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A study of the interactive relationship between oil price and exchange rate: A copula approach and a DCC-MGARCH model
The Journal of Economic Asymmetries 12 (2015) 173–189
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A study of the interactive relationship between oil price and exchange rate: A copula approach and a DCC-MGARCH model Angham ben brayek b, Saber Sebai a, Kamel Naoui b,n a b
Department of Finance and Accounting, High Institute of Accounting and Administration, University of Manouba, Manouba, Tunisia Tunis School of Business, Tunisia
a r t i c l e i n f o
abstract
Article history: Received 20 April 2015 Received in revised form 11 September 2015 Accepted 14 September 2015
This paper examines the relationship between oil prices and the US dollar exchange rate using a copula approach and the DCC-MGARCH model. In order to identify a possible impact and interdependence between oil prices and exchange rates during the global financial crisis, we divided the study period into sub-periods, pre-crisis, crisis and postcrisis periods. We found that oil prices and exchange rates are independent during the pre-crisis period. However, evidence of this impact and a positive dependence between our variables were reported after the crisis onset. In addition, we found that oil prices influenced exchange rates and vice versa during the crisis period, but not during the precrisis period. These results have important implications on risk management and monetary policy to control inflationary pressures from oil prices and fiscal policy in oilexporting countries. & 2015 Published by Elsevier B.V.
JEL Classification: E44 C22 keywords Copulas DCC-MGARCH Dependence measures Crude oil price U.S. dollar exchange rates
1. Introduction Crude oil is one of the most important commodities of the global economy. Previous studies pointed out that changing oil prices affect stock markets activity. Firstly, oil prices have been significantly fluctuating over the last three decades and have become more volatile than they were during the Second World War period and the early 1970s. Increased volatility in oil prices was noticed after the international oil crises of 1973 and 1979. This trend was reinforced by the collapse of oil prices during the 1980s. More importantly, over the past five years, oil prices have sharply increased from $ 42 per barrel in early 2005 to reach $ 147 the barrel in July 2008. Plourde and Watkins (1998) and Regnier (2007) found that oil price volatility is significantly higher than that of other energy products since the mid-1980s. Moreover, unrest in Libya and the ongoing threats to political instability in other Middle Eastern and North African countries contributed in increasing oil prices, which may slow down global economic growth. Secondly, some studies found evidence of an inefficient behavior of international oil markets, which made forecasting oil prices volatility and covering oil risk more complicated (Green & Mork, 1991; Shambora & Rossiter, 2007; Arouri, Dinh, & Nguyen 2010). Finally, oil prices are priced in US dollars, and their fluctuations highly depend on the dollar’s exchange rate, which has experienced frequent and uncertain changes in recent years. In this regard, several observers argue that appreciating oil prices results from the dollar’s recession. Indeed, in order to hedge n
Corresponding author. E-mail addresses: [email protected] (A.b. brayek), [email protected] (S. Sebai), [email protected] (K. Naoui).
http://dx.doi.org/10.1016/j.jeca.2015.09.002 1703-4949/& 2015 Published by Elsevier B.V.
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against the falling dollar, investors are moving towards investments in oil, raw materials and oil exportation to convert their incomes into other currencies. However, it is also conceivable that increase in oil prices and the dollar’s recession do not directly depend on each other, but both are the result of a common factor which is the withdrawal of investors from the complex asset markets in the United States. This can change the correlation pattern between the dollar and oil prices because of the dollar’s transaction requirements or the cyclical effects, which could not, in any case, be assumed on the idea of a stable correlation pattern.
2. The literature review Modeling and forecasting co-movement between oil prices and the dollar’s exchange rate are crucial, not only for market operations and risk management issues, but also for the proper regulation of foreign exchange markets for all the economies that operate with floating exchange rate regimes. Krugman (1983), Golub (1983) and Rogoff (1991) pointed to the potential importance of oil prices as a predictor of exchange rate movements. Empirical work on the interactions between oil prices and exchange rates are, however, much less extensive than those on the effects of oil prices on economic activities. Following the global financial crisis, most studies mainly found a positive relationship between oil prices and US dollar-based exchange rates. This meant that an increase in oil prices is influenced by a strong dollar as indicated by Dibooglu (1996), Amano and van Norden (1998), Bénassy-Quéré, Mignon, and Penot (2007), Chen and Chen (2007), Basher, Haug, and Sadorsky (2012). Amano and van Norden (1998) found, using an error correction model (ECM), a stable relationship between oil price and the US dollar’s exchange rate over the period 1972–1993. In addition, they found a one-way causality relationship between oil prices and exchange rates. This suggests that an oil price shock can heavily influence exchange rate fluctuations during the study period. Bénassy-Quéré et al. (2007) studied causality between oil and the dollar’s real effective exchange rate over a longer period. They found that a 10% increase in oil prices coincides with an appreciation of the dollar by 4.3% in the Long term. However, some studies claimed no such causality between the US exchange rate and appreciation of oil prices (Narayan, Narayan, & Prasad, 2008; Zhang, Fan, Tsai, & Wei 2008; Akram, 2009; Wu, Chung, & Chang, 2012). We summarize, in the following table, the main relevant literature on the topic, as a matter of providing a comparative perspective for readers. Authors
Object
Study period
Monthly data between February 1972 and January 1993 Bénassy-Quéré Monthly data beet al. (2007) tween 1974 and 2005 Monthlydata beChen and Chen This paper examines the long-term re(2007) lationship between oil prices and real ex- tween 1972 and 2005 change rates. Daily date beBasher et al. (2012) The authors study the dynamic relationship between oil prices and exchange rates tween 1988 and 2008 of market share during their emergence. Amano and van Norden (1998)
The authors put an emphasis on the relative importance of real shocks over monetary policy to explain exchange rate movements They study cointegration and causality between oil prices and exchange rates
Narayan et al. (2008)
The authors examine the relationship between oil prices and exchange rates
Zhang et al. (2008) The authors test the interaction between change in oil prices and the US exchange rate Akram (2009)
Wu et al. (2012)
Reboredo (2011)
The author seeks to determine whether depreciation contributes to the appreciation of commodity prices The authors examine the economic value of co-evolution between oil prices and the dollar This paper examines the dependence structure or co-movements between oil prices and exchange rates This paper examines the dependence structure between oil prices and exchange rates The relationship between oil prices and stock market indices of different countries
Riadh Aloui, Ben Aïssa, and Duc Khuong (2013) Kunlapath Sukcharoen et al. (2014) Reboredo and Riv- This paper examines the relationship beera-Castro tween oil prices and exchange rates
Daily data between 2000 and 2006 Daily data between 2000 and 2005 Quarterly data between 1990 to 2007 Weekly data between 1990 to 2009 Daily data between 2000 to 2010 Daily data between 2000 to 2011 Daily data between 1982–2007 Daily data between 2000 and
Methodology Main results Causality test, Using a GRANGER test: oil prices influence the cointegration US real effective exchange rate, not the opposite. It is also the main source of persistent exand ECM change rate shocks Causality test, A 10% increase in oil prices coincides with an cointegration appreciation of 4.3% in the long term and ECM Panel and Oil prices are the main cause of foreign excointegration change rate movement; they are also robust to different measures of oil prices. VAR The positive impact on oil prices tend to reduce prices of new shares on the market and the dollar-weighted indices in short-term transactions. GARCH and An appreciation of oil prices led to an appreEGARCH ciation of the dollar Cointegration test, VAR, ARCH and VaR VAR
Copula GARCH Copula comouvement Copula GARCH Copula GARCH VAR
The US dollar’s recession has been a key factor in appreciating crude oil prices
A depreciation of the US dollar led to raising basic product prices including crude oil prices The dependence structure between oil prices and exchange rates becomes negative and decreased continuously since 2003 Dependence of oil prices on exchange rates is generally low although it has significantly increased because of the crisis. Increase in oil prices coincides with an appreciation of the dollar The results indicate a weak dependence between oil prices and stock indices for most cases There is a negative dependence between oil prices and exchange rates during the crisis and
A.b. brayek et al. / The Journal of Economic Asymmetries 12 (2015) 173–189 (2013) Filis, Degiannakis, This paper examines the relationship beand Floros, 2011 tween oil prices and stock market indices Ibrahim Turhan, Ahmet Sensoy, and Erk Hacihasanoglu (2014)
This study examines oil price co-movements with exchange rates.
2011 Data between 1987–2009
DCC-GARCHGJR
Daily data beDCC tween 2003–2008
175
the impact is empirically valid. During economic crises, the oil market is not a “safe haven” that offers protection against market losses. The study reveals that the link between oil prices and exchange rate has increased over the last decade; they are strongly and negatively correlated (which also combines with an increase in oil prices with the US dollar’s recession compared to other currencies).
In summary, oil price increase assumes a decline/recession or the appreciation of the US dollar. This may be a result of dependence between the different countries as far as oil prices are concerned. For example, Lizardo and Mollick (2010), using co-integration tests, show that appreciation of oil prices led to a sharp depreciation of the US dollar against the currencies of oil exporters such as Canada, Mexico and Russia. Instead, the dollar value increased against currencies of net oil-importing countries, like Japan, when real oil prices increased. Countries which are neither oil exporters nor importers, such as the UK and the European Union, face a depreciation of the dollar.
3. Methodology Our purpose is to examine the relationship between oil and currency markets through studying current market trading activities. The data includes crude oil prices and nominal exchange rates expressed in US dollar (USD) over the period between January 3, 2000 and 17 April 2014. Exchange rate is an amount of USD for each unit of the seven major currencies of international trade: The Euro (EUR), the Australian Dollar (AUD), the Canadian dollar (CAD), the Mexican Peso (MXN), the Norwegian kroner (NOK), the British pound (GBP), and the Japanese Yen (JPY). An increase in nominal exchange rates may reflect a recession of the US dollar against foreign currencies. Data frequency is daily. As our focus is oil prices, and for comparison purposes, we use the most important criterion of the West Texas Intermediate (WTI) at Cushing. The Brent index serves as a pricing benchmark for two thirds of the world’s internationally traded crude oil supplies. For the purpose of the study, we express rates by their logarithm; the first rate (innovation) is designated as return on assets:
⎛ Pi, t ⎞ Ri, t = 100* log ⎜ ⎟; ⎝ Pi, t − 1 ⎠
i = 1, 2, .. 17
(A.1)
with Ri, t = daily productivity with security i to T Pi, t = Price of security i at time t. Using the Breakpoint test, our sample will be divided into three sub-periods, a pre-crisis period which spreads from 1.03.00 to 12.31.06, a crisis period stretching from 1.01.07 to 12.31.08 and at a post crisis period, from 1.01.09 until 7.14.14. In the following, we try to combine some analytical tools that have been recently introduced in applied finance. The first is developed by Nelson (1991) as an original specification of conditional correlations between several endogenous variables or markets (models called “multivariate”). These models allow for tracing the evolution of correlations between two or more actives. The second tool is copula functions that make it possible to implement more consistent distribution laws and stylized facts observed in financial markets than the tools currently used. Finally, there is the Dynamic Conditional Correlation (DCC) model which allows the correlation matrix to be dynamic over time while retaining few parameters. 3.1. The ARCH/GARCH models These models measure the transmission of crises as volatility spreads. They calculate variance/covariance matrices between securities markets. According to Engle (1982) with his ARCH process generalized by Engle (1982), GARCH models have proved their ability to capture the specific properties of financial time series: volatility clustering and fatter tails. For simplicity reasons, GARCH (1.1) of Bollesrslev is a customized response. It functions similar to an infinite order ARCH model. Indeed, it integrates all information with fewer parameters. Application of this model on financial variables is of a particular interest since it allows studying both the relationship between returns and varying volatilities. In general, a GARCH (p, q) is defined by the following equations:
yt = f ( yt − 1 , … yt − k /Ωt − 1) + ut σt2 = c +
p
∑i
αi Ut2− i +
(A.2)
q
∑ j βj σt2− j
ut /Ωt − 1 → D (0, σt2 )
(A.3)
where yt is the asset market performance, ut is errors (remnants or innovations), D( ) is conditional distribution of innovations, Ωt − 1 is an information set at time (t 1), and σt2 is conditional variance of returns and innovations. We consider a Gaussian error distribution in which the parameters of medium conditional and variant conditional
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equations are estimated by a maximum likelihood estimator “EMV”. As for GARCH (1.1), the β coefficient is usually high (very close to 1) for high frequency data series and the sum indicates persistence of shocks. The introduction of this model was to model volatility of time series and its transmission from one series to another. Thus, the impact can be defined as the spread of price volatility of financial market assets of countries in crisis to other financial markets of other countries. This occurs during periods of financial turmoil as Pericoli and Sbracia (2001) showed. Therefore, the model calculates the variance/covariance matrices between securities markets. The traditional GARCH model assumes a normal distribution of innovations. However, it is well known that many financial time series are non-normal and tend to have fat tails (Mandelbrot, 1963; Fama, 1965). To better understand the characteristic of fat tails, Bollerslev (1987) proposes the use of conditional Student-t distribution. Nelson (1991) and Theodossiou (2000) propose respectively the use of the generalized error distribution and asymmetric generalized error distribution. In this study, we consider various distributions for the error term ε_t, including the normal distribution and the Student-t distribution. 3.2. The DCC-MGARCH model DCC models allow the correlation matrix to be dynamic over time while retaining few parameters. We can then model both variances and conditional correlations of several series. This model, proposed by Engle (2002) and Tse and Tsui (2002), is written as follows:
⎧ Ht = Dt RDt ⎪ ⎪ ⎨ Dt = diag ( h11t , ⎪ −1 −1 ⎪ ⎩ Rt = (diagQ t ) 2 Q t (diagQ t ) 2
h22t , …,
hNNt ) (A.4)
or Q t represents the covariance matrix of the standardized residuals, the dimension (N N), the symmetric and positive definite. 3.3. Copula functions The relationship between foreign exchange crises and financial crises have motivated several authors to use different approaches they consider useful in order to define and study the concept of impact. Despite extensive studies, the relationship remains unclear and depends on the approach and assumptions used. A copula is a multivariate uniform distribution. It is a, relatively, old static tool introduced by Sklar (1959) and revived by Genest and Mackay (1986). For simplicity and because multivariate theory is an extension of the bivariate approach, we will place a particular focus on the theory of bivariate couples. Thus, a bivariate copula function C [0, 1]2- [1,0] is defined by the following:
C (u, 0) = C (0, u) = etC (u, 1) = C (1, 0) = u; ∀ u€ [0, 1] C (v1, v2 )–C (v1, u2 )–C (u1, v2 ) + (u1, u2 ) ≥ 0
(A.5) (A.6)
(u1, u2 ) € [0, 1]2 , (v1, v2 ) € [0, 1]2 telque0 ≤ u1 ≤ v1 ≤ 1et 0 ≤ u2 ≤ v2 ≤ 1 The property (i), in particular, reflects that any copula is a distribution whose marginal distributions are a uniform law set to I ¼[0, 1]. Property (ii) is 2-growth and inequality in the distribution of the rectangle C. It reflects the fact that if C admits a density c (uv), then it is positive. When U_1 and U_2, two uniform random variables on [0, 1], then we have:
C (u1, u2 ) = P (U1 ≤ u1, U2 ≤ u2 )v (u1, u2 ) ∈ [0, 1]2 This definition ensures that the copula is a probability distribution with uniform margins. “(Clauss, 2011, copula theory, p. 5).
4. Results In the charts below, we notice that daily returns are relatively stable during the period preceding the start of the global financial crisis (January 2000 to the third quarter of 2008), triggered by the massive failures during the US subprime crisis and the banking sector. 4.1. Descriptive statistics “kurtosis” and “Skweness” coefficients tell us about the nature of the distributions of the series and they essentially test
Mean Median Maximum Minimum Std. dev. Skewness Kurtosis Jarque–Bera Q (12)
Q2 (12) ARCH (12)
WTI
AUD
CAD
EUR
JPY
MXN
NOK
GBP
BRENT
0.005709 0.000000 7.128381 7.42286 1.013235 0.34483 8.673799 5074.372 31.993*** 952.79**
0.004140 0.017631 2.292070 3.04172 0.327011 0.50760 10.83499 9695.549 69.083*** 2731.3***
0.003194 0.006943 1.812280 1.66527 0.219830 0.14478 7.417425 3044.145 71.693*** 1540.3***
0.003708 0.009602 1.504412 1.62122 0.261090 0.15505 5.578902 1048.019 31.729** 337.74***
1.34E 12 0.000000 1.258913 1.67056 0.308407 0.13044 4.515115 367.151 43.328*** 76.270***
0.003689 0.000000 1.677857 2.642911 0.263464 0.883734 13.39761 17278.38 24.425*** 3474.4***
0.003433 0.000000 1.803261 2.229164 0.300419 0.352510 6.047368 1519.700 108.49*** 1289***
0.00042 0.00250 1.35882 1.73348 0.22774 0.30200 6.87133 2384.685 59.23*** 583.4***
0.014094 0.000000 5.582162 8.63839 0.946085 0.42595 8.584428 4958.263 15.645* 449.09***
203.11***
237.13***
133.58***
48.925***
17.771***
611.00***
130.14***
42.60***
37.28763***
2
Notes: The table displays summary statistics of daily returns over the period from January 3, 2000 to April 17, 2014.Q(12)and Q (12) are the Ljung–Box statistics for serial correlation of order 12 in returns and squared returns. ARCH is the Lagrange Multiplier test for autoregressive conditional heteroscedasticity. ** and *** indicate the rejection of the null hypothesis of no autocorrelation, normality and homoscedasticity at the 5% and 1% levels of significance respectively.We then establish the causal test between oil prices and different exchange rates to determine the causality direction in the three study periods.
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Table 1 Descriptive statistics.
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the normality assumption. In our study, the null hypothesis of normality for the daily returns of exchange rates is rejected. We notice first that the kurtosis coefficient is very high, well above 3. This phenomenon of excess kurtosis confirms the strong leptokurtic character of stock returns series (Table 1). The Ljung–Box Q-statistics of order 12 show the existence of autocorrelation in allthe returns series. The Ljung–Box statistics of order 12 applied to squared returns are highly significant. The results of the Lagrange Multiplier tests point to the presenceof ARCH effects in the return data, thus supporting our decision to use the GARCH-based approach. The usefulness of this test is to investigate the causal relationship between oil prices and exchange rates. This test is important because it provides information on the causality direction of these variables. There are basically three possibilities for this test. It could be unidirectional, bidirectional, or neutral. During the pre-crisis period, we see that oil prices influence the AUD exchange rate, the CAD exchange rate and the NOK exchange rate. As for the BRENT price, the results indicate that it influences all exchange rates except JPY. In times of crisis, we found a one-way causal relationship between oil prices and the AUD exchange rate and oil prices affect all exchange rates. After the crisis, we found that oil prices affect all exchange rates. 4.2. DCC-MGARCH model results We use the DCC model developed by Engle (2002) to explore the evolution of conditional correlations between exchange rates and oil prices during the subprime crisis. The importance of this analysis is the use of multivariate GARCH. The assumption of changes in correlations are relatively neglected in empirical studies because of the difficulties in taking then in to consideration. The estimation of these correlations takes therefore into account all the information available at a given time. Indeed, these correlations, like conditional variances, are explained by three main factors including their own past trends; a factor representing the effect of recent shocks and the constant. In addition, this new class of multivariate GARCH models is distinguished by its estimation simplicity. Indeed, the latter being carried out in two stages: the first estimates various GARCH and is applied for each series separately. The second step estimates the dynamic correlations emanating Table 2 Granger causality VAR. Pre-crisis Excluded
Chi-sq
Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent BRENT Dependent BRENT
variable: AUD 9.92852 variable: CAD 22.9762 variable: EUR 0.61297 variable: GBP 0.77535 variable: JPY 3.30106 variable: MXN 1.60319 variable: NOK 9.98357 variable: AUD 36.7150 variable: CAD 34.7571
Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT
variable: EUR 8.82973 variable: JPY 0.122930 variable: GBP 21.5991 variable: MXN 13.0381 variable: NOK 25.6856
df
Prob.
2
0.007
2
0.000
2
0.736
2
0.678
2
0.191
2
0.448
2
0.006
2
0.000
2
0.000
2
0.012
2
0.9404
2
0.000
2
0.001
2
0.000
Crisis Excluded Dependent AUD Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent AUD MXN GBP Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT
Chi-sq variable: WTI 7.63399 variable: AUD 49.6326 variable: CAD 53.7650 variable: EUR 62.8830 variable: GBP 50.8851 variable: JPY 12.2594 variable: MXN 28.8993 variable: NOK 134.871 variable: BRENT 4.82100 8.164152 5.69959 variable: AUD 69.91902 variable: CAD 66.3572 variable: EUR 58.5706 variable: GBP 51.5171 variable: JPY 5.68763 variable: MXN 36.6241 variable: NOK 107.964
df
Prob.
2
0.022
2
0.000
2
0.000
2
0.000
2
0.000
2
0.002
2
0.000
2
0.0000
2 2 2
0.089 0.0169 0.057
2
0.000
2
0.000
2
0.000
2
0.000
2
0.058
2
0.000
2
0.000
Post-crisis Excluded
Chi-sq
Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent BRENT Dependent BRENT
variable: AUD 230.394 variable: CAD 256.377 variable: EUR 116.963 variable: GBP 85.460 variable: JPY 19.6758 variable: MXN 150.294 variable: NOK 183.019 variable: AUD 231.186 variable: CAD 266.974
Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT
variable: EUR 78.5796 variable: GBP 100.4783 variable: JPY 16.6262 variable: MXN 130.249 variable: NOK 167.749
df
2
Prob. 0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.0000
2
0.0000
2
0.000
2
0.000
2
0.000
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Table 3 Results of the estimation of DCC GARCH (1.1) WTI-AUD. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
θ1 θ2
0.032123 0.966814 0.00659042 0.005241 0.814927
Probability 0.000 0.0000 0.000 0.6729 0.0142
Coefficients 0.14597 0.872655 0.00708086 0.0252 0.986357
Post-crisis Probability 0.0061 0.000 0.209 0.0197 0.000
Coefficients 0.054160 0.939411 0.00365332 0.009767 0.977292
Probability 0.000 0.000 0.1569 0.1569 0.000
Table 4 Results of the estimation of DCC GARCH (1.1) WTI-CAD. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.032515 0.962471 0.0044183
0.0000 0.000 0.000
θ1 θ2
0.23289 0.771341
0.000 0.000
Coefficients 0.092727 0.930854 0.02766624 0.020398 0.881801
Post-crisis Probability
Coefficients
Probability
0.0168 0.000 0.000
0.039189 0.959917 0.0027486
0.000 0.000 0.0000
0.2573 0.0063
0.012927 0.431968
0.3454 0.4061
Table 5 Results of the estimation of DCC GARCH (1.1) WTI-JPY. Pre-crisis
Crisis
Post-crisis
Coefficients
Probability
Coefficients
Probability
Coefficients
Probability
α1 β1 ρi, j
0.045787 0.317090 0.0127002
0.0711 0.4766 0.0000
0.050396 0.919099 0.0953766
0.0466 0.000 0.000
0.015754 0.976744 0.0030249
0.0633 0.000 0.000
θ1 θ2
0.010683 0.990141
0.0142 0.000
0.01507 0.884111
0.1359 0.000
0.016626 0.452958
0.2455 0.3020
Table 6 Results of the estimation of DCC GARCH (1.1) WTI-EUR. Pre-crisis
Crisis
Post-crisis
Coefficients
Probability
Coefficients
Probability
Coefficients
Probability
α1 β1 ρi, j
0.009066 0.788279 0.0145882
0.5474 0.000 0.000
0.069699 0.959829 0.0096113
0.0153 0.000 0.000
0.021787 0.980241 0.02858389
0.0001 0.000 0.000
θ1 θ2
0.038254 0.488803
0.1466 0.068
0.036964 0.872033
0.000 0.000
0.022865 0.746676
0.2587 0.000
Table 7 Results of the estimation of DCC GARCH (1.1) WTI-MXN. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.049397 0.924226 0.00844543
0.0001 0.000 0.000
θ1 θ2
0.008577 0.4852
0.7648 0.7195
Coefficients 0.185784 0.826813 0.03670046 0.029399 0.950092
Post-crisis Probability
Coefficients
Probability
0.0024 0.000 0.000
0.073980 0.909931 0.0115109
0.000 0.000 0.000
0.000 0.000
0.007595 0.375794
0.7498 0.9168
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Table 8 Results of the estimation of DCC GARCH (1.1) WTI-GBP. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.027555 0.961442 0.01809597
0.0006 0.000 0.1788
θ1 θ2
0.034547 0.282410
0.1788 0.4570
Coefficients 0.066893 0.935962 0.0046623 0.003033 0.995269
Post-crisis Probability
Coefficients
Probability
0.0032 0.000 0.209
0.025338 0.971507 0.0079668
0.0001 0.000 0.000
0.000 0.290
0.006888 0.948094
0.4064 0.000
Table 9 Results of the estimation of DCC GARCH (1.1) WTI-NOK. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.020138 0.971481 0.01426964
0.0024 0.000 0.000
θ1 θ2
0.025396 0.460274
0.3214 0.3044
Coefficients 0.077451 0.931229 0.02467348 0.033181 0.809568
Post-crisis Probability 0.0055 0.000 0.000 0.000 0.000
Coefficients 0.027196 0.970033 0.01248263 0.01918 0.074126
Probability 0.000 0.000 0.2864 0.2864 0.9287
Table 10 Results of the estimation of DCC GARCH (1.1) BRENT-AUD. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
0.032123 0.966814 0.02889
θ1 θ2
0.016846 0.803126
Probability 0.000 0.0000 0.000 0.000 0.000
Coefficients 0.111554 0.855336 0.07072461 0.020793 0.777765
Post-crisis Probability
Coefficients
Probability
0.000 0.000 0.000
0.059059 0.934364 0.0295549
0.000 0.000 0.000
0.000 0.000
0.00627 0.610457
0.7701 0.5471
Table 11 Results of the estimation of DCC GARCH (1.1) BRENT-CAD. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.032430 0.962820 0.04230
0.000 0.000 0.000
θ1 θ2
0.021338 0.777843
0.000 0.000
Coefficients 0.081833 0.907689 0.0543826 0.026559 0.427529
Post-crisis Probability 0.0205 0.000 0.000 0.2969 0.4031
Coefficients 0.039189 0.959917 0.0379465 0.012535 0.462597
Probability 0.000 0.000 0.000 0.4936 0.5709
Table 12 Results of the estimation of DCC GARCH (1.1) BRENT- EUR. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
0.01877 0.975695 0.017992
θ1 θ2
0.007406 0.820849
Probability 0.000 0.000 0.000 0.4682 0.000
Coefficients 0.050387 0.95784 0.0409612 0.033237 0.790313
Post-crisis Probability
Coefficients
Probability
0.000 0.000 0.000
0.021787 0.980241 0.0315329
0.000 0.000 0.000
0.000 0.000
0.019461 0.803088
0.3343 0.000
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Table 13 Results of the estimation of DCC GARCH (1.1) BRENT-GPB. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.027555 0.961442 0.010416
0.000 0.000 0.000
θ1 θ2
0.00289 0.992698
0.4292 0.000
Coefficients 0.07008 0.926483 0.087726 0.04735 0.760071
Post-crisis Probability
Coefficients
Probability
0.0033 0.000 0.000
0.025338 0.971507 0.01979552
0.000 0.000 0.000
0.000 0.000
0.026241 0.5833731
0.2780 0.0389
Table 14 Results of the estimation of DCC GARCH (1.1) BRENT-JPY. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
θ1 θ2
0.0177728 0.974833 0.0183584 0.017661 0.986283
Probability
Coefficients
Post-crisis Probability
Coefficients
Probability
0.000 0.000 0.000
0.050396 0.919099 0.11298
0.0466 0.000 0.000
0.015754 0.976744 0.0128718
0.000 0.000 0.000
0.000 0.000
0.047734 0.500155
0.000 0.1893
0.008561 0.96850
0.3751 0.000
Table 15 Results of the estimation of DCC GARCH (1.1) BRENT-MXN. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
θ1 θ2
0.049397 0.924226 0.0021061 0.019123 0.774944
Post-crisis
Probability
Coefficients
Probability
Coefficients
Probability
0.000 0.000 0.000
0.137261 0.852274 0.107516
0.0164 0.000 0.000
0.073980 0.909931 0.0388768
0.000 0.000 0.000
0.000 0.000
0.003919 0.835942
0.8794 0.2207
0.030847 0.678742
0.1818 0.000
Table 16 Results of the estimation of DCC GARCH (1.1) BRENT-NOK. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
0.020138 0.971481 0.0061
θ1 θ2
0.009122 0.799068
Probability 0.002 0.000 0.000 0.3757 0.0014
Coefficients 0.053695 0.950713 0.068805 0.034684 0.777056
Post-crisis Probability
Coefficients
Probability
0.0022 0.000 0.000
0.027196 0.970033 0.0396247
0.000 0.000 0.000
0.000 0.000
0.004150 0.851394
0.7836 0.044
from the first step (Tables 2–11). The results of exchange rates and estimations of oil prices in various countries during the three sub-periods are shown in the following tables: During the first period, we found that the estimated GARCH model's parameters are positive and are statistically significant, suggesting that the adoption of a GARCH to specify the variables is appropriate. However, remarkable differences can be found between the different pairs of the studied exchange rates and oil prices, in particular the contribution of ARCH and GARCH effects in short and long term persistence. Indeed, short-term persistence (α) remains low in most conditional variance equations. However, the sum of the two parameters (α þ β) is very close to unity. Hence, we conclude to the persistence of conditional variance in the studied series. The parameters θ1 et θ 2 of the DCC model are less than 1, therefore the conditions of the model are valid (Tables 12–19). For the DCC parameters of the pairs of exchange rates and oil prices, we found that they are different from one country to another and they are high for some countries’ returns and weak for others. We can, therefore, conclude that there is a strong positive and significant correlation between oil price and the following exchange ratesduring the crisis: USD/AUD-WTI, USD/
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Table 17 Adequacy test of the copula function. Pre-crisis
CAD- WTI GBP -WTI MXN -WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT Crisis
CAD-WTI GBP-WTI MXN-WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT Post-crisis
CAD- WTI GBP -WTI MXN-WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT
Frank
Normal
Clayton
Student
0.2173 0.1314 0.6049 0.1084 0.07143 0.2243 0.3172 0.03546 0.0004955 0.0004995 0.1533 0.06244 0.05155
0.3851 0.06843 0.3282 0.05844 0.02348 0.1573 0.4241 0.05045 0.0004955 0.0004995 0.2532 0.0974 0.0004955
– 0.03347 0.03546 0.05544 0.03546 0.05145 0.6588 0.1484 0.04641 0.008492 0.3292 0.1883 0.0004955
0.004496 0.001499 0.03147 0.008492 0.0004995 0.0168 0.00112 0.0004995 0.0004995 0.0056 0.0984 0.001499 0.0004955
Frank
Normal
Clayton
Gumbel
Student
0.001499 0.005495 0.000499 0.000499 0.001499 0.005495 0.0004995 0.0004995 0.004496 0.009491 0.0004995 0.004496 0.0004995
0.004496 0.008492 0.0005 0.00049 0.003497 0.006494 0.001499 0.0004995 0.01648 0.007493 0.0004995 0.003497 0.0004995
0.03347 0.1164 0.000512 0.03746 0.03946 0.06743 0.03846 0.01049 0.06344 0.04446 0.004496 0.04346 0.004996
– – – – – – 0.007493 0.0004995 0.01349 0.01349 0.0004995 0.01948 0.0004995
0.02346 0.07742 0.0004 0.2323 0.01449 0.01249 0.0004995 0.0004995 0.004496 0.009491 0.0004995 0.004496 0.0004995
Frank
Normal
Clayton
Student
0.0004995 0.000499 0.000499 0.0004995 0.0004995 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955
0.0014 0.000496 0.000499 0.000499 0.0004995 0.000495 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955
0.001499 0.000498 0.0049 0.003497 0.000512 0.003497 0.001499 0.000678 0.001475 0.003997 0.0005177 0.004747 0.0005599
0.0004995 0.000499 0.0004995 0.00049 0.000499 0.000499 0.0004995 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955
GBP-WTI, USD/MXN-WTI, USD/CAD-WTI, USD/NOK-WTI. Furthermore, the resulting claim is that correlation between BRENT and all the exchange rates is positive. This results in an increase in oil prices influenced by the exchange of the US dollar against other currencies; while correlation between WTI-JPY and WTI-EUR is negative, an increase of oil prices correlates with an increase the US dollar. Using dynamic correlation modeling, Ibrahim Turhan et al. (2014) studied comovements of oil prices and exchange rates of the G20 between 2000 and 2013. They found that the relationship between oil prices and exchange rates has increased in the last decade. The two are strongly and negatively correlated (which also combines oil prices increase with the depreciation of the US dollar against other currencies). During the subprime crisis, we notice an increase in dynamic conditional correlation which indicates a highly increasing interdependence between exchange rates and oil prices of the studied countries. Obviously, we notice that the estimated conditional correlations are relatively strong and can be interpreted as high intensity measures of the relationship between exchange rates and oil prices of the studied countries. Moreover, whatever returns considered, trends of strong and weak correlations appear. This reflects, undoubtedly, a persistence phenomenon. Furthermore, it appears that these correlations have increased in recent years, following the subprime crisis and is becoming higher. This reflects a growing interdependence between these markets. We also notice that correlation between
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Table 18 Kendall's Rate.
WTI-AUD WTI-/CAD WTI-EUR WTI-GBP WTI-JPY WTI-MXN BRENT-AUD BRENT-CAD BRENT-EUR BRENT-GBP BRENT-JPY BRENT-MXN BRENT-NOK
Pre-crisis
Crisis
Post-crisis
0.00194 0.00346 0.00384 0.01273 0.02806 0.00252 0.011501 0.017514 0.000531 0.001992 0.008187 0.006361 0.002432
0.04604 0.00715 0.01337 0.03378 0.01249 0.00392 0.01666 0.026366 3.18E-05 0.001807 0.010975 0.00929 0.002975
0.01218 0.01165 0.01094 0.00417 0.02206 0.004642 0.04408 0.036402 0.046768 0.073874 0.052746 0.046622 0.04994
Pre-crisis
Crisis
Post-crisis
0.003199 0.005133 0.005920 0.019031 0.041551 0.003486 0.065616 0.052186 0.069311 0.10913 0.088852 0.065256 0.076307
0.067179 0.009803 0.020665 0.049182 0.018727 0.007380 0.01713 0.017129 0.01427 0.019383 0.01219 0.021582 0.017831
0.018117 0.017297 0.016079 0.005758 0.032924 0.006450 0.02529 0.02113 0.022186 0.027943 0.016375 0.032012 0.027287
Table 19 Spearman Rho.
WTI-AUD WTI-CAD WTI-EUR WTI-GBP WTI-JPY WTI-MXN BRENT-AUD BRENT-CAD BRENT-EUR BRENT-GBP BRENT-JPY BRENT-MXN BRENT-NOK
oil prices and exchange rates is positive between the following pairs: WTI-AUD, WTI-CAD, WTI-NOK, WTI-MXN, BRENTAUD, BRENT-CAD, BRENT-EUR, BRENT-GBP, BRENT-JPY, BRENT-NOK and BRENT-MXN. This correlation pattern became stronger during the subprime crisis. Thus, increase of oil prices coincides with an appreciation of the dollar. For other exchange rates pairs, correlation is negative; this leads to an increase in oil prices which leads to a depreciation of the dollar. 4.3. Selecting the most suitable copula Our results clearly indicate that every period has a different kind of copula. During the pre-crisis period, we found Frank and Normal type copula, which are symmetrical copula. Meanwhile, during the crisis and post crisis periods, we found Clayton and Student-type copula, which are asymmetrical copula. Therefore, after the Subprime crisis, the exchange rate market moved up to asymmetry. For the relationship between BRENT and exchange rates, we found that the Clayton copula is most appropriate for the three study periods. 4.4. Estimates and results of the parameters of the copula function
Pre-crisis
θ
CAD- WTI GBP -WTI MXN-WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT
0.129 0.25 0.35 0.252 0.678 0.252 0.041 0.008 0.008
Crisis
Post-crisis
θ
θ
0.069 0.116 0.038 0.042 0.03 0.041 0.129 0.208 0.105
0.054 0.054 0.074 0.049 0.041 0.091 0.061 0.077 0.087
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NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT
0.003 0.043 0.012 0.201
0.104 0.112 0.131 0.014
0.087 0.065 0.085 0.078
The Clayton copula was selected to explore the nature of dependence between oil prices and exchange rates. There is a positive dependence between oil prices and exchange rates (Figs. 1–3). We notice that the dependence parameters increased during the crisis period for the Clayton copula between oil prices AUD
3
1.5
2
1.0
1
0.5
0
0.0
-1
-0.5
-2
-1.0
-3
-1.5
-4
CAD
2.0
-2.0 00
01
02
03
04
05
06
07
08
09
10
11
13 14
12
00
EUR
2.0
01
02
03
04
05
06
1.5
1.5
07
08
09
10
11
12
13
14
GBP
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5 -2.0
-2.0 00
01
02
03
04
05
06
07
08
09
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11
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13 14
00
01
02
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04
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JPY
1.5
08
09
10
11
12
13 14
08
09
10
11
12
13
08
09
10
11
12
13
MXN
2
1.0
07
1
0.5
0
0.0 -0.5
-1
-1.0 -2
-1.5
-3
-2.0 00
01
02
03
04
05
06
07
08
09
10
11
12
13 14
NOK
2
00
01
02
03
04
05
06
07
14
WTI
8 6
1
4 2
0
0
-1
-2 -4
-2
-6 -8
-3 00
01
02
03
04
05
06
07
08
09
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11
12
00
13 14
01
02
03
04
05
06
07
BRENT 6 4 2 0 -2 -4 -6 -8 -10 00
01
02
03
04
05
06
07
08
09
10
Fig. 1. The daily production of crude oil and exchange rates.
11
12
13
14
14
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Fig. 2. Graphic of DCC-MGARCH model.
and other currencies. The Clayton copula is more suitable to capture lower tail dependence. This means that exchange rates and oil prices increasingly depended on each other at the onset of the subprime crisis. We can, therefore, conclude that an increase in oil prices coincides with a depreciation of the dollar. Similarly, Riadh Aloui et al. (2013) found that an increase in oil prices coincides with a depreciation of the dollar. Juan C Ledge (2013) found a negative dependence between oil prices and exchange rates during the crisis and the impact is empirically tested. Our results are not consistent with previous studies that used data prior to the period of the recent global financial crisis (for example, Amano & van Norden, 1998; Chen
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Fig. 2. (continued)
& Chen, 2007). The negative relationship between oil prices and the dollar’s exchange rate may be explained by the fact that oil is a hedging mechanism against inflation and an increasing security against risk. For example, when the dollar declines, countries whose currencies have declined look for the cheapest oil price to purchase and increase their demand for oil, which, in return, leads to an increase in oil prices. Conversely, oil producers might want to increase oil pricesas their purchasing power decreases. Having estimated the parameters of copulas and dependence between oil prices and exchange rates, we will adopt
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Fig. 2. (continued)
Kendall’s rate and Spearman rho to measure impact. When these two coefficients increase, we conclude to the presence of impact. In the following, we present the results of these coefficients before and after the subprime crisis.
4.5. Results of correlation coefficients Kendall’s rate, τ, measures the strength of association between two random variables X and Y. it is a real number with a value ranging between [ 1, 1]. Kendall’s rates increased during the crisis period except those between WTI-JPY, WTI-MXN, WTI-NOK, BRENT-EUR, BRENT-GBP and BRENT-NOK. During the post-crisis period, there is a decrease in Kendall’s rate compared to the crisis period with the exception of the Kendalls rate between WTI-NOK, WTI-MXN and BRENT-JPY which registered an increase in Kendall’s rate. During the precrisis period, there is an increase in Kendall’s rates between WTI-CAD, WTI-EUR, WTI-JPY, WTI-NOK and BRENT-NOK. There is, therefore, dependence between oil prices and exchange rates. This relationship has increased during the crisis for some exchange rates like AUD, GBP, EUR and CAD. This increase confirms the existence of an impact between oil prices and exchange rates. Similarly, in the post-crisis period, the impact is there. Spearman Rho increased during the crisis period except for WTI-JPY, MXN-WTI, WTI-NOK, BRENT-AUD, BRENT-CAD, BRENT-EUR, BRENT-GBP, BRENT-JPY, BRENT-MXN and BRENT-NOK, thus an impact is there during this period. Whereas, during the post-crisis period, the rate decreased,compared to the period of calm, for all exchange rates except for WTI-AUD, WTI-GBP and WTI-MXN. Consequently, impact of exchange rate is valid.
5. Conclusion This article examines the impact between daily oil prices and exchange rates in September using a copula approach and the dynamic conditional correlation approach DCC-MGARCH. First, we used a standard GARCH (1.1) to model the different error distribution margins. The adoption of this filtering method is motivated by the stylized facts of our data including serial dependence and volatility clustering. First, we found that causal relationships and the different exchange rates increased after the crisis period. We, also, noticed that the exchange rate used in our sample influences the exchange rate after the crisis. Overall, our results show that the Clayton copula is the best model with a conditional dependency structure to estimate the relationship between oil markets and exchange rates. They also indicate significant and asymmetric tail dependence for all couples. In addition, an increase in oil price coincides with a weaker dollar. From a forecasting perspective, our portfolio simulations illustrate the idea that taking into account extreme coevolution improves forecast accuracy of market risk. In addition, the DCC-MGARCH model shows that the dynamic conditional correlation between copulas increases during times of crisis. Finally, our results conclude to the existence of an impact between oil prices and exchange rates during the crisis. Consistent with previous studies on co-evolution of financial markets, we notice an increase in extreme dependence of several pairs of foreign exchange markets and oil prices during the crisis.
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Fig. 3. Graphic of different couples.
Recommendation Volatility of oil prices has a negative impact on the economy, as demonstrated in the literature. A shock related to oil prices, as an example of a classic negative offer shock, increases the overall volume of offer, and leads to higher prices and lower production and employment (Dornbusch, Fisher, & Startz, 2001). However, the overall volume of demand declines, as
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appreciation of commodity prices results in a decrease in demand for goods and services. This results in a contraction of global production and employment. The macroeconomic consequences of oil shocks are transmitted through supply and demand and are potentially minimized by the reactions of economic policy. In general, the impact of world oil prices on macroeconomic variables has been studied by researchers for academic purposes and for the resolution of important strategic issues. The issue was the focus of an abundant research, because shocks to oil prices in the early 70s have evolved both in time and in space (affecting both developing and industrial countries). Taking into account the recent increases in world oil prices and the prospect of persistence of this trend in the short-term, or even beyond, and the constraints on supply, the impact of shocks to oil prices is clear on key macroeconomic variables. Research-wise, this remains a relevant topicto explore. Economic policies wise, high oil prices directly affect companies (companies), households (consumers) and the state. First, they trade oil products domestically, as well as many intermediate inputs at increased production costs. Thus, companies can reduce their labor demands and investment, which, inevitably, results in a depreciation of production. Second, short-term oil demand is inelastic to a large extent; consumers have to reduce their consumption of other goods and services (the substitution effect) to pay higher energy bills. Third, net oil importing countries face difficulties of balance of payments, as they have to mobilize additional resources to pay for higher oil import bills. The state also faces more serious budget problems, which can affect its ability to fund social programs aimed at reducing poverty.
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The Journal of Economic Asymmetries journal homepage: www.elsevier.com/locate/jeca
A study of the interactive relationship between oil price and exchange rate: A copula approach and a DCC-MGARCH model Angham ben brayek b, Saber Sebai a, Kamel Naoui b,n a b
Department of Finance and Accounting, High Institute of Accounting and Administration, University of Manouba, Manouba, Tunisia Tunis School of Business, Tunisia
a r t i c l e i n f o
abstract
Article history: Received 20 April 2015 Received in revised form 11 September 2015 Accepted 14 September 2015
This paper examines the relationship between oil prices and the US dollar exchange rate using a copula approach and the DCC-MGARCH model. In order to identify a possible impact and interdependence between oil prices and exchange rates during the global financial crisis, we divided the study period into sub-periods, pre-crisis, crisis and postcrisis periods. We found that oil prices and exchange rates are independent during the pre-crisis period. However, evidence of this impact and a positive dependence between our variables were reported after the crisis onset. In addition, we found that oil prices influenced exchange rates and vice versa during the crisis period, but not during the precrisis period. These results have important implications on risk management and monetary policy to control inflationary pressures from oil prices and fiscal policy in oilexporting countries. & 2015 Published by Elsevier B.V.
JEL Classification: E44 C22 keywords Copulas DCC-MGARCH Dependence measures Crude oil price U.S. dollar exchange rates
1. Introduction Crude oil is one of the most important commodities of the global economy. Previous studies pointed out that changing oil prices affect stock markets activity. Firstly, oil prices have been significantly fluctuating over the last three decades and have become more volatile than they were during the Second World War period and the early 1970s. Increased volatility in oil prices was noticed after the international oil crises of 1973 and 1979. This trend was reinforced by the collapse of oil prices during the 1980s. More importantly, over the past five years, oil prices have sharply increased from $ 42 per barrel in early 2005 to reach $ 147 the barrel in July 2008. Plourde and Watkins (1998) and Regnier (2007) found that oil price volatility is significantly higher than that of other energy products since the mid-1980s. Moreover, unrest in Libya and the ongoing threats to political instability in other Middle Eastern and North African countries contributed in increasing oil prices, which may slow down global economic growth. Secondly, some studies found evidence of an inefficient behavior of international oil markets, which made forecasting oil prices volatility and covering oil risk more complicated (Green & Mork, 1991; Shambora & Rossiter, 2007; Arouri, Dinh, & Nguyen 2010). Finally, oil prices are priced in US dollars, and their fluctuations highly depend on the dollar’s exchange rate, which has experienced frequent and uncertain changes in recent years. In this regard, several observers argue that appreciating oil prices results from the dollar’s recession. Indeed, in order to hedge n
Corresponding author. E-mail addresses: [email protected] (A.b. brayek), [email protected] (S. Sebai), [email protected] (K. Naoui).
http://dx.doi.org/10.1016/j.jeca.2015.09.002 1703-4949/& 2015 Published by Elsevier B.V.
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against the falling dollar, investors are moving towards investments in oil, raw materials and oil exportation to convert their incomes into other currencies. However, it is also conceivable that increase in oil prices and the dollar’s recession do not directly depend on each other, but both are the result of a common factor which is the withdrawal of investors from the complex asset markets in the United States. This can change the correlation pattern between the dollar and oil prices because of the dollar’s transaction requirements or the cyclical effects, which could not, in any case, be assumed on the idea of a stable correlation pattern.
2. The literature review Modeling and forecasting co-movement between oil prices and the dollar’s exchange rate are crucial, not only for market operations and risk management issues, but also for the proper regulation of foreign exchange markets for all the economies that operate with floating exchange rate regimes. Krugman (1983), Golub (1983) and Rogoff (1991) pointed to the potential importance of oil prices as a predictor of exchange rate movements. Empirical work on the interactions between oil prices and exchange rates are, however, much less extensive than those on the effects of oil prices on economic activities. Following the global financial crisis, most studies mainly found a positive relationship between oil prices and US dollar-based exchange rates. This meant that an increase in oil prices is influenced by a strong dollar as indicated by Dibooglu (1996), Amano and van Norden (1998), Bénassy-Quéré, Mignon, and Penot (2007), Chen and Chen (2007), Basher, Haug, and Sadorsky (2012). Amano and van Norden (1998) found, using an error correction model (ECM), a stable relationship between oil price and the US dollar’s exchange rate over the period 1972–1993. In addition, they found a one-way causality relationship between oil prices and exchange rates. This suggests that an oil price shock can heavily influence exchange rate fluctuations during the study period. Bénassy-Quéré et al. (2007) studied causality between oil and the dollar’s real effective exchange rate over a longer period. They found that a 10% increase in oil prices coincides with an appreciation of the dollar by 4.3% in the Long term. However, some studies claimed no such causality between the US exchange rate and appreciation of oil prices (Narayan, Narayan, & Prasad, 2008; Zhang, Fan, Tsai, & Wei 2008; Akram, 2009; Wu, Chung, & Chang, 2012). We summarize, in the following table, the main relevant literature on the topic, as a matter of providing a comparative perspective for readers. Authors
Object
Study period
Monthly data between February 1972 and January 1993 Bénassy-Quéré Monthly data beet al. (2007) tween 1974 and 2005 Monthlydata beChen and Chen This paper examines the long-term re(2007) lationship between oil prices and real ex- tween 1972 and 2005 change rates. Daily date beBasher et al. (2012) The authors study the dynamic relationship between oil prices and exchange rates tween 1988 and 2008 of market share during their emergence. Amano and van Norden (1998)
The authors put an emphasis on the relative importance of real shocks over monetary policy to explain exchange rate movements They study cointegration and causality between oil prices and exchange rates
Narayan et al. (2008)
The authors examine the relationship between oil prices and exchange rates
Zhang et al. (2008) The authors test the interaction between change in oil prices and the US exchange rate Akram (2009)
Wu et al. (2012)
Reboredo (2011)
The author seeks to determine whether depreciation contributes to the appreciation of commodity prices The authors examine the economic value of co-evolution between oil prices and the dollar This paper examines the dependence structure or co-movements between oil prices and exchange rates This paper examines the dependence structure between oil prices and exchange rates The relationship between oil prices and stock market indices of different countries
Riadh Aloui, Ben Aïssa, and Duc Khuong (2013) Kunlapath Sukcharoen et al. (2014) Reboredo and Riv- This paper examines the relationship beera-Castro tween oil prices and exchange rates
Daily data between 2000 and 2006 Daily data between 2000 and 2005 Quarterly data between 1990 to 2007 Weekly data between 1990 to 2009 Daily data between 2000 to 2010 Daily data between 2000 to 2011 Daily data between 1982–2007 Daily data between 2000 and
Methodology Main results Causality test, Using a GRANGER test: oil prices influence the cointegration US real effective exchange rate, not the opposite. It is also the main source of persistent exand ECM change rate shocks Causality test, A 10% increase in oil prices coincides with an cointegration appreciation of 4.3% in the long term and ECM Panel and Oil prices are the main cause of foreign excointegration change rate movement; they are also robust to different measures of oil prices. VAR The positive impact on oil prices tend to reduce prices of new shares on the market and the dollar-weighted indices in short-term transactions. GARCH and An appreciation of oil prices led to an appreEGARCH ciation of the dollar Cointegration test, VAR, ARCH and VaR VAR
Copula GARCH Copula comouvement Copula GARCH Copula GARCH VAR
The US dollar’s recession has been a key factor in appreciating crude oil prices
A depreciation of the US dollar led to raising basic product prices including crude oil prices The dependence structure between oil prices and exchange rates becomes negative and decreased continuously since 2003 Dependence of oil prices on exchange rates is generally low although it has significantly increased because of the crisis. Increase in oil prices coincides with an appreciation of the dollar The results indicate a weak dependence between oil prices and stock indices for most cases There is a negative dependence between oil prices and exchange rates during the crisis and
A.b. brayek et al. / The Journal of Economic Asymmetries 12 (2015) 173–189 (2013) Filis, Degiannakis, This paper examines the relationship beand Floros, 2011 tween oil prices and stock market indices Ibrahim Turhan, Ahmet Sensoy, and Erk Hacihasanoglu (2014)
This study examines oil price co-movements with exchange rates.
2011 Data between 1987–2009
DCC-GARCHGJR
Daily data beDCC tween 2003–2008
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the impact is empirically valid. During economic crises, the oil market is not a “safe haven” that offers protection against market losses. The study reveals that the link between oil prices and exchange rate has increased over the last decade; they are strongly and negatively correlated (which also combines with an increase in oil prices with the US dollar’s recession compared to other currencies).
In summary, oil price increase assumes a decline/recession or the appreciation of the US dollar. This may be a result of dependence between the different countries as far as oil prices are concerned. For example, Lizardo and Mollick (2010), using co-integration tests, show that appreciation of oil prices led to a sharp depreciation of the US dollar against the currencies of oil exporters such as Canada, Mexico and Russia. Instead, the dollar value increased against currencies of net oil-importing countries, like Japan, when real oil prices increased. Countries which are neither oil exporters nor importers, such as the UK and the European Union, face a depreciation of the dollar.
3. Methodology Our purpose is to examine the relationship between oil and currency markets through studying current market trading activities. The data includes crude oil prices and nominal exchange rates expressed in US dollar (USD) over the period between January 3, 2000 and 17 April 2014. Exchange rate is an amount of USD for each unit of the seven major currencies of international trade: The Euro (EUR), the Australian Dollar (AUD), the Canadian dollar (CAD), the Mexican Peso (MXN), the Norwegian kroner (NOK), the British pound (GBP), and the Japanese Yen (JPY). An increase in nominal exchange rates may reflect a recession of the US dollar against foreign currencies. Data frequency is daily. As our focus is oil prices, and for comparison purposes, we use the most important criterion of the West Texas Intermediate (WTI) at Cushing. The Brent index serves as a pricing benchmark for two thirds of the world’s internationally traded crude oil supplies. For the purpose of the study, we express rates by their logarithm; the first rate (innovation) is designated as return on assets:
⎛ Pi, t ⎞ Ri, t = 100* log ⎜ ⎟; ⎝ Pi, t − 1 ⎠
i = 1, 2, .. 17
(A.1)
with Ri, t = daily productivity with security i to T Pi, t = Price of security i at time t. Using the Breakpoint test, our sample will be divided into three sub-periods, a pre-crisis period which spreads from 1.03.00 to 12.31.06, a crisis period stretching from 1.01.07 to 12.31.08 and at a post crisis period, from 1.01.09 until 7.14.14. In the following, we try to combine some analytical tools that have been recently introduced in applied finance. The first is developed by Nelson (1991) as an original specification of conditional correlations between several endogenous variables or markets (models called “multivariate”). These models allow for tracing the evolution of correlations between two or more actives. The second tool is copula functions that make it possible to implement more consistent distribution laws and stylized facts observed in financial markets than the tools currently used. Finally, there is the Dynamic Conditional Correlation (DCC) model which allows the correlation matrix to be dynamic over time while retaining few parameters. 3.1. The ARCH/GARCH models These models measure the transmission of crises as volatility spreads. They calculate variance/covariance matrices between securities markets. According to Engle (1982) with his ARCH process generalized by Engle (1982), GARCH models have proved their ability to capture the specific properties of financial time series: volatility clustering and fatter tails. For simplicity reasons, GARCH (1.1) of Bollesrslev is a customized response. It functions similar to an infinite order ARCH model. Indeed, it integrates all information with fewer parameters. Application of this model on financial variables is of a particular interest since it allows studying both the relationship between returns and varying volatilities. In general, a GARCH (p, q) is defined by the following equations:
yt = f ( yt − 1 , … yt − k /Ωt − 1) + ut σt2 = c +
p
∑i
αi Ut2− i +
(A.2)
q
∑ j βj σt2− j
ut /Ωt − 1 → D (0, σt2 )
(A.3)
where yt is the asset market performance, ut is errors (remnants or innovations), D( ) is conditional distribution of innovations, Ωt − 1 is an information set at time (t 1), and σt2 is conditional variance of returns and innovations. We consider a Gaussian error distribution in which the parameters of medium conditional and variant conditional
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equations are estimated by a maximum likelihood estimator “EMV”. As for GARCH (1.1), the β coefficient is usually high (very close to 1) for high frequency data series and the sum indicates persistence of shocks. The introduction of this model was to model volatility of time series and its transmission from one series to another. Thus, the impact can be defined as the spread of price volatility of financial market assets of countries in crisis to other financial markets of other countries. This occurs during periods of financial turmoil as Pericoli and Sbracia (2001) showed. Therefore, the model calculates the variance/covariance matrices between securities markets. The traditional GARCH model assumes a normal distribution of innovations. However, it is well known that many financial time series are non-normal and tend to have fat tails (Mandelbrot, 1963; Fama, 1965). To better understand the characteristic of fat tails, Bollerslev (1987) proposes the use of conditional Student-t distribution. Nelson (1991) and Theodossiou (2000) propose respectively the use of the generalized error distribution and asymmetric generalized error distribution. In this study, we consider various distributions for the error term ε_t, including the normal distribution and the Student-t distribution. 3.2. The DCC-MGARCH model DCC models allow the correlation matrix to be dynamic over time while retaining few parameters. We can then model both variances and conditional correlations of several series. This model, proposed by Engle (2002) and Tse and Tsui (2002), is written as follows:
⎧ Ht = Dt RDt ⎪ ⎪ ⎨ Dt = diag ( h11t , ⎪ −1 −1 ⎪ ⎩ Rt = (diagQ t ) 2 Q t (diagQ t ) 2
h22t , …,
hNNt ) (A.4)
or Q t represents the covariance matrix of the standardized residuals, the dimension (N N), the symmetric and positive definite. 3.3. Copula functions The relationship between foreign exchange crises and financial crises have motivated several authors to use different approaches they consider useful in order to define and study the concept of impact. Despite extensive studies, the relationship remains unclear and depends on the approach and assumptions used. A copula is a multivariate uniform distribution. It is a, relatively, old static tool introduced by Sklar (1959) and revived by Genest and Mackay (1986). For simplicity and because multivariate theory is an extension of the bivariate approach, we will place a particular focus on the theory of bivariate couples. Thus, a bivariate copula function C [0, 1]2- [1,0] is defined by the following:
C (u, 0) = C (0, u) = etC (u, 1) = C (1, 0) = u; ∀ u€ [0, 1] C (v1, v2 )–C (v1, u2 )–C (u1, v2 ) + (u1, u2 ) ≥ 0
(A.5) (A.6)
(u1, u2 ) € [0, 1]2 , (v1, v2 ) € [0, 1]2 telque0 ≤ u1 ≤ v1 ≤ 1et 0 ≤ u2 ≤ v2 ≤ 1 The property (i), in particular, reflects that any copula is a distribution whose marginal distributions are a uniform law set to I ¼[0, 1]. Property (ii) is 2-growth and inequality in the distribution of the rectangle C. It reflects the fact that if C admits a density c (uv), then it is positive. When U_1 and U_2, two uniform random variables on [0, 1], then we have:
C (u1, u2 ) = P (U1 ≤ u1, U2 ≤ u2 )v (u1, u2 ) ∈ [0, 1]2 This definition ensures that the copula is a probability distribution with uniform margins. “(Clauss, 2011, copula theory, p. 5).
4. Results In the charts below, we notice that daily returns are relatively stable during the period preceding the start of the global financial crisis (January 2000 to the third quarter of 2008), triggered by the massive failures during the US subprime crisis and the banking sector. 4.1. Descriptive statistics “kurtosis” and “Skweness” coefficients tell us about the nature of the distributions of the series and they essentially test
Mean Median Maximum Minimum Std. dev. Skewness Kurtosis Jarque–Bera Q (12)
Q2 (12) ARCH (12)
WTI
AUD
CAD
EUR
JPY
MXN
NOK
GBP
BRENT
0.005709 0.000000 7.128381 7.42286 1.013235 0.34483 8.673799 5074.372 31.993*** 952.79**
0.004140 0.017631 2.292070 3.04172 0.327011 0.50760 10.83499 9695.549 69.083*** 2731.3***
0.003194 0.006943 1.812280 1.66527 0.219830 0.14478 7.417425 3044.145 71.693*** 1540.3***
0.003708 0.009602 1.504412 1.62122 0.261090 0.15505 5.578902 1048.019 31.729** 337.74***
1.34E 12 0.000000 1.258913 1.67056 0.308407 0.13044 4.515115 367.151 43.328*** 76.270***
0.003689 0.000000 1.677857 2.642911 0.263464 0.883734 13.39761 17278.38 24.425*** 3474.4***
0.003433 0.000000 1.803261 2.229164 0.300419 0.352510 6.047368 1519.700 108.49*** 1289***
0.00042 0.00250 1.35882 1.73348 0.22774 0.30200 6.87133 2384.685 59.23*** 583.4***
0.014094 0.000000 5.582162 8.63839 0.946085 0.42595 8.584428 4958.263 15.645* 449.09***
203.11***
237.13***
133.58***
48.925***
17.771***
611.00***
130.14***
42.60***
37.28763***
2
Notes: The table displays summary statistics of daily returns over the period from January 3, 2000 to April 17, 2014.Q(12)and Q (12) are the Ljung–Box statistics for serial correlation of order 12 in returns and squared returns. ARCH is the Lagrange Multiplier test for autoregressive conditional heteroscedasticity. ** and *** indicate the rejection of the null hypothesis of no autocorrelation, normality and homoscedasticity at the 5% and 1% levels of significance respectively.We then establish the causal test between oil prices and different exchange rates to determine the causality direction in the three study periods.
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Table 1 Descriptive statistics.
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the normality assumption. In our study, the null hypothesis of normality for the daily returns of exchange rates is rejected. We notice first that the kurtosis coefficient is very high, well above 3. This phenomenon of excess kurtosis confirms the strong leptokurtic character of stock returns series (Table 1). The Ljung–Box Q-statistics of order 12 show the existence of autocorrelation in allthe returns series. The Ljung–Box statistics of order 12 applied to squared returns are highly significant. The results of the Lagrange Multiplier tests point to the presenceof ARCH effects in the return data, thus supporting our decision to use the GARCH-based approach. The usefulness of this test is to investigate the causal relationship between oil prices and exchange rates. This test is important because it provides information on the causality direction of these variables. There are basically three possibilities for this test. It could be unidirectional, bidirectional, or neutral. During the pre-crisis period, we see that oil prices influence the AUD exchange rate, the CAD exchange rate and the NOK exchange rate. As for the BRENT price, the results indicate that it influences all exchange rates except JPY. In times of crisis, we found a one-way causal relationship between oil prices and the AUD exchange rate and oil prices affect all exchange rates. After the crisis, we found that oil prices affect all exchange rates. 4.2. DCC-MGARCH model results We use the DCC model developed by Engle (2002) to explore the evolution of conditional correlations between exchange rates and oil prices during the subprime crisis. The importance of this analysis is the use of multivariate GARCH. The assumption of changes in correlations are relatively neglected in empirical studies because of the difficulties in taking then in to consideration. The estimation of these correlations takes therefore into account all the information available at a given time. Indeed, these correlations, like conditional variances, are explained by three main factors including their own past trends; a factor representing the effect of recent shocks and the constant. In addition, this new class of multivariate GARCH models is distinguished by its estimation simplicity. Indeed, the latter being carried out in two stages: the first estimates various GARCH and is applied for each series separately. The second step estimates the dynamic correlations emanating Table 2 Granger causality VAR. Pre-crisis Excluded
Chi-sq
Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent BRENT Dependent BRENT
variable: AUD 9.92852 variable: CAD 22.9762 variable: EUR 0.61297 variable: GBP 0.77535 variable: JPY 3.30106 variable: MXN 1.60319 variable: NOK 9.98357 variable: AUD 36.7150 variable: CAD 34.7571
Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT
variable: EUR 8.82973 variable: JPY 0.122930 variable: GBP 21.5991 variable: MXN 13.0381 variable: NOK 25.6856
df
Prob.
2
0.007
2
0.000
2
0.736
2
0.678
2
0.191
2
0.448
2
0.006
2
0.000
2
0.000
2
0.012
2
0.9404
2
0.000
2
0.001
2
0.000
Crisis Excluded Dependent AUD Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent AUD MXN GBP Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT
Chi-sq variable: WTI 7.63399 variable: AUD 49.6326 variable: CAD 53.7650 variable: EUR 62.8830 variable: GBP 50.8851 variable: JPY 12.2594 variable: MXN 28.8993 variable: NOK 134.871 variable: BRENT 4.82100 8.164152 5.69959 variable: AUD 69.91902 variable: CAD 66.3572 variable: EUR 58.5706 variable: GBP 51.5171 variable: JPY 5.68763 variable: MXN 36.6241 variable: NOK 107.964
df
Prob.
2
0.022
2
0.000
2
0.000
2
0.000
2
0.000
2
0.002
2
0.000
2
0.0000
2 2 2
0.089 0.0169 0.057
2
0.000
2
0.000
2
0.000
2
0.000
2
0.058
2
0.000
2
0.000
Post-crisis Excluded
Chi-sq
Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent WTI Dependent BRENT Dependent BRENT
variable: AUD 230.394 variable: CAD 256.377 variable: EUR 116.963 variable: GBP 85.460 variable: JPY 19.6758 variable: MXN 150.294 variable: NOK 183.019 variable: AUD 231.186 variable: CAD 266.974
Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT Dependent BRENT
variable: EUR 78.5796 variable: GBP 100.4783 variable: JPY 16.6262 variable: MXN 130.249 variable: NOK 167.749
df
2
Prob. 0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.000
2
0.0000
2
0.0000
2
0.000
2
0.000
2
0.000
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Table 3 Results of the estimation of DCC GARCH (1.1) WTI-AUD. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
θ1 θ2
0.032123 0.966814 0.00659042 0.005241 0.814927
Probability 0.000 0.0000 0.000 0.6729 0.0142
Coefficients 0.14597 0.872655 0.00708086 0.0252 0.986357
Post-crisis Probability 0.0061 0.000 0.209 0.0197 0.000
Coefficients 0.054160 0.939411 0.00365332 0.009767 0.977292
Probability 0.000 0.000 0.1569 0.1569 0.000
Table 4 Results of the estimation of DCC GARCH (1.1) WTI-CAD. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.032515 0.962471 0.0044183
0.0000 0.000 0.000
θ1 θ2
0.23289 0.771341
0.000 0.000
Coefficients 0.092727 0.930854 0.02766624 0.020398 0.881801
Post-crisis Probability
Coefficients
Probability
0.0168 0.000 0.000
0.039189 0.959917 0.0027486
0.000 0.000 0.0000
0.2573 0.0063
0.012927 0.431968
0.3454 0.4061
Table 5 Results of the estimation of DCC GARCH (1.1) WTI-JPY. Pre-crisis
Crisis
Post-crisis
Coefficients
Probability
Coefficients
Probability
Coefficients
Probability
α1 β1 ρi, j
0.045787 0.317090 0.0127002
0.0711 0.4766 0.0000
0.050396 0.919099 0.0953766
0.0466 0.000 0.000
0.015754 0.976744 0.0030249
0.0633 0.000 0.000
θ1 θ2
0.010683 0.990141
0.0142 0.000
0.01507 0.884111
0.1359 0.000
0.016626 0.452958
0.2455 0.3020
Table 6 Results of the estimation of DCC GARCH (1.1) WTI-EUR. Pre-crisis
Crisis
Post-crisis
Coefficients
Probability
Coefficients
Probability
Coefficients
Probability
α1 β1 ρi, j
0.009066 0.788279 0.0145882
0.5474 0.000 0.000
0.069699 0.959829 0.0096113
0.0153 0.000 0.000
0.021787 0.980241 0.02858389
0.0001 0.000 0.000
θ1 θ2
0.038254 0.488803
0.1466 0.068
0.036964 0.872033
0.000 0.000
0.022865 0.746676
0.2587 0.000
Table 7 Results of the estimation of DCC GARCH (1.1) WTI-MXN. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.049397 0.924226 0.00844543
0.0001 0.000 0.000
θ1 θ2
0.008577 0.4852
0.7648 0.7195
Coefficients 0.185784 0.826813 0.03670046 0.029399 0.950092
Post-crisis Probability
Coefficients
Probability
0.0024 0.000 0.000
0.073980 0.909931 0.0115109
0.000 0.000 0.000
0.000 0.000
0.007595 0.375794
0.7498 0.9168
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Table 8 Results of the estimation of DCC GARCH (1.1) WTI-GBP. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.027555 0.961442 0.01809597
0.0006 0.000 0.1788
θ1 θ2
0.034547 0.282410
0.1788 0.4570
Coefficients 0.066893 0.935962 0.0046623 0.003033 0.995269
Post-crisis Probability
Coefficients
Probability
0.0032 0.000 0.209
0.025338 0.971507 0.0079668
0.0001 0.000 0.000
0.000 0.290
0.006888 0.948094
0.4064 0.000
Table 9 Results of the estimation of DCC GARCH (1.1) WTI-NOK. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.020138 0.971481 0.01426964
0.0024 0.000 0.000
θ1 θ2
0.025396 0.460274
0.3214 0.3044
Coefficients 0.077451 0.931229 0.02467348 0.033181 0.809568
Post-crisis Probability 0.0055 0.000 0.000 0.000 0.000
Coefficients 0.027196 0.970033 0.01248263 0.01918 0.074126
Probability 0.000 0.000 0.2864 0.2864 0.9287
Table 10 Results of the estimation of DCC GARCH (1.1) BRENT-AUD. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
0.032123 0.966814 0.02889
θ1 θ2
0.016846 0.803126
Probability 0.000 0.0000 0.000 0.000 0.000
Coefficients 0.111554 0.855336 0.07072461 0.020793 0.777765
Post-crisis Probability
Coefficients
Probability
0.000 0.000 0.000
0.059059 0.934364 0.0295549
0.000 0.000 0.000
0.000 0.000
0.00627 0.610457
0.7701 0.5471
Table 11 Results of the estimation of DCC GARCH (1.1) BRENT-CAD. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.032430 0.962820 0.04230
0.000 0.000 0.000
θ1 θ2
0.021338 0.777843
0.000 0.000
Coefficients 0.081833 0.907689 0.0543826 0.026559 0.427529
Post-crisis Probability 0.0205 0.000 0.000 0.2969 0.4031
Coefficients 0.039189 0.959917 0.0379465 0.012535 0.462597
Probability 0.000 0.000 0.000 0.4936 0.5709
Table 12 Results of the estimation of DCC GARCH (1.1) BRENT- EUR. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
0.01877 0.975695 0.017992
θ1 θ2
0.007406 0.820849
Probability 0.000 0.000 0.000 0.4682 0.000
Coefficients 0.050387 0.95784 0.0409612 0.033237 0.790313
Post-crisis Probability
Coefficients
Probability
0.000 0.000 0.000
0.021787 0.980241 0.0315329
0.000 0.000 0.000
0.000 0.000
0.019461 0.803088
0.3343 0.000
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Table 13 Results of the estimation of DCC GARCH (1.1) BRENT-GPB. Pre-crisis
Crisis Coefficients
Probability
α1 β1 ρi, j
0.027555 0.961442 0.010416
0.000 0.000 0.000
θ1 θ2
0.00289 0.992698
0.4292 0.000
Coefficients 0.07008 0.926483 0.087726 0.04735 0.760071
Post-crisis Probability
Coefficients
Probability
0.0033 0.000 0.000
0.025338 0.971507 0.01979552
0.000 0.000 0.000
0.000 0.000
0.026241 0.5833731
0.2780 0.0389
Table 14 Results of the estimation of DCC GARCH (1.1) BRENT-JPY. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
θ1 θ2
0.0177728 0.974833 0.0183584 0.017661 0.986283
Probability
Coefficients
Post-crisis Probability
Coefficients
Probability
0.000 0.000 0.000
0.050396 0.919099 0.11298
0.0466 0.000 0.000
0.015754 0.976744 0.0128718
0.000 0.000 0.000
0.000 0.000
0.047734 0.500155
0.000 0.1893
0.008561 0.96850
0.3751 0.000
Table 15 Results of the estimation of DCC GARCH (1.1) BRENT-MXN. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
θ1 θ2
0.049397 0.924226 0.0021061 0.019123 0.774944
Post-crisis
Probability
Coefficients
Probability
Coefficients
Probability
0.000 0.000 0.000
0.137261 0.852274 0.107516
0.0164 0.000 0.000
0.073980 0.909931 0.0388768
0.000 0.000 0.000
0.000 0.000
0.003919 0.835942
0.8794 0.2207
0.030847 0.678742
0.1818 0.000
Table 16 Results of the estimation of DCC GARCH (1.1) BRENT-NOK. Pre-crisis
Crisis Coefficients
α1 β1 ρi, j
0.020138 0.971481 0.0061
θ1 θ2
0.009122 0.799068
Probability 0.002 0.000 0.000 0.3757 0.0014
Coefficients 0.053695 0.950713 0.068805 0.034684 0.777056
Post-crisis Probability
Coefficients
Probability
0.0022 0.000 0.000
0.027196 0.970033 0.0396247
0.000 0.000 0.000
0.000 0.000
0.004150 0.851394
0.7836 0.044
from the first step (Tables 2–11). The results of exchange rates and estimations of oil prices in various countries during the three sub-periods are shown in the following tables: During the first period, we found that the estimated GARCH model's parameters are positive and are statistically significant, suggesting that the adoption of a GARCH to specify the variables is appropriate. However, remarkable differences can be found between the different pairs of the studied exchange rates and oil prices, in particular the contribution of ARCH and GARCH effects in short and long term persistence. Indeed, short-term persistence (α) remains low in most conditional variance equations. However, the sum of the two parameters (α þ β) is very close to unity. Hence, we conclude to the persistence of conditional variance in the studied series. The parameters θ1 et θ 2 of the DCC model are less than 1, therefore the conditions of the model are valid (Tables 12–19). For the DCC parameters of the pairs of exchange rates and oil prices, we found that they are different from one country to another and they are high for some countries’ returns and weak for others. We can, therefore, conclude that there is a strong positive and significant correlation between oil price and the following exchange ratesduring the crisis: USD/AUD-WTI, USD/
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Table 17 Adequacy test of the copula function. Pre-crisis
CAD- WTI GBP -WTI MXN -WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT Crisis
CAD-WTI GBP-WTI MXN-WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT Post-crisis
CAD- WTI GBP -WTI MXN-WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT
Frank
Normal
Clayton
Student
0.2173 0.1314 0.6049 0.1084 0.07143 0.2243 0.3172 0.03546 0.0004955 0.0004995 0.1533 0.06244 0.05155
0.3851 0.06843 0.3282 0.05844 0.02348 0.1573 0.4241 0.05045 0.0004955 0.0004995 0.2532 0.0974 0.0004955
– 0.03347 0.03546 0.05544 0.03546 0.05145 0.6588 0.1484 0.04641 0.008492 0.3292 0.1883 0.0004955
0.004496 0.001499 0.03147 0.008492 0.0004995 0.0168 0.00112 0.0004995 0.0004995 0.0056 0.0984 0.001499 0.0004955
Frank
Normal
Clayton
Gumbel
Student
0.001499 0.005495 0.000499 0.000499 0.001499 0.005495 0.0004995 0.0004995 0.004496 0.009491 0.0004995 0.004496 0.0004995
0.004496 0.008492 0.0005 0.00049 0.003497 0.006494 0.001499 0.0004995 0.01648 0.007493 0.0004995 0.003497 0.0004995
0.03347 0.1164 0.000512 0.03746 0.03946 0.06743 0.03846 0.01049 0.06344 0.04446 0.004496 0.04346 0.004996
– – – – – – 0.007493 0.0004995 0.01349 0.01349 0.0004995 0.01948 0.0004995
0.02346 0.07742 0.0004 0.2323 0.01449 0.01249 0.0004995 0.0004995 0.004496 0.009491 0.0004995 0.004496 0.0004995
Frank
Normal
Clayton
Student
0.0004995 0.000499 0.000499 0.0004995 0.0004995 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955
0.0014 0.000496 0.000499 0.000499 0.0004995 0.000495 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955
0.001499 0.000498 0.0049 0.003497 0.000512 0.003497 0.001499 0.000678 0.001475 0.003997 0.0005177 0.004747 0.0005599
0.0004995 0.000499 0.0004995 0.00049 0.000499 0.000499 0.0004995 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955 0.0004955
GBP-WTI, USD/MXN-WTI, USD/CAD-WTI, USD/NOK-WTI. Furthermore, the resulting claim is that correlation between BRENT and all the exchange rates is positive. This results in an increase in oil prices influenced by the exchange of the US dollar against other currencies; while correlation between WTI-JPY and WTI-EUR is negative, an increase of oil prices correlates with an increase the US dollar. Using dynamic correlation modeling, Ibrahim Turhan et al. (2014) studied comovements of oil prices and exchange rates of the G20 between 2000 and 2013. They found that the relationship between oil prices and exchange rates has increased in the last decade. The two are strongly and negatively correlated (which also combines oil prices increase with the depreciation of the US dollar against other currencies). During the subprime crisis, we notice an increase in dynamic conditional correlation which indicates a highly increasing interdependence between exchange rates and oil prices of the studied countries. Obviously, we notice that the estimated conditional correlations are relatively strong and can be interpreted as high intensity measures of the relationship between exchange rates and oil prices of the studied countries. Moreover, whatever returns considered, trends of strong and weak correlations appear. This reflects, undoubtedly, a persistence phenomenon. Furthermore, it appears that these correlations have increased in recent years, following the subprime crisis and is becoming higher. This reflects a growing interdependence between these markets. We also notice that correlation between
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Table 18 Kendall's Rate.
WTI-AUD WTI-/CAD WTI-EUR WTI-GBP WTI-JPY WTI-MXN BRENT-AUD BRENT-CAD BRENT-EUR BRENT-GBP BRENT-JPY BRENT-MXN BRENT-NOK
Pre-crisis
Crisis
Post-crisis
0.00194 0.00346 0.00384 0.01273 0.02806 0.00252 0.011501 0.017514 0.000531 0.001992 0.008187 0.006361 0.002432
0.04604 0.00715 0.01337 0.03378 0.01249 0.00392 0.01666 0.026366 3.18E-05 0.001807 0.010975 0.00929 0.002975
0.01218 0.01165 0.01094 0.00417 0.02206 0.004642 0.04408 0.036402 0.046768 0.073874 0.052746 0.046622 0.04994
Pre-crisis
Crisis
Post-crisis
0.003199 0.005133 0.005920 0.019031 0.041551 0.003486 0.065616 0.052186 0.069311 0.10913 0.088852 0.065256 0.076307
0.067179 0.009803 0.020665 0.049182 0.018727 0.007380 0.01713 0.017129 0.01427 0.019383 0.01219 0.021582 0.017831
0.018117 0.017297 0.016079 0.005758 0.032924 0.006450 0.02529 0.02113 0.022186 0.027943 0.016375 0.032012 0.027287
Table 19 Spearman Rho.
WTI-AUD WTI-CAD WTI-EUR WTI-GBP WTI-JPY WTI-MXN BRENT-AUD BRENT-CAD BRENT-EUR BRENT-GBP BRENT-JPY BRENT-MXN BRENT-NOK
oil prices and exchange rates is positive between the following pairs: WTI-AUD, WTI-CAD, WTI-NOK, WTI-MXN, BRENTAUD, BRENT-CAD, BRENT-EUR, BRENT-GBP, BRENT-JPY, BRENT-NOK and BRENT-MXN. This correlation pattern became stronger during the subprime crisis. Thus, increase of oil prices coincides with an appreciation of the dollar. For other exchange rates pairs, correlation is negative; this leads to an increase in oil prices which leads to a depreciation of the dollar. 4.3. Selecting the most suitable copula Our results clearly indicate that every period has a different kind of copula. During the pre-crisis period, we found Frank and Normal type copula, which are symmetrical copula. Meanwhile, during the crisis and post crisis periods, we found Clayton and Student-type copula, which are asymmetrical copula. Therefore, after the Subprime crisis, the exchange rate market moved up to asymmetry. For the relationship between BRENT and exchange rates, we found that the Clayton copula is most appropriate for the three study periods. 4.4. Estimates and results of the parameters of the copula function
Pre-crisis
θ
CAD- WTI GBP -WTI MXN-WTI NOK-WTI AUD-WTI EUR-WTI CAD-BRENT GBP-BRENT MXN-BRENT
0.129 0.25 0.35 0.252 0.678 0.252 0.041 0.008 0.008
Crisis
Post-crisis
θ
θ
0.069 0.116 0.038 0.042 0.03 0.041 0.129 0.208 0.105
0.054 0.054 0.074 0.049 0.041 0.091 0.061 0.077 0.087
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NOK-BRENT AUD-BRENT EUR-BRENT JPY-BRENT
0.003 0.043 0.012 0.201
0.104 0.112 0.131 0.014
0.087 0.065 0.085 0.078
The Clayton copula was selected to explore the nature of dependence between oil prices and exchange rates. There is a positive dependence between oil prices and exchange rates (Figs. 1–3). We notice that the dependence parameters increased during the crisis period for the Clayton copula between oil prices AUD
3
1.5
2
1.0
1
0.5
0
0.0
-1
-0.5
-2
-1.0
-3
-1.5
-4
CAD
2.0
-2.0 00
01
02
03
04
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06
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13 14
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00
EUR
2.0
01
02
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07
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14
GBP
1.0
1.0
0.5
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0.0
0.0
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00
01
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1.5
08
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13 14
08
09
10
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12
13
08
09
10
11
12
13
MXN
2
1.0
07
1
0.5
0
0.0 -0.5
-1
-1.0 -2
-1.5
-3
-2.0 00
01
02
03
04
05
06
07
08
09
10
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13 14
NOK
2
00
01
02
03
04
05
06
07
14
WTI
8 6
1
4 2
0
0
-1
-2 -4
-2
-6 -8
-3 00
01
02
03
04
05
06
07
08
09
10
11
12
00
13 14
01
02
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04
05
06
07
BRENT 6 4 2 0 -2 -4 -6 -8 -10 00
01
02
03
04
05
06
07
08
09
10
Fig. 1. The daily production of crude oil and exchange rates.
11
12
13
14
14
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Fig. 2. Graphic of DCC-MGARCH model.
and other currencies. The Clayton copula is more suitable to capture lower tail dependence. This means that exchange rates and oil prices increasingly depended on each other at the onset of the subprime crisis. We can, therefore, conclude that an increase in oil prices coincides with a depreciation of the dollar. Similarly, Riadh Aloui et al. (2013) found that an increase in oil prices coincides with a depreciation of the dollar. Juan C Ledge (2013) found a negative dependence between oil prices and exchange rates during the crisis and the impact is empirically tested. Our results are not consistent with previous studies that used data prior to the period of the recent global financial crisis (for example, Amano & van Norden, 1998; Chen
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Fig. 2. (continued)
& Chen, 2007). The negative relationship between oil prices and the dollar’s exchange rate may be explained by the fact that oil is a hedging mechanism against inflation and an increasing security against risk. For example, when the dollar declines, countries whose currencies have declined look for the cheapest oil price to purchase and increase their demand for oil, which, in return, leads to an increase in oil prices. Conversely, oil producers might want to increase oil pricesas their purchasing power decreases. Having estimated the parameters of copulas and dependence between oil prices and exchange rates, we will adopt
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Fig. 2. (continued)
Kendall’s rate and Spearman rho to measure impact. When these two coefficients increase, we conclude to the presence of impact. In the following, we present the results of these coefficients before and after the subprime crisis.
4.5. Results of correlation coefficients Kendall’s rate, τ, measures the strength of association between two random variables X and Y. it is a real number with a value ranging between [ 1, 1]. Kendall’s rates increased during the crisis period except those between WTI-JPY, WTI-MXN, WTI-NOK, BRENT-EUR, BRENT-GBP and BRENT-NOK. During the post-crisis period, there is a decrease in Kendall’s rate compared to the crisis period with the exception of the Kendalls rate between WTI-NOK, WTI-MXN and BRENT-JPY which registered an increase in Kendall’s rate. During the precrisis period, there is an increase in Kendall’s rates between WTI-CAD, WTI-EUR, WTI-JPY, WTI-NOK and BRENT-NOK. There is, therefore, dependence between oil prices and exchange rates. This relationship has increased during the crisis for some exchange rates like AUD, GBP, EUR and CAD. This increase confirms the existence of an impact between oil prices and exchange rates. Similarly, in the post-crisis period, the impact is there. Spearman Rho increased during the crisis period except for WTI-JPY, MXN-WTI, WTI-NOK, BRENT-AUD, BRENT-CAD, BRENT-EUR, BRENT-GBP, BRENT-JPY, BRENT-MXN and BRENT-NOK, thus an impact is there during this period. Whereas, during the post-crisis period, the rate decreased,compared to the period of calm, for all exchange rates except for WTI-AUD, WTI-GBP and WTI-MXN. Consequently, impact of exchange rate is valid.
5. Conclusion This article examines the impact between daily oil prices and exchange rates in September using a copula approach and the dynamic conditional correlation approach DCC-MGARCH. First, we used a standard GARCH (1.1) to model the different error distribution margins. The adoption of this filtering method is motivated by the stylized facts of our data including serial dependence and volatility clustering. First, we found that causal relationships and the different exchange rates increased after the crisis period. We, also, noticed that the exchange rate used in our sample influences the exchange rate after the crisis. Overall, our results show that the Clayton copula is the best model with a conditional dependency structure to estimate the relationship between oil markets and exchange rates. They also indicate significant and asymmetric tail dependence for all couples. In addition, an increase in oil price coincides with a weaker dollar. From a forecasting perspective, our portfolio simulations illustrate the idea that taking into account extreme coevolution improves forecast accuracy of market risk. In addition, the DCC-MGARCH model shows that the dynamic conditional correlation between copulas increases during times of crisis. Finally, our results conclude to the existence of an impact between oil prices and exchange rates during the crisis. Consistent with previous studies on co-evolution of financial markets, we notice an increase in extreme dependence of several pairs of foreign exchange markets and oil prices during the crisis.
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Fig. 3. Graphic of different couples.
Recommendation Volatility of oil prices has a negative impact on the economy, as demonstrated in the literature. A shock related to oil prices, as an example of a classic negative offer shock, increases the overall volume of offer, and leads to higher prices and lower production and employment (Dornbusch, Fisher, & Startz, 2001). However, the overall volume of demand declines, as
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appreciation of commodity prices results in a decrease in demand for goods and services. This results in a contraction of global production and employment. The macroeconomic consequences of oil shocks are transmitted through supply and demand and are potentially minimized by the reactions of economic policy. In general, the impact of world oil prices on macroeconomic variables has been studied by researchers for academic purposes and for the resolution of important strategic issues. The issue was the focus of an abundant research, because shocks to oil prices in the early 70s have evolved both in time and in space (affecting both developing and industrial countries). Taking into account the recent increases in world oil prices and the prospect of persistence of this trend in the short-term, or even beyond, and the constraints on supply, the impact of shocks to oil prices is clear on key macroeconomic variables. Research-wise, this remains a relevant topicto explore. Economic policies wise, high oil prices directly affect companies (companies), households (consumers) and the state. First, they trade oil products domestically, as well as many intermediate inputs at increased production costs. Thus, companies can reduce their labor demands and investment, which, inevitably, results in a depreciation of production. Second, short-term oil demand is inelastic to a large extent; consumers have to reduce their consumption of other goods and services (the substitution effect) to pay higher energy bills. Third, net oil importing countries face difficulties of balance of payments, as they have to mobilize additional resources to pay for higher oil import bills. The state also faces more serious budget problems, which can affect its ability to fund social programs aimed at reducing poverty.
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