, and the subprime financial crisis. For the futures series of the heating oil returns, the null hypothesis of market efficiency is rejected only in 1986, 1993 and 1996. The deviation from a random walk in 1986 was caused by the large fluctuation of oil supply production (e.g., in early 1986 Saudi Arabia increased production of oil from two million barrels per day to five million). The timing 1996 corresponds to the OPEC announcement to reduce oil production in response to slack world oil demand, rising non-OPEC oil production, and weak oil prices. Finally, regarding the Propane, the VR tests for the spot series returns indicate that these series have experienced a several periods of markets inefficiency. The null hypothesis of weak-form efficiency is rejected over the periods 1995–1996, 2007–2009, and 2011–2014. As mentioned earlier, the first two periods coincide with the OPEC announcement regarding the reduction of oil production, and the increasing uncertainties caused by the recent global financial crisis, whereas the third period coincides with the Spring Arab. For the futures returns series, the obtained results are quite different than the spot series. The futures series have enjoyed a long periods of markets inefficiency mainly between 2006 and 2010.
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Fig. 2. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 10 and 20 for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
Fig. 3. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 2 and 5 for the future crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
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Fig. 4. These figures report the trajectories of the p-value of the wild bootstrapping Lo and MacKinlay (1988) Variance Ratio (VR) with k = 10 and 20 for the future crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
Fig. 5. These figures report the trajectories of the p-value of the wild bootstrapping Chow and Denning (1993) Variance Ratio (VR) using k = 2, 5, 10 and 20 for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
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Fig. 6. These figures report the trajectories of the p-value of the wild bootstrapping Chow and Denning (1993) Variance Ratio (VR) using k = 2, 5, 10 and 20 for the future crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively.
4.2.2. DFA statistic Empirical results of the DFA method are reported in Figs. 7 and 8 for the spot and futures crude oil, RBOB regular gasoline, No.2 heating oil and the propane returns series. For consistency of the estimated fractionally parameter d employing DFA, we use a different values of the window length.5 Empirical results show that the estimated long memory parameter is significantly different from zero and negative in the majority of cases which means the presence of anti-persistence behavior. Concerning the market efficiency hypothesis, we find that for the crude oil returns series the null hypothesis of market efficiency has been rejected during the 1995–2000 and 2008–2010 periods for the spot series and during the 1992–2001 and 2008–2010 periods for the futures returns series. Regarding the RBOB regular gasoline, the null hypothesis of market efficiency has been rejected for the periods 2008–2009 and 2012–2014 for the spot returns series and 2011–2014 for the futures series. For the spot No.2 heating oil and propane time series, the periods of markets inefficiency correspond to the 1994–2001 and 2008–2010 periods for the No.2 heating oil and to the 2009–2012 periods for the propane time series. With regard to the futures returns series, empirical results show that the periods of market inefficiency are the 1999–2000, 2002–2003 and 2007–2010 periods the for crude oil series, the 2011–2014 period for the RBOB regular gasoline series, the 1990–2001 and 2009–2011 periods for
5 See footnote 2.
the No.2 heating oil series, and the 2002–end of 2005 and 2007–2010 periods for the propane returns series. 4.3. Ranking of the spot and futures energy markets In Tables 3 and 4, we report the ranking of the spot and futures energy markets based on the percentage of insignificant estimated values at the 5% level of the two variants of VR tests (Lo and MacKinlay, 1988 for the different values of k, and Chow and Denning, 1993), and the Detrended Fluctuation Analysis (DFA). As argued by Lim (2007), the use of the popular median measure of Cajueiro and Tabak (2004) would give a biased view of the degree of market efficiency for the whole sample period, and hence defeat the fundamental objective of using a rolling sample approach. Hence, in this study, we employ the percentage of insignificant H statistic for each time window as an indicator for assessing the relative efficiency of energy markets. Specifically, a window is defined as significant if the statistic rejects the null hypothesis of pure white noise at the specified threshold level for the p-value, which is set at 5%. As we can see, the different statistics used in this paper provide mixed results, mainly for the first rank. Regarding the spot market, the crude oil seems to be the most efficient market, based on the VR test of Lo and MacKinlay (1988) for all values of k except k = 20, and the VR test of Chow and Denning (1993). On the contrary, based on the DFA test, the most efficient spot market is heating oil. At the other end of the spectrum, the Propane market experienced the most frequent departure from efficiency, according to all tests.
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Fig. 7. (a), (b), (c) and (d) represent the trajectories of the estimated long memory parameter using the DFA method for the spot crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively using the rolling sample approach.
Fig. 8. (a), (b), (c) and (d) represent the trajectories of the estimated long memory parameter using the DFA method for the futures crude oil, RBOB regular gasoline, No. 2 Heating oil and Propane time series, respectively using the rolling sample approach.
With regard to the futures energy markets, although there is a clear consensus for the most efficient market
(futures crude oil) based on the DFA and the VR test of Chow and Denning (1993), empirical results do not
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Table 3 Ranking of spot energy markets based on the percentage of energy markets efficiency. Percentage
Spot crude oil Spot RBOB regular gasoline Spot heating oil Spot propane
Ranking
VR (k = 2 )
VR (k = 5)
VR (k = 10)
VR (k = 20)
VR ( k = 2)
(k = 5)
(k = 10)
(k = 20)
97.0% 96.5% 83.3% 75.8%
98.4% 94.9% 93.0% 79.2%
98.1% 97.4% 96.5% 96.7%
99.2% 99.7% 98.8% 97.1%
1 2 3 4
1 2 3 4
1 2 4 3
2 1 3 4
Percentage
Spot crude oil Spot RBOB regular gasoline Spot heating oil Spot propane
VR
VR
VR
Ranking
DFA (m = 50)
DFA (m = 100)
CD Test
DFA (m = 50)
DFA (m = 100)
CD Test
50.84% 47.84% 52.11% 51.12%
49.16% 45.38% 54.59% 43.58%
99.1% 96.9% 91.2% 75.8%
2 3 1 4
2 3 1 4
1 2 3 4
Table 4 Ranking of futures energy markets based on the percentage of energy markets efficiency. Percentage
Futures crude oil Futures RBOB regular gasoline Futures heating oil Futures propane
Ranking
VR (k = 2)
VR (k = 5)
VR (k = 10)
VR (k = 20)
VR (k = 2)
VR (k = 5)
VR (k = 10)
VR (k = 20)
99.5% 100%. 99.8% 75.9%
99.7% 89.9% 99.1% 72.2%
98.5% 99.0% 96.9% 89.9%
98.9% 99.8% 99.6% 88.4%
2 1 3 4
1 3 2 4
2 1 3 4
3 1 2 4
Percentage
Futures crude oil Futures RBOB regular gasoline Futures heating oil Futures propane
Ranking
DFA (m = 50)
DFA (m = 100)
CD Test
DFA (m = 50)
DFA (m = 100)
CD Test
49.35% 23.80% 39.77% 22.42%
43.95% 29.10% 35.40% 17.23%
99.8% 99.5% 99.7% 70.6%
1 3 2 4
1 3 2 4
1 3 2 4
converge on the first rank (either crude oil or RBOB) based on the VR test of Lo and MacKinlay (1988) for different values of k. At the other end of the spectrum, futures propane market experienced the most frequent departure from efficiency, based on all tests. Finally, it is noteworthy that contrasting the Kim wild bootstrapping VR tests with the DFA indicates that the latter is more likely to reject the null hypothesis of random walk over longer time windows. 5. Conclusion This paper examines the weak-form efficiency of four energy markets (crude oil, RBOB regular gasoline, No. 2 heating oil, and propane), in close association with the adaptive market hypothesis. Instead of static approaches, we use a time-varying approach to see the dynamics efficiency of the four energy markets. This approach allows us to detect periods of efficiency/inefficiency and so the changing degree of energy market efficiency over time. Thus, the relative efficiency of energy markets can easily be assessed by comparing the total time periods these markets exhibit significant nonlinear serial dependence. As tests of market efficiency, we use the wild bootstrapping variance ratio tests, and the detrended fluctuation analysis (DFA) long memory parameters. Our empirical results reveal that the efficiency of energy markets is not uniform over time, which is consistent with the adaptive market
hypothesis. Specifically, results show strong evidence of time varying market efficiency of the spot and futures energy returns series. Empirical results also show that nonlinear dependence in energy returns is quite localized in time. This finding implies that time-varying parameter models might be superior to constant parameter models in capturing energy market dynamics. Furthermore, our research provides insights into the ranking of spot and futures energy markets. Overall, we find that the spot and futures crude oil and RBOB regular gasoline are among the most efficient markets while the spot and futures propane time series are at the end of the ranking. However, it should be noted that for the spot market, the result is controversial using the DFA. Specifically, we find that the spot propane is ranked first while the spot RBOB and the spot heating oil are among the less efficient markets. Overall, the findings of this paper provide evidence of the importance of the rolling approach in explaining the behavior of energy returns and thus contribute to better understanding the dynamics of spot and futures energy markets. They also provide important information for the regulators and investors and have implications for investment strategies. Specifically, the evidence of long range serial dependence implies the potential of returns predictability in some energy markets especially during those identified time periods of inefficiency. Further, market inefficiency implies that there exist yet markets
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Further reading Hurst, H.E., 1951. Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civ. Eng. 116, 770–808.