Causal relationship between spot and futures prices with multiple time horizons: A nonparametric wavelet Granger causality test

Journal Pre-proof Causal relationship between spot and futures prices with multiple time horizons: A nonparametric wavelet Granger causality test Erdost Torun, Tzu-Pu Chang, Ray Y. Chou

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S0275-5319(19)30045-5

DOI:

https://doi.org/10.1016/j.ribaf.2019.101115

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RIBAF 101115

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Research in International Business and Finance

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Causal relationship between spot and futures prices with multiple time horizons: A nonparametric wavelet Granger causality test Erdost Torun, Tzu-Pu Chang*, Ray Y. Chou Erdost Torun Assistant Professor, Department of International Business and Trade, Dokuz Eylul University, Turkey

Tzu-Pu Chang*

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Assistant Professor, Department of Finance, National Yunlin University of Science and Technology, Taiwan Pervasive Artificial Intelligence Research Labs, Taiwan

Ray Y. Chou Corresponding Author. Tel: [email protected].

+886-5-5342601

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5338,

Fax:

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*

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Research Fellow, Institute of Economics, Academia Sinica, Taiwan

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Graphical abstract

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+886-5-5312079,

E-mail:

Abstract: This study investigates the causal information flow between 45 major daily spot returns and their corresponding futures in developing, emerging, and commodity indices through a novel nonparametric wavelet Granger causality test (NWGC) that is capable of detecting causality patterns in various time scales without any stationarity assumption or multivariate autoregressive modeling requirement. We provide new evidence for a complex causality pattern phenomenon. First, there may not be just one dichotomous answer about the Granger causality test for each market data in a time domain, as markets exhibit different causal information flows for different

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time scales. Second, each market may show distinct causality patterns compared to other markets.

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Key words: Granger causality, futures market, wavelet, time-frequency analysis

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JEL Classification: C14, G10

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1. Introduction Ever since the work of Granger (1969), a growing large body of research studies has applied the Granger causality test to examine the causal relationship between economic or financial series. In fact, one strand of the financial literature focuses on the lead-lag correlation between spot and futures contracts in financial markets, but conclusions therein have been debated for a long period.

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Theoretically, if instantaneous trading is possible, then futures and spot prices are expected to have no causal relationship, because they both reflect the same aggregate value of the underlying assets

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(Abhyankar, 1998; Kumar, 2018). In the real world, on the one hand, empirical studies detect the price discovery process in the futures market and suggest that futures lead the spot market

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(Hasbrouck, 2003; Covrig et al., 2004). On the other hand, however, some evidence shows that

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the spot market plays a dominant role in the price discovery process (Yang et al., 2012; Judge and Reancharoen, 2014).

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One possible explanation for these contradicting findings is that the financial market is actually a complex system with heterogeneity, and such heterogeneity within it may result from

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differences in agents’ endowments, geographical locations, time horizons, and so on (Corsi, 2009). Among the factors, our paper focuses on the issue of multiple time horizons that cause heterogeneity in the financial market. The intuition is that the financial market consists of different types of participants, such as market makers, speculators, institutional investors, and individual

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investors, who have their own trading strategies with different time horizons and trading frequency. Unsurprisingly, several excellent financial studies have introduced various time horizons into simultaneous model estimation, especially for volatility. For example, Ghysels et al. (2006) apply various mixed data sampling (MIDAS) regressions to predict volatility, while Corsi

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(2009) proposes a heterogeneous autoregressive model of realized volatility (HAR-RV) with different time periods. With respect to the causality test, however, the conventional Granger causality test does not incorporate multiple time horizons at the same time. Hence, the main purpose of this paper is to apply a nonparametric wavelet Granger causality (NWGC, hereafter) test, developed by Chen et

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al. (2006) and Dhamala et al. (2008a), to revisit the causal relationship between futures and spot markets. There are two major advantages of the NWGC test. First, wavelet analysis provides time

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and frequency representation of the data, thus allowing for more information about the evolution of data. Therefore, the novel NWGC test, an extension of the Granger causality test based on

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wavelet analysis, can easily deal with the issue of multiple time scales. Second, the NWGC test is

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exempt from explicit autoregressive modeling that imposes difficulties on data parameterization, meaning that it is free from both model misspecification and distribution assumption under the

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modeling procedure.

Some advanced causality tests have actually been established over the first decade of the new

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millennium. Eichler (2007) proposes a graphical approach test based on the spectral density matrix in the frequency domain, but restricts his research to the case of a weakly stationary process. Diks and Panchenko (2006) introduce a nonparametric causality test assuming that the time series is strictly stationary, which is not a realistic assumption. Moreover, this test relies on the residuals

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obtained from the vector autoregressive (VAR) model, which may not reflect the true dynamics of the data and suffers a misspecification of the bivariate model. In the newly expanding literature attempting to combine wavelet analysis and Granger causality, wavelet analysis is used as a part of causality analysis, especially as a preliminary step for decomposing the data before using the traditional causality test (e.g., In and Kim, 2006; Chou and Chen, 2011; Benhmad, 2012).

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However, the NWGC test is superior to this kind of method in terms of being fully nonparametric. In addition, Chen et al. (2006) and Dhamala et al. (2008a) prove that the NWGC test can represent the true time-frequency pattern of a series and correctly cover the true network interaction pattern, implying that this test is suitable for financial data analysis and revealing information flow among a series.1

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To our best knowledge this paper is the first in the futures market literature to empirically apply the NWGC test. We comprehensively investigate the causal information flow between 45

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major daily spot returns and their corresponding futures markets, including 19 stock indices in developed markets, 13 stock indices in emerging markets, and 13 commodity indices. Although

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the directions of predictive information flow obtained through NWGC and traditional Granger

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causality are not substantially different, this paper shows new evidence that causal information flow may change depending upon the time scales and data. Specifically, we present two main

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conclusions. First, there may not be just one dichotomous answer about the Granger causality test for each market in a time domain, as markets exhibit different causal information flows for

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different time scales and have complex and detailed causal information flow patterns that the traditional Granger causality test, which gives dichotomous results, cannot fully explain in detail.

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Second, each market may show a distinct causality pattern from other markets in different time

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Several advanced Granger causality approaches have been substantially extended and developed by neuroscientists. Their field calls Granger causality “connectivity analysis”, which denotes statistical dependence or mutual information between two neuronal systems (Friston et al., 2013). Seth et al. (2015) provide an excellent summary of the landmarks in Granger causality established by neuroscientists from 1999 to 2015. More recently, Schmidt et al. (2016) develop a large-scale Granger causality approach that combines principal component analysis with multivariate VAR that is feasible for spatially high-dimensional neuroimaging data. Frässle et al. (2017) and Frässle et al. (2018) propose the regression dynamic causal modeling (DCM) that efficiently computes whole-brain connectivity in functional Magnetic Resonance Imaging (fMRI) data. Barnett and Seth (2017) and Gao et al. (2017) improve Granger causality tests and eliminate possible spurious causality in continuous time neurophysiological data and information graph analysis, respectively. See Sheikhattar et al. (2018) also for a significant development of an adaptive Granger causality framework.

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scales, and hence there may not be only one theory explaining the futures-spot market nexus for all scales, but rather each theory may be valid for a specific time scale in a given market. The rest of the paper is organized as follows. Section 2 reviews the literature on causality between the futures and spot markets. Section 3 describes data and methodology. Section 4

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presents the results. A brief summary concludes this work in Section 5.

2. Literature review

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There is a vast amount of literature focusing on predictive information flow between futures and spot markets through multivariate models using daily and intraday data. As mentioned above,

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however, there is no clear consensus on the nature of the causal relationship, and results vary

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particularly across markets in different countries. Thus, this section aims to review the main results of some related works.

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The adherents in favor of predictive information flow running from futures to the spot market claim that the futures market has the advantages of high liquidity, low transaction costs, easily

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available short positions, and fewer trading restrictions that result in a rapid dissemination of new information (Abhyankar, 1998; Covrig et al., 2004). With regards to stock indices in the U.S. market, such as S&P 500 and Nasdaq-100, Hasbrouck (2003) reports that index futures appear to lead the stock index and conclude that there is a dominant role for index futures to play in the price

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discovery process. Covrig et al. (2004) indicate the existence of strong predictive information flow from futures to spot contracts in Japan. Aside from this evidence in developed markets, the literature also finds unidirectional causality from futures to spot contracts in emerging and commodity markets (e.g., Yang et al., 2001; Adämmer et al., 2016).

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Some researchers oppositely argue that the spot markets play a dominant role in the price discovery process since informed traders in the spot market are unwilling to trade in the futures market due to entry barriers, regulations, or trading system changes. Yang et al. (2012) consider that greater barriers in China’s futures market exclude many informed traders from entry into this high turnover market. Hence, stock index futures do not perform well in their price discovery

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function in the case of China. After the decrease in the minimum tick size in Taiwan’s stock market, Chen and Gau (2009) find that the price discovery ability of the spot market is substantially

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better and that the information share of the spot market is extremely higher than that in Taiwan’s futures market. Moreover, Cabrera et al. (2009) indicate that the currency spot market is more

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informative than the currency futures market, because the size of the latter is much smaller than

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the former.

There is also a strand of the literature that reports a bi-directional causal information flow

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between the spot and futures markets. Kawaller et al. (1987) consider that the futures and spot markets respond together as new information affects them both. Hence, each market possibly leads

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the other when participants in one market discover information on impending price movements. Kavussanos et al. (2008) investigate causality between the price movements of daily FTSE/ATHEX-20 and FTSE/ATHEX Mid-40 stock index futures and their underlying indices, indicating a bi-directional relationship between cash and futures prices. In addition, Bekiros and

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Diks (2008) note a bi-directional Granger causality between WTI oil spot and futures prices. In sum, although research studies focusing on developed markets are relatively homogeneous

in terms of the important role the futures market plays in the price discovery process, their findings for developing countries and commodity markets are more complicated. However, as mentioned earlier, very little research has investigated the causal information flow between futures and spot

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markets with different time horizons. Among a few exceptions, In and Kim (2006) study the causal relationship between the daily S&P 500 futures index and its corresponding spot market index, using wavelet analysis as a preliminary step of decomposing the time series before applying the traditional Granger causality test and finding a bi-directional causal information flow for various time scales. Aloui et al. (2018) apply three wavelet tools, i.e. individual power spectrum, cross-

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wavelet power, and wavelet coherency, to investigate the co-movements between 11 pairs of stock indices and futures indices. Accordingly, they conclude that the lead-lag relationships are mixed

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among different markets. Aside from these works, our paper applies the NWGC test, which is exempt from explicit autoregressive modeling and can represent fully both the spectral properties

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of the given data and the causal relationships with different time scales simultaneously, in order to

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comprehensively revisit the lead-lag relationship between 45 major spot markets and their corresponding futures contracts. Moreover, the NWGC test provides statistical inferences about

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the directions of information flows, thus allowing us to understand the lead-lag relationship more

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precisely.

3. Data and methodology 3.1 Data

The data used in this study consist of 45 futures and their corresponding spot return series for

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commodity, developed market, and developing market indices on a daily basis. The table in the appendix shows notations, definitions, and descriptive statistics of the data used herein. We dived the data (obtained from Datastream) into three groups: developed market index futures (DM), emerging market index (EM), and commodity futures (CM). Although wavelet transformation is exempt from the assumption of stationary distribution, the return series are used in order to make

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a comparison with conventional Granger causality tests. Descriptive statistics imply that our data have non-symmetric and leptokurtic non-normal distribution.

3.2 Methodology Granger Causality Test

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Granger causality detects the direction of an informational influence between two time series through a linear prediction and hence is a linear measure of information flow based on the

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predictive ability of one time series on the other. Granger (1969) proposes that if information in the lagged values of a time series, 𝑥1,𝑡 , has predictive ability on another time series, 𝑥2,𝑡 , then it is

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said that “𝑥1,𝑡 Granger causes 𝑥2,𝑡 ”. The parametric form of this causal relationship can be

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established through vector autoregressive models. We construct univariate and bivariate

𝑥1,𝑡 = ∑∞ 𝑗=1 𝑎11,𝑗 𝑥1,(𝑡−𝑗) + 𝜀1,𝑡

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𝑥2,𝑡 = ∑∞ 𝑗=1 𝑎21,𝑗 𝑥1,(𝑡−𝑗) + 𝜀2,𝑡

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autoregressive models of stationary time series, 𝑥1,𝑡 and 𝑥2,𝑡 , as follows:

(1a) (1b) (1c)

∞ 𝑥2,𝑡 = ∑∞ 𝑗=1 𝑎21,𝑗 𝑥1,(𝑡−𝑗) + ∑𝑗=1 𝑎22,𝑗 𝑥2,(𝑡−𝑗) + 𝜀2|1,𝑡 .

(1d)

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∞ 𝑥1,𝑡 = ∑∞ 𝑗=1 𝑎11,𝑗 𝑥1,(𝑡−𝑗) + ∑𝑗=1 𝑎12,𝑗 𝑥2,(𝑡−𝑗) + 𝜀1|2,𝑡

Here, 𝜀 denotes the prediction error. Granger causality is based on prediction errors since it measures the directions of the prediction in coupling. If 𝑣𝑎𝑟(𝜀1|2,𝑡 ) < var(𝜀1,𝑡 ), then 𝑥2,𝑡 is said to have a causal influence on 𝑥1,𝑡 since using 𝑥2,𝑡 improves the predictability of 𝑥1,𝑡 . One can express this causal influence in the time domain (time-domain Granger causality, TDGC hereafter) by:

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𝐺𝑗→𝑖 = ln (

𝑣𝑎𝑟(𝜀1,𝑡 ) 𝑣𝑎𝑟(𝜀1|2,𝑡 )

).

(2)

Economic time series have a complex structure of oscillations under different periods. Causality at each frequency of oscillation can be measured on a spectral domain, and causal influence between these oscillations can be revealed by spectral analysis. Geweke (1982) defines the spectral decomposition of Granger causality as: 𝑆11 (𝑓)

].

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Σ (𝑆11 (𝑓)−(Σ22 − 12 )|𝐻12 (𝑓)|2 ) Σ11

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𝐼(𝑓)𝑗→𝑖 = [

(3)

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Here, S denotes the power spectrum at given frequency 𝑓; Σ refers to the error covariance matrix

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of the bivariate system equations of Equations (1c) and (1d); and H denotes the spectral transfer function obtained from the transformation of system equations in the Fourier domain.

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We quantify the spectral density matrix as:

𝐒(𝑓) = 𝐇(𝑓)𝚺𝐇∗ (𝑓).

(4)

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Here, * denotes the matrix adjoint; and Σ and H matrices are obtained as a part of autoregressive data modeling. The parametric estimation of these quantities from finite data may produce

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erroneous results when autoregressive system equations are not truncated to proper model orders, and widely used criteria for choosing the optimum autoregressive model order cannot be satisfied perfectly. Moreover, the autoregressive modeling approach may fail to capture all the spectral

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features of the given data. Chen et al. (2006) and Dhamala et al. (2008a) propose the nonparametric Granger causality estimation approach to overcome these difficulties and provide provisions for the estimation of the spectral transfer function and error covariance matrix through Fourier and Wavelet transformations.

Nonparametric Wavelet-based Granger Causality (NWGC) 10

The novelty of this approach is basically the combination of spectral causality formulae proposed by Geweke (1982) with both wavelet analysis and the Wilson-Burg factorization method being employed to obtain a totally nonparametric Granger causality framework. In this nonparametric Granger causality approach, spectral density matrices obtained from wavelet transformation are subjected to Wilson-Burg spectral density factorization and variance

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decomposition for Granger causality estimation. This research employs wavelet analysis rather than Fourier transform since the latter assumes the data are stationary, which is too restrictive,

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whereas wavelet transform is robust to non-stationary and non-linear data (Benhmad, 2012).2 This approach quantifies the spectral matrix elements obtained through a wavelet

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transformation of a time series as 𝑆𝑎𝑏 = 〈𝑊𝑋𝑎 (𝑡, 𝑓)𝑊𝑋𝑏 (𝑡, 𝑓)∗ 〉 𝑤ℎ𝑒𝑟𝑒 𝑎 = 1,2; 𝑏 = 1,2. Here,

function, Ψ(𝜂), which is formulated as:

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𝑊𝑋𝑎 (𝑡, 𝑓) denotes the continuous mother wavelet transformation using the mother wavelet

∞

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𝑊𝑋 (𝑡, 𝑠) = |𝑠|0.5 ∫−∞ 𝑥(𝜂)Ψ∗ (

𝜂−𝑡 𝑠

) 𝑑𝜂.

(5)

Here, * denotes the complex conjugate. The time-frequency representation of the data is obtained

function.

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by varying the scale parameter s and translating along time t, thus giving the position of the wavelet

Following Dhamala et al. (2008a, b), we choose the Morlet wavelet, which is a plane wave

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modulated by a Gaussian envelop, Ψ*     1/4 exp(i )exp( 2 / 2) with   6 , as the wavelet

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Various economics time series applications also employ wavelet transform, such as filtering of seasonality, denoising, variance covariance estimation, identification of structural breaks, long memory process, etc. (Gençay et al. 2001). Wavelet transformation offers new insights on the scale-based changes for exploratory data analysis in economics and finance. Wavelet analysis is also superior to kernel estimation by allowing local heterogeneity in dataand scale-based decomposition via unearthing the relationships between economic variables at the disaggregate (scale) level rather than at the aggregate level. Thus, forecasting taking account into scale-based relationships gives a more realistic prediction via modelling local aspects of a series (Crowley, 2007). For a technical discussion and wavelet applications in finance and economics, see Ramsey (2002) and Crowley (2007).

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function. The Gaussian envelop, exp( 2 / 2) , effectively localizes the wavelet in time, and  determines the time/frequency resolution. The terms scale and frequency are used interchangeably ( s  f ) . Time and frequency resolution are inversely proportional, and higher values of 

provide a higher frequency resolution, but lower time resolution (Dhamala et al., 2008b). However, the Morlet wavelet gives an optimum time-frequency distribution of data and is suitable for cycle

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analysis since it is a complex wavelet that is capable of gathering information about the frequency pattern of data. Hence, unlike Fourier analysis, Morlet wavelet analysis is suitable for data

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containing transient or irregular cycles with a varying period that make the data non-stationary

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(Aguiar-Contraria et al., 2012). The Morlet wavelet is also capable of capturing high frequency, or short-term, variations.

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Dhamala et al. (2008a) use the Wilson-Burg matrix factorization theorem of Wilson (1972, 1978) to factorize spectral density matrix S into a set of unique minimum phase (hence, stable

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inverse) functions:

𝐒 = 𝜓𝜓 ∗ ,

(6)

factor, 𝜋

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where * denotes the matrix adjoint, and 𝜓 denotes the minimum-phase spectral density matrix with

𝜓(exp(𝑖𝑓)) = ∑∞ 𝑘=0 𝐴𝑘 exp(𝑖𝑘𝑓)

.

Here,

𝐴𝑘

equals

(1/

2𝜋) ∫−𝜋 𝜓(exp(𝑖𝑓)) exp(−𝑖𝑘𝑓)𝑑𝑓, where 𝜓(0) = 𝐴0 , which is a real upper triangular matrix with

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positive diagonal elements. After a comparison of Equations (4) and (6), we write the error covariance matrix as: Σ=𝐴0 𝐴𝑇0 .

(7)

𝑇 −𝑇 ∗ Likewise, by rewriting Equation (6) as 𝐒 = 𝜓𝐴−1 0 𝐴0 𝐴0 𝐴0 𝜓 and comparing Equations (4) and

(7), the transfer function can be rewritten as: 𝐇 = 𝜓𝐴−1 0 . 12

(8)

Here,  *  H H * , and T denotes the matrix transposition. Spectral matrix factorization is a key and novel step to non-parametrically obtain 𝐇 and Σ from spectral analysis. The Wilson-Burg factorization method is chosen due to its superb numerical efficiency versus alternative spectral factorization algorithms, such as the elimination of the matrix inversion step and a reduction in computational effort from O( N 3 ) operations to

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O( N 2 ) operations per iteration. Moreover, it guarantees the existence of factorization of rational

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spectral density matrices through the convergence theorem for an iterative method used in this algorithm (Dhamala et al., 2008b). The Wilson-Burg algorithm avoids an expensive matrix

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inversion step and uses only convolutions and deconvolutions at each iteration step. We estimate nonparametric wavelet Granger causality by substituting the noise covariance

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matrix and transfer functions in Equations (7) and (8) obtained through Wilson-Burg factorization

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into the spectral Granger causality formula of Equation (3). Since the power spectrum, error covariance matrix, and transfer function can be directly obtained from the time series, nonparametric Granger causality does not require any assumption about the order of the

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autoregressive model. This nonparametric approach is especially important for time series with oscillations and long memory, which require a high autoregressive order due to the high correlation structure in the parametric approach. Hence, the possibility of spurious causality due to

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misspecified errors is eliminated with the nonparametric Granger causality approach. Since the analytical solution for the Granger causality structure is not a priori known, the

significance of nonparametric Granger causality can be tested via surrogate data. Following the approach of Detto et al. (2012), we can test the null hypothesis of no causal influence between time series through the iterative amplitude adjusted Fourier transform (IAAFT) of Schreiber and Schmitz (2000). IAAFT is based on synthesizing data with the same probability density function 13

and linear correlation structure as the original data, while any other form of coupling or nonlinear correlation structure, which is encoded by correlations in the phase angle in the spectral space, is destroyed. IAAFT surrogates a new time series through a controlled shuffle of the original series based on the phase-randomized surrogate of rank-ordered Gaussian realizations. Although some nonparametric alternative causality tests are used for causality testing in the

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literature, these alternatives suffer from strict distribution assumptions or modeling difficulties. For example, the nonparametric causality tests of Diks and Panchenko (2006) and nonlinear

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causality tests proposed by Hiemstra and Jones (1994) assume that the data are strictly stationary, which is not a realistic assumption. Moreover, applying these tests to residuals obtained from the

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VAR model may not reflect the true dynamics of the original data due to misspecification error of

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the bivariate models. Hence, we choose NWGC, because it is both free of the difficulties

4. Empirical results

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mentioned before and because it is simple to use.3

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This section first compares the TDGC and NWGC results in general and then discusses details of the NWGC results. Table 1 presents the NWGC and TDGC results to compare the test results about the main causality tendency in general. Instead of a detailed numerical presentation of the TDGC results, only the directions of causality are presented so as to save space, but detailed results

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are provided by the authors upon request. Likewise, only the main tendency of NWGC results are presented first rather than the results of each time scale to compare the results with TDGC in Table 1. Detailed NWGC figures and summary results of these figures are illustrated in Appendix Figures A1 to A3 and Table 3. The maximum lag is set to 10, and the optimum lag length is chosen via

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We thank Dr. Matteo Detto from Princeton University for providing the core codes. We then modify the codes for our research purpose.

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Akaike information criterion for vector autoregressive modeling in the TDGC computation process. [Insert Table 1 here] A comparison of the results, shown in Table 1, indicate that TDGC and NWGC exhibit striking similarity about the main causality tendency for the DM and CM groups. Hence, this

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finding is empirical evidence that NWGC could be used for detecting information flow to obtain more information about causality patterns in time scales, which is consistent with the proofs in

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Dhammala et al. (2008a, b) and Detto et al. (2012) about the feasibility of NWGC at detecting causality in positive sciences.

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Although there is a similarity of tests for the DM and CM groups, the results differ in the EM

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group. This difference likely occurs due to difficulties in vector autoregressive modeling and misspecification error caused by emerging financial markets’ features that cause highly complex

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interactions. Emerging markets typically undergo more severe crises, and these markets are also subjected to economic and political reforms in their underlying economy. Hence, relatively

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transitional and unstable economies affect the financial market dynamics. Moreover, these economies have unstable political environments along with increasing complexity of their financial markets. Higher risk factors and a bombardment of countless news/shocks with varying magnitude and duration may make these economies relatively more reactive and sensitive to news

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from developed markets. Listed companies in the indices may also be affected by these factors in different ways. These conditions could cause difficulty in building a multivariate autoregressive model that adequately represents the data’s features. Since it is impossible to find either an exact or a maximum lag number to build a multivariate model taking into full account both data features and interactions, we simply re-calculate TDGC

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through a multivariate model with the optimum lag chosen by the Schwartz information criteria instead of Akaike’s for those indices that have different causality results from the others in the EM group in order to show the difficulty in the multivariate modeling procedure for TDGC: ASE, BOVESPA, and JSE40. The TDGC results remain the same for only JSE40. The results for other indices present interesting changes in the TDGC analysis: unidirectional causality from futures to

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the spot market is detected for ATHEX and BOVESPA. The results are provided by the authors upon request. These findings point out both the crucial importance of parametric modeling in

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TDGC and evidence in favor of NWGC. It is difficult to detect which factors affect the parametric model exactly in the TDGC process. Moreover, since NWGC is totally nonparametric - hence free

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of parametric modeling difficulties - and fully represents spectral properties of the data, NWGC

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could also be used as a superior method for causality analysis. Hence, causality analysis can be more reliable and informative for analysis. Table 2 presents the summary of the results shown in

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Table 1 to reveal the general tendency of overall causality.

[Insert Table 2 here]

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Table 2 shows the overall TDGC and NWGC results, in which the similarity of the overall test results can be observed more clearly. Bidirectional causality is the most frequent causality type in all data groups. The TDGC and NWGC results indicate that there is no unidirectional causality pattern from futures to the spot market for the group DM. The causality tests also find that all

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contracts in the EM group have either a bi-directional or unidirectional causality pattern. Results of causality tests for commodity futures differ for only COFFEE. NWGC finds bi-causality whereas TDGC detects unidirectional causality from the spot market to futures for COFFEE. This finding could present evidence that NWGC has the potential to detect causality that would be ignored by TDGC.

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Instead of presenting all NWGC coefficients for numerous datasets, we plot the NWGC coefficients of a given futures contract versus the cycle length, which is the reciprocal of a given frequency level, so as to present the results in a more compact way. Appendix Figures A1 to A3 illustrate the visualized NWGC test results. A detailed inspection of the figures finds evidence that markets may have distinct causality patterns. For example, Figure 1a reveals that the S&P500 has

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Granger causality from futures to the spot market for the time scales of 5 trading days and shorter. Interestingly, the causal relationship from the spot market to the futures market of the S&P500 is

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detected for the time scales of around 10 trading days and shorter. Another example is the causality test for gold spot and futures markets from the result shown on Figure 1b. Gold exhibits a causality

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pattern from spot to futures up to around 10 trading days, whereas causality from futures to spot

dominant in the price discovery process.

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is detected for all time scales. It means that, in terms of gold, the futures market is extremely

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[Figures 1a and 1b here]

Table 3 presents a summary of time scales and frequency level of significant NWGC

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coefficients. The NWGC figures as well as Table 3 show the complex nature of varying causality patterns based on time scales and market. Hence, NWGC provides more information about the dynamic nature of causality patterns in short/long periods. This dynamic nature is crucial for investment strategies and other financial decisions. Through NWGC, market participants could

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have information on causal interactions among markets under a given time scale that are determined based on investment strategy. For example, when cycles with a period of less than 20 trading days are set as short-term cycles, NWGC provides detailed information about whether contracts have only a short-term causality pattern or whether longer-term causality exists in addition to short-term causality. Table 4 shows the detailed NWGC results.

17

[Insert Table 3 here] [Insert Table 4 here] For bidirectional causality patterns of developed markets, the majority of causality from futures to the spot market is seen only over the short-term cycles. However, bidirectional causality patterns have the same proportion for short and longer terms from spot to futures. Hence, we

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conclude that short-term causality exists for all contracts, but there is also longer-term causal information flow in some contracts of developed market index futures. Unidirectional causality

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from futures to spot, which is found for only one contract of developed market index futures, occurs only in the short term. Hence, short-term bidirectional causality is the dominant pattern for

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developed market index futures.

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In emerging market index futures, the majority of bi-causality exists only in the short term. Similarly, unidirectional causality in both directions exists mostly in the short run. Interestingly,

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causality patterns in commodity indices are mainly different than causality patterns in stock indices. Only bidirectional causality is detected in commodity indices, while long-term causality

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in both directions is observed for the majority of stock indices. There are two noteworthy findings in Table 4.4 First, although bidirectional causality is the predominant pattern, these bidirectional relationships usually happen at different frequencies. For instance, as shown in Figure 1a, S&P500 futures Granger-cause the underlying spot market at

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higher frequency, while S&P500 spot market Granger-causes the corresponding futures at lower frequency. Second, we find that seven causal information flows are significant over whole frequencies. All of them are detected in commodity indices, showing that the behaviors of

4

We heartily thank a referee for this valuable comment.

18

commodity markets differ from those of equity markets. In addition, these causalities entirely denote that futures can Granger-cause spot markets. From these results, we conclude that information flow between spot and futures markets is highly complicated since each market has distinct causality patterns though with some general similarities. In fact, we try to explain the determinants of the aforementioned long-/short-term similarities. We check some possible determinants (such as trading volume, liquidity, and

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volatility), but the evidence is still inconclusive. One recent study, Białkowski and Koeman (2018),

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suggests that the spot market design is an important factor for the effectiveness of the futures market. Therefore, their argument may offer a further direction for us to analyze the determinants

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of similarities shown in Table 4.

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To sum up, our findings indicate that a short-term bidirectional causal relationship is the most widely seen pattern between the spot and futures indices of developed and emerging markets. This

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finding is consistent with Kawaller et al. (1987), indicating that both spot and futures prices are affected by each other’s price movement when new information arrives. Movements in the futures

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market affect market expectations of the spot market since the former conveys all available information that could potentially impact the spot market. Hence, the futures market reacts more quickly to lead the spot market. Conversely, the spot market leads the futures market when the former embodies information affecting future prices.

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The results also indicate that each futures index may show distinct changing patterns based on

a time scale, implying that the theories about future-spot market interactions explain causality patterns to some extent, but these theories are not capable of fully explaining the causality. Hence, although the price discovery theory, which indicates that the futures market drives the spot market due to lower transaction costs and flexibility of short selling, is the most widely acceptable theory

19

in terms of empirical evidence so far, NWGC finds that no unique theory is completely capable of explaining dynamic causal interactions between spot and futures indices. Hence, financial market players, such as long-term investors or speculators, should take into account the complicated changing causality patterns in various time scales. Short-term and long-term financial strategies on futures-spot interactions may need different actions based on the causality patterns enlightened

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by NWGC. Moreover, since financial players may easily benefit from NWGC due to its simplicity and nonparametric nature, we suggest using the NWGC test in order to obtain more information

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on market behaviors.

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5. Conclusion

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This study investigates the lead-lag relationship between 45 major daily spot markets and their corresponding futures of developing, emerging, and commodity indices through the novel

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nonparametric wavelet Granger causality method (NWGC), which is capable of detecting causality patterns in different time scales without both a stationarity assumption and multivariate

ur na

autoregressive modeling requirement. The nonparametric wavelet Granger causality, which is proven to capture spectral properties of data exactly, provides more robust and detailed results for predictive information flow between spot and futures data. Traditional time domain Granger causality and NWGC in general give similar results in terms

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of tendency for the main causality pattern in that bidirectional causality most frequently occurs in all contract groups. A detailed analysis of NWGC finds evidence that causal information flow may change, depending upon the time scale and market data, though there are similarities between the test results. Hence, NWGC provides more information about the dynamic nature of causality patterns over short and long periods. This dynamic nature is especially crucial for decisions on

20

investment and hedging strategies. Through NWGC, market participants have information on causal interactions among markets in a given time scale that can help determine their investment strategy. Because using just TDGC is not enough to reveal dynamic patterns in causality, NWGC can also be employed at the same time for causal pattern analysis in order to gain more information about the futures-spot market relationship phenomenon. Long-term investors, hedgers, and traders

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should take into account these patterns with different time scales when developing investment

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ur na

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re

-p

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strategies with different time horizons.

21

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Nonparametric Wavelet Granger Causality between D1: CURRENCY and D2: ISPCS00-sp500 0.14 FS SF CI(95%) CI(99%) CI(90%)

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Figure 1b. Visualized NWGC test result of Gold

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Notes: F and S denote futures and spot return series, respectively. F→S and S→F refer to causality directions from futures to spot and spot to futures, respectively. Dot-dash blue line and solid blue line denote the causality from futures to spot and spot to futures, respectively. CI(90%), CI(95%), and CI(99%) denote 10%, 5%, and 1% statistical significance levels, respectively. Dot-dash cyan, red, and green lines show the 10%, 5%, and 1% statistical significance level lines, respectively. Causality coefficient lines exceeding any significance level line denote the rejection of the null hypothesis of no causality in a given time scale. The vertical axis shows the causality coefficients. The horizontal axis shows the time scale, or period, which is the reciprocal of a given frequency. Origin is labeled as “inf”, which denotes infinity, because the horizontal axis is defined in terms of a time scale to facilitate visual inspection of the figures.

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Appendix Nonparametric Wavelet Granger Causality between D1: ETICS04 and D2: AMSTEOE-ETICS04

Nonparametric Wavelet Granger Causality between D1: VTFCS00 and D2: ATXFIVE-VTFCS00

0.18

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Nonparametric Wavelet Granger Causality between D1: AAPCS00 and D2: ASXAORD-ALLORDINATES

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Figure A1 panel a. Visualized NWGC results of developed markets’ stock indices

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Nonparametric Wavelet Granger Causality between D1: CURRENCY and D2: LSXCS00-ftse100

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Nonparametric Wavelet Granger Causality between D1: CURRENCY and D2: LSXCS00-ftse100

Nonparametric Wavelet Granger Causality between D1: date and D2: HSICS00-HSICS00

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Figure A1 panel b. Visualized NWGC results of developed markets’ stock indices

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2.85

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Nonparametric Wavelet Granger Causality between D1: OSXCS04 and D2: OSLOOBX-OSXCS04

Nonparametric Wavelet Granger Causality between D1: OMFCS04 and D2: SWEDOMX-OMFCS04

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Nonparametric Wavelet Granger Causality between D1: PSXCS00 and D2: POPSI20-PSXCS00

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0.3

6.66

cycle length (number of trading days)

Nonparametric Wavelet Granger Causality between D1: CURRENCY and D2: GEXCS00-stoxx50 0.35

10.00

0.12 0.1 0.08 0.06 0.04 0.02

3.33

2.85

2.50

2.22

2.00

0 Inf

20.00

10.00

cycle length (number of trading days)

6.66

5.00

4.00 period (time)

3.33

cycle length (number of trading days)

q) STOXX50

r) TOPIX

Figure A1 panel c. Visualized NWGC results of developed markets’ stock indices

29

2.85

2.50

2.22

2.00

Nonparametric Wavelet Granger Causality between D1: CDDCS00 and D2: TTOSP60-CDDCS00 0.2 FS SF CI(90%) CI(95%) CI(99%)

0.18 0.16

0.12 0.1 0.08 0.06 0.04 0.02 0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

2.00

of

cycle length (number of trading days)

ro

s) TSX60

-p

Notes: F and S denote futures and spot return series, respectively. F→S and S→F refer to causality directions from futures to spot and spot to futures, respectively. Dot-dash blue line and solid blue line denote the causality from futures to spot and spot to futures, respectively. CI(90%), CI(95%), and CI(99%) denote 10%, 5%, and 1% statistical significance levels, respectively. Dot-dash cyan, red, and green lines show the 10%, 5%, and 1% statistical significance level lines, respectively. Causality coefficient lines exceeding any significance level line denote the rejection of the null hypothesis of no causality in a given time scale. The vertical axis shows the causality coefficients. The horizontal axis shows the cycle length, or period, which is the reciprocal of a given frequency. Origin is labeled as “inf”, which denotes infinity, because the horizontal axis is defined in terms of a time scale to facilitate visual inspection of the figures.

ur na

lP

re

Figure A1 panel d. Visualized NWGC results of developed markets’ stock indices

Jo

spectral G-causality

0.14

30

Nonparametric Wavelet Granger Causality between D1: date and D2: ASICS04-ASICS04

Nonparametric Wavelet Granger Causality between D1: date and D2: TRTCS00-TRTCS00

0.35

0.35 FS SF CI(90%) CI(95%) CI(99%)

0.3

0.25

0.2

0.15

0.2

0.15

0.1

0.1

0.05

0.05

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

0 Inf

2.00

cycle length (number of trading days)

a) ASE20

20.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

2.00

cycle length (number of trading days)

b) BIST30

Nonparametric Wavelet Granger Causality between D1: date and D2: BUXCS00-BUXCS00

Nonparametric Wavelet Granger Causality between D1: date and D2: BMICS00-BMICS00

0.18

0.25 FS SF CI(90%) CI(95%) CI(99%)

0.14 0.12 0.1 0.08

re

0.15

FS SF CI(90%) CI(95%) CI(99%)

-p

0.16

spectral G-causality

0.2

spectral G-causality

10.00

ro

0 Inf

of

spectral G-causality

0.25 spectral G-causality

FS SF CI(90%) CI(95%) CI(99%)

0.3

0.1

0.06 0.04

0.05

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

lP

0.02

2.85

cycle length (number of trading days)

c) BOVESPA

2.50

2.22

2.00

0 Inf

ur na

0.3 0.25 0.2 0.15 0.1 0.05 0 Inf

20.00

Jo

spectral G-causality

0.35

10.00

e) FTSEA50

6.66

5.00

4.00 period (time)

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

2.00

d) BUX Nonparametric Wavelet Granger Causality between D1: HHICS04 and D2: HKHCHIE-HHICS04

0.35 FS SF CI(90%) CI(95%) CI(99%)

FS SF CI(90%) CI(95%) CI(99%)

0.3

0.25 spectral G-causality

0.4

10.00

cycle length (number of trading days)

Nonparametric Wavelet Granger Causality between D1: date and D2: SCNCS00-SCNCS00 0.45

20.00

0.2

0.15

0.1

0.05

3.33

2.85

2.50

2.22

2.00

cycle length (number of trading days)

0 Inf

20.00

10.00

6.66

f) HSHARES

5.00

4.00 period (time)

3.33

cycle length (number of trading days)

Figure A2 panel a. Visualized NWGC results of emerging markets’ stock indices

31

2.85

2.50

2.22

2.00

Nonparametric Wavelet Granger Causality between D1: date and D2: KLCCS00-KLCCS00

Nonparametric Wavelet Granger Causality between D1: date and D2: SALCS00-SALCS00

0.2

0.2 FS SF CI(90%) CI(95%) CI(99%)

0.18 0.16

0.16 0.14

0.12 0.1 0.08

0.12 0.1 0.08

0.06

0.06

0.04

0.04

0.02

0.02

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

0 Inf

2.00

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

2.00

cycle length (number of trading days)

cycle length (number of trading days)

h) KLCI

Nonparametric Wavelet Granger Causality between D1: date and D2: KKXCS00-KKXCS00

ro

g) JSE40

Nonparametric Wavelet Granger Causality between D1: SPXCS04 and D2: INNSE50-SPXCS04

0.25

0.35 FS SF CI(90%) CI(95%) CI(99%)

0.3

spectral G-causality

0.25

0.2

re

0.15

FS SF CI(90%) CI(95%) CI(99%)

-p

0.2

spectral G-causality

of

spectral G-causality

0.14 spectral G-causality

FS SF CI(90%) CI(95%) CI(99%)

0.18

0.1

0.15

0.1

0.05

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

cycle length (number of trading days)

2.85

2.50

2.22

ur na

i) KOSPI200

lP

0.05

2.00

0 Inf

20.00

0.25

0.2

0.15

0.1

0.05

0 Inf

Jo

spectral G-causality

0.3

20.00

10.00

6.66

5.00

4.00 period (time)

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

2.00

j) NIFTY50 Nonparametric Wavelet Granger Causality between D1: date and D2: TTXCS00-TTXCS00

0.35

FS SF CI(90%) CI(95%) CI(99%)

FS SF CI(90%) CI(95%) CI(99%)

0.3

0.25 spectral G-causality

0.35

6.66

cycle length (number of trading days)

Nonparametric Wavelet Granger Causality between D1: date and D2: RTSCS00-RTSCS00 0.4

10.00

0.2

0.15

0.1

0.05

3.33

2.85

2.50

2.22

2.00

0 Inf

20.00

10.00

cycle length (number of trading days)

6.66

5.00

4.00 period (time)

3.33

cycle length (number of trading days)

k) RTS

l) TAIEX

Figure A2 panel b. Visualized NWGC results of emerging markets’ stock indices

32

2.85

2.50

2.22

2.00

Nonparametric Wavelet Granger Causality between D1: date and D2: WIGCS00-WIGCS00 0.25 FS SF CI(90%) CI(95%) CI(99%)

0.15

0.1

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

of

0.05

2.00

ro

cycle length (number of trading days)

m) WIG20

re

-p

Notes: F and S denote futures and spot return series, respectively. F→S and S→F refer to causality directions from futures to spot and spot to futures, respectively. Dot-dash blue line and solid blue line denote the causality from futures to spot and spot to futures, respectively. CI(90%), CI(95%), and CI(99%) denote 10%, 5%, and 1% statistical significance levels, respectively. Dot-dash cyan, red, and green lines show the 10%, 5%, and 1% statistical significance level lines, respectively. Causality coefficient lines exceeding any significance level line denote the rejection of the null hypothesis of no causality in a given time scale. The vertical axis shows the causality coefficients. The horizontal axis shows the cycle length, or period, which is the reciprocal of a given frequency. Origin is labeled as “inf”, which denotes infinity, because the horizontal axis is defined in terms of a time scale to facilitate visual inspection of the figures.

ur na

lP

Figure A2 panel c. Visualized NWGC results of emerging markets’ stock indices

Jo

spectral G-causality

0.2

33

Nonparametric Wavelet Granger Causality between D1: date and D2: LLCCS00-LLCCS00

Nonparametric Wavelet Granger Causality between D1: LCACS00 and D2: S90940-Cocoa

0.18

1.5 FS SF CI(90%) CI(95%) CI(99%)

0.16

0.12

spectral G-causality

spectral G-causality

0.14

FS SF CI(90%) CI(95%) CI(99%)

0.1 0.08 0.06

1

0.5

0.04

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

0 Inf

2.00

cycle length (number of trading days)

a) BRENT

20.00

10.00

b) COCOA

Nonparametric Wavelet Granger Causality between D1: NKCCS00 and D2: S70899-Coffee 0.09

FS SF CI(90%) CI(95%) CI(99%)

4.00 period (time)

3.33

2.85

2.50

2.22

0.35

0.08

2.00

0.07

spectral G-causality

0.3 0.25

0.05 0.04

re

0.2

0.06

FS SF CI(90%) CI(95%) CI(99%)

-p

0.4

spectral G-causality

5.00

cycle length (number of trading days)

Nonparametric Wavelet Granger Causality between D1: CC.CS00 and D2: S70991-Corn

0.45

0.15 0.1

0.03 0.02

0.05

20.00

10.00

c) COFFEE

6.66

5.00

4.00 period (time)

3.33

lP

0.01

0 Inf

2.85

cycle length (number of trading days)

2.50

2.22

2.00

0 Inf

20.00

0.08

0.06

0.02

0 Inf

20.00

Jo

0.04

10.00

6.66

5.00

4.00 period (time)

FS SF CI(90%) CI(95%) CI(99%)

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

2.00

cycle length (number of trading days)

Nonparametric Wavelet Granger Causality between D1: date and D2: NNGCS00-NNGCS00 FS SF CI(90%) CI(95%) CI(99%)

0.6

0.5 spectral G-causality

0.1

6.66

0.7

ur na

0.12

10.00

d) CORN

Nonparametric Wavelet Granger Causality between D1: NCTCS00 and D2: S70890(P)-Cotton 0.14

spectral G-causality

6.66

ro

0 Inf

of

0.02

0.4

0.3

0.2

0.1

3.33

2.85

2.50

2.22

2.00

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

cycle length (number of trading days)

cycle length (number of trading days)

e) COTTON

f) GAS

Figure A3 panel a. Visualized NWGC results of commodity markets’ indices

34

2.85

2.50

2.22

2.00

Nonparametric Wavelet Granger Causality between D1: date and D2: NGCCS00-NGCCS00

Nonparametric Wavelet Granger Causality between D1: date and D2: NPLCS00-NPLCS00

0.7

0.45 FS SF CI(90%) CI(95%) CI(99%)

0.6

FS SF CI(90%) CI(95%) CI(99%)

0.4 0.35

spectral G-causality

spectral G-causality

0.5

0.4

0.3

0.3 0.25 0.2 0.15

0.2 0.1 0.1

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

0 Inf

2.00

20.00

10.00

6.66

4.00 period (time)

3.33

2.85

2.50

2.22

h) PLATINUM

ro

g) GOLD

2.00

Nonparametric Wavelet Granger Causality between D1: CBOCS00 and D2: S70964-Soyaoil

Nonparametric Wavelet Granger Causality between D1: date and D2: NSLCS00-NSLCS00 short

0.12

0.35 FS SF CI(90%) CI(95%) CI(99%)

0.1

spectral G-causality

0.25

0.2

0.06

re

0.15

0.08

FS SF CI(90%) CI(95%) CI(99%)

-p

0.3

spectral G-causality

5.00

cycle length (number of trading days)

cycle length (number of trading days)

0.1

0.04

0.02

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

cycle length (number of trading days)

i) SILVER

lP

0.05

2.50

2.22

2.00

0 Inf

20.00

0.06

0.02

0 Inf

20.00

Jo

0.04

10.00

6.66

5.00

4.00 period (time)

FS SF CI(90%) CI(95%) CI(99%)

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

2.00

cycle length (number of trading days)

Nonparametric Wavelet Granger Causality between D1: CW.CS00 and D2: WHEATSF-Wheat FS SF CI(90%) CI(95%) CI(99%)

0.08 0.07

spectral G-causality

0.08

6.66

0.09

ur na

0.1

10.00

j) SOYAOIL

Nonparametric Wavelet Granger Causality between D1: CS.CS00 and D2: S70981-Soyabean 0.12

spectral G-causality

of

0.05

0.06 0.05 0.04 0.03 0.02 0.01

3.33

2.85

2.50

2.22

2.00

0 Inf

20.00

10.00

cycle length (number of trading days)

6.66

5.00

4.00 period (time)

3.33

2.85

cycle length (number of trading days)

k) SOYBEAN

l) WHEAT

Figure A3 panel b. Visualized NWGC results of commodity markets’ indices

35

2.50

2.22

2.00

Nonparametric Wavelet Granger Causality between D1: NCLCS00 and D2: S71926-WTI 0.18 FS SF CI(90%) CI(95%) CI(99%)

0.16

0.12 0.1 0.08 0.06 0.04

0 Inf

20.00

10.00

6.66

5.00

4.00 period (time)

3.33

2.85

2.50

2.22

of

0.02

2.00

cycle length (number of trading days)

ro

m) WTI

-p

Notes: F and S denote futures and spot return series, respectively. F→S and S→F refer to causality directions from futures to spot and spot to futures, respectively. Dot-dash blue line and solid blue line denote the causality from futures to spot and spot to futures, respectively. CI(90%), CI(95%), and CI(99%) denote 10%, 5%, and 1% statistical significance levels, respectively. Dot-dash cyan, red, and green lines show the 10%, 5%, and 1% statistical significance level lines, respectively. Causality coefficient lines exceeding any significance level line denote the rejection of the null hypothesis of no causality in a given time scale. The vertical axis shows the causality coefficients. The horizontal axis shows the cycle length, or period, which is the reciprocal of a given frequency. Origin is labeled as “inf”, which denotes infinity, because the horizontal axis is defined in terms of a time scale to facilitate visual inspection of the figures.

ur na

lP

re

Figure A3 panel c. Visualized NWGC results of commodity markets’ indices

Jo

spectral G-causality

0.14

36

BI

F→S S→F

NO

BI

F→S S→F NO

Group EM

T,N T,N

T,N T,N T,N T,N T,N

ASE20 BIST30 BOVESPA BUX FTSEA50 HSHARES JSE40 KLCI KOSPI200 NIFTY50 RTS TAIEX WIG20

T T,N T T,N T,N N T,N T,N T,N T,N -

T T,N T,N

N N T,N -

-

ro

T,N T,N -

-p

T,N T,N T,N T,N T,N

T,N -

re

-

-

lP

T,N T,N T,N T,N

BI

F→S S→F NO

Group CM

ur na

Group DM AEX ATX5 AORD BEL20 CAC40 DAX30 DJIA FTSE100 HIS IBEX35 MIB NIKKEI OBX OMX30 PSI20 S&P500 STOXX50 TOPIX TSX60

of

Table 1. General Comparison of TDGC and NWGC Results Based on Causality Tendency.

BRENT COCOA COFFEE CORN COTTON GAS GOLD PLATINUM SILVER SOYAOIL SOYBEAN WHEAT WTI

T,N T,N N T,N T,N T,N T,N T,N T,N T,N T,N T,N T,N

T -

-

-

Jo

Notes: DM, EM, and CM denote the data group for developed market index futures, emerging market index futures, and commodity market futures, respectively. BI denotes bi-causality. F→S and S→F denote uni-directional causality from futures to spot and spot to futures, respectively. NO denotes no significant causality. T and N denote a causality type detected through the time domain Granger causality test and nonparametric wavelet-based Granger causality tests, respectively.

37

Group Developed Market Group Emerging Market Group Commodity Market

Time domain Granger causality BI F→S S→F 16 (84%) 0(0%) 1 (5%) 9 (69%) 3 (23%) 1 (8%) 12 (92%) 1 (8%) 0 (0%)

NO 2 (11%) 0 (0%) 0 (0%)

Nonparametric wavelet Granger causality BI NO F→S S→F 16 (84%) 0(0%) 1 (5%) 2 (11%) 8 (62%) 2 (15%) 3 (23 %) 0 (0%) 13 (100%) 0 (0%) 0 (0%) 0 (0%)

ro

Contract group

of

Table 2. Numbers and Ratios of Causality Types Detected in Each Data Group.

Jo

ur na

lP

re

-p

Notes: BI denotes bi-causality. F→S and S→F denote uni-directional causality from futures to spot and spot to futures, respectively. NO denotes no significant causality. TDGC and NWGC denote the time domain Granger causality test and wavelet-based non-parametric Granger causality tests, respectively. Numbers in parenthesis are ratios for the number of causality seen in each type of causality divided by the number of all contracts in a given group.

38

Group Commodity Market

F→S

BI F→S S→F BI F→S S→F BI F→S S→F

16 0 1 8 2 3 13 0 0

Short Term 13 (81%) 6 (75%) 2 (100%) 4 (31%) -

ro

Number

-p

Group Emerging Market

Causality

re

Group Developed Market

of

Table 3. Number and Ratio of Contracts in Each Type of Causality.

Long Term 3 (19%) 2 (25%) 0 (0%) 9 (69%) -

S→F Short Term 8 (50%) 1 (100%) 5 (63%) 2 (67%) 5 (38%) -

Long Term 8 (50%) 0 (0%) 3 (37%) 1 (33%) 8 (62%) -

Jo

ur na

lP

Notes: BI denotes bi-directional causality. F→S is uni-directional causality running from futures to spot. S→F refers to uni-directional causality running from spot to futures. Number means the total number of contracts having a given causality pattern. Numbers in parenthesis are ratios for the number of causality patterns seen in each type of causality divided by all contracts in a given group. Short Term denotes causality for only equal or less than 20 trading days. Long Term denotes causality for longer than 20 trading days.

39

BEL20

CAC40

DAX30

0.11-0.13, 0.20↑

9-8, 5↓

0.15↑

7↓

0.39↑

3↓

0.05-0.06, 0.15↑

20-15, 7↓

0.04,0.26↑

25, 4↓

0.01, 0.25↑

100, 4↓

0.01, 0.05↑

100, 20↓

None

None

FTSE100

HIS

Group EM ASE20

BIST30

BOVESPA

BUX

0.17

6

0.3↑

3↓

0.03, 0.09↑

33, 11↓

0.25↑

4↓

0.04, 0.14-0.20

25,7-5

0.08, 0.21↑

12, 5↓

0.37

3

0.12↑

8↓

0.09↑

11↓

F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F

None

FTSEA50

HSHARES

JSE40

KLCI

KOSPI200

Cycle Length (trading days)

ro

5-4

Frequency (cycle per trading day)

0.08,0.15, 0.23↑

None

0.35↑

3↓

0.08↑

12↓

None

None

0.03, 0.11↑

33,9↓

0.07-0.08, 0.3↑

14-12, 3↓

0.02,0.05, 0.10↑

50,20, 10↓

None

None

0.1, 0.2↑

10, 5↓

0.05, 0.13↑

20, 8↓

0.05-0.06, 0.5

20-16, 2

0.27↑

3↓

0.15

7

0.02↑

50↓

0.11-0.12, 0.20↑

8-9, 5↓

0.01, 0.07↑

100, 9↓

0.02, 0.10-0.11, 0.3↑

50, 10-9, 3↓

40

Group CM BRENT

12,7, 4↓

-p

0.20-0.25

Jo

DJIA

F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F

CD

re

AORD

Cycle Length (trading days)

lP

ATX5

Frequency (cycle per trading day)

ur na

Group DM AEX

CD

of

Table 4. Detailed NWGC Results.

COCOA

COFFEE

CORN

COTTON

GAS

GOLD

PLATINUM

SILVER

CD

Frequency (cycle per trading day)

Cycle Length (trading days)

F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F

0.05, 0.09↑

20, 11↓

0.04, 0.07↑

25, 14↓

All

All

0.07, 0.14-0.18, 0.5 All

14,7-5,2

0.2

5

0.05↑

20↓

0.02-0.05, 0.11↑

50-20, 11↓

All

All

0.01, 0.06, 0.3↑

100, 16, 3↓

All

All

0.04-0.06, 0.16↑

25-17, 7↓

All

All

0.11↑

9↓

All

All

0.03, 0.11↑

33, 9↓

All

All

0.04.0.12

25-8

All

OMX30

PSI20

S&P500

TOPIX

TSX60

None

None

None

None

0.03, 0.08, 0.17↑ 0.12, 0.23

33,12, 6↓

0.01, 0.27

100, 4

0.01, 0.10, 0.25↑ None

100, 10,4↓

None

None

0.16↑

6↓

0.09↑

11↓

RTS

TAIEX

8, 4 WIG20

None

0.19↑

5↓

None

None

0.06.0.14↑

17,7↓

0.04, 0.12↑ 0.07, 0.45

SOYAOIL

of

33

F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F

ro

0.03

0.2↑

5↓

0.04, 0.09↑

25,11↓

0.25↑

4↓

0.09↑

11↓

0.3↑

3↓

Jo

STOXX50

NIFTY50

SOYBEAN

25, 8↓ 14, 2

-p

OBX

10↓

0.1

10

0.15, 0.25↑

7,4↓

None

None

re

NIKKEI

0.10↑

WHEAT

WTI

F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F

0.03↑

33↓

0.12↑

8↓

0.05↑

20↓

0.03-0.04

33-25

0.09↑

11↓

0.04,0.18↑

25,6↓

0.01↓, 0.05↑

100↑, 20↓

0.05↑

20↓

lP

MIB

F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F F→ S S→ F

ur na

IBEX35

0.02↑

50↓

0.14↑

7↓

0.09↑

11↓

Notes: CD denotes the causality direction. Cycle length is defined as the reciprocal of a given frequency level. F→S and S→F refer to the direction of causality from futures market to spot market and from spot market to futures market, respectively. DM, EM, and CM denote the data group for developed market index

41

Jo

ur na

lP

re

-p

ro

of

futures, emerging market index futures, and commodity market futures, respectively. The word “All” indicates the significant causality for all frequency level. “None” refers to no significant causality is found for all frequency levels. Numbers separated with a dash denote the range of time scales or frequency levels between given numbers. Up arrow icon (↑) denotes “equal and higher than” whereas down arrow icon (↓) denotes “equal and lower than” in terms of frequency and cycle length. For example, 0.20↑ in frequency column refers to all cycles with the frequency greater than or equal to 0.20 cycles per day. Correspondingly, 5↓ in cycle length column refers to all cycles with the cycle length less than or equal to 5 trading days.

42

of

APPENDIX. Notations, Definitions, and Descriptive Statistics of Return Series

Austrian Traded Index - Austria

AORD

All Ordinaries Index - Australia

BEL20

Euronext Brussels 20 Index - Belgium

CAC40

CAC40 Index - France

DAX30

DAX30 Performance Index - Germany

DJIA

Dow Jones Industrial Average Index U.S.A.

lP

ur na

Financial Times Stock Exchange 100 Index - UK

HIS

Hang Seng Index - Hong Kong

Jo

FTSE100

IBEX35

IBEX 35 Index - Spain

MIB

FTSE MIB Index - Italy

SD

Skewness

Kurtosis

JB

F S F S F S F S F S F S F

0.0002 0.0002 0.0000 0.0000 0.0001 0.0002 0.0002 0.0002 0.0000 0.0000 0.0003 0.0003 0.0002

1/4/1995 1/4/1995 10/1/2004 10/1/2004 5/3/2000 5/3/2000 10/1/2004 10/1/2004 1/11/1999 1/11/1999 7/2/1991 7/2/1991 10/7/1997

0.0147 0.0146 0.0200 0.0201 0.0102 0.0097 0.0129 0.0124 0.0148 0.0148 0.0148 0.0146 0.0126

-0.2164 -0.1328 -0.2099 -0.1294 -0.3934 -0.5784 -0.0636 0.0101 -0.0175 0.0074 -0.2934 -0.1171 0.1044

9.7867 8.8874 8.1933 8.3651 8.4970 9.6926 10.0237 8.9220 7.7185 7.9123 9.9756 7.8067 12.8804

9399.68 7059.18 2643.44 2809.40 4733.39 7080.71 9916.96 7047.59 3735.04 4047.99 11556.61 5461.66 16468.90

S F

0.0002 0.0002

10/7/1997 5/3/1984

0.0123 0.0120

-0.1285 -0.5817

10.2847 13.5677

8959.56 34817.80

S F S F S F

0.0002 0.0003 0.0004 0.0003 0.0003 0.0001 0.0001

5/3/1984 1/19/1988 1/19/1988 4/22/1992 4/22/1992

0.0113 0.0184 0.0167 0.0153 0.0146 0.0153

-0.4880 -0.4565 -0.5526 -0.0869 -0.0137 -0.1900

12.3340 20.7991 19.0898 7.3290 7.8094 8.5539

27131.25 84691.23 69349.63 4294.60 5292.10 3291.42

0.0155

-0.0758

8.5251

3244.61

re

ATX5

Descriptive Statistics Mean Starta

ro

Panel A. Developed Market Indices – Group DM AEX Amsterdam Exchange Index - Holland

F/S

-p

Abbreviation Definition

S

43

3/23/2004 3/23/2004

F S

OMX30

OMX Stockholm 20 Index - Sweden

PSI20

PSI 20 Index - Portugal

S&P500

Standard and Poor’s 500 Index - U.S.A.

STOXX50

EURO STOXX 50 Index

TOPIX

Tokyo Stock Price Index - Japan

lP

S&P/TSX 60 Index - Canada

ur na

TSX60

Panel B. Emerging Market Indices – Group EM ASE20 FTSE/ATHEX Large Cap Index - Greece

BIST National 30 Index - Turkey

Jo

BIST30 BOVESPA

BOVESPA Index -Brazil

BUX

Budapest Price Index - Hungary

FTSEA50

F S F S F S F S F S F

FTSE China A 50 Index - Shanghai/China

-0.0935

12.1697

23566.94

0.0147

-0.1460

9.1029

10458.85

1/11/1995 1/11/1995 2/16/2005 2/16/2005 6/21/1996 6/21/1996 4/26/1982 4/26/1982 6/23/1998 6/23/1998 9/6/1988

0.0157 0.0153 0.0154 0.0150 0.0131 0.0122 0.0127 0.0116 0.0164 0.0157 0.0144

-1.0701 -0.5143 -0.0802 0.0471 -0.2835 -0.2994 -2.2055 -1.1971 0.0046 -0.0025 -0.1350

16.0613 9.6835 7.0167 7.4904 11.5476 10.1207 77.9430 29.7856 7.3438 6.9082 12.3811

33751.10 8810.14 1518.97 1896.20 13569.82 9442.44 1854451.00 237962.70 3065.32 2481.36 24680.25

9/6/1988

0.0130

-0.1638

9.3499

11328.50

9/8/1999 9/8/1999

0.0129 0.0127

-0.5086 -0.6261

10.4265 11.8157

8470.28 11952.13

8/30/1999

0.0218

0.4051

9.7143

6706.45

8/30/1999

0.0206

0.1631

7.0856

2463.03

2/8/2005 2/8/2005 1/2/1995 1/2/1995 1/4/1996 1/4/1996 9/6/2006 9/6/2006

0.0194 0.0195 0.0235 0.0222 0.0202 0.0183 0.0200 0.0197

-0.1391 -0.1386 0.1381 0.4801 -0.3923 -0.3990 -0.1092 -0.2153

5.9725 5.8935 11.3572 16.3897 15.3087 12.0492 5.5859 5.5303

848.25 804.08 13794.28 35553.16 26120.34 14170.31 503.98 493.01

9/7/1988 9/7/1988

-p

Oslo OBX Index - Norway

re

OBX

0.0001 0.0001 0.0003 0.0004 0.0003 0.0003 0.0001 0.0001 0.0003 0.0003 0.0000 0.0000 0.0001 0.0001 0.0002 0.0002

S F S F S F S F S F S F S

0.0004 0.0005 0.0004 0.0004 0.0005 0.0005 0.0006 0.0005 0.0002 0.0002 44

0.0150

of

Nikkei Index - Japan

ro

NIKKEI

KLCI

FTSE BURSA Malaysia KLCI Index Malaysia

KOSPI200

Korea Composite Stock Price Index South Korea

NIFTY50

National Stock Exchange of India 50 Index - India

Russian Trading System Index - Russia

TAIEX

Taiwan Capitalization Weighted Stock Index - Taiwan

ur na

lP

RTS

WIG20

1/6/2004

S F S F

0.0003 0.0004 0.0005 0.0001

1/6/2004 7/3/1995 7/3/1995

S F

0.0001 0.0002

S F

Warsaw General Index 20 - Poland

Panel C. Commodities – Group CM BRENT Crude Oil - Brent Dated FOB U$$/bbl Cocoa - ICCO Daily Price US$/mt

COFFEE

Coffee - Brazilian (NY) Cents/lb

CORN

Corn No. 2 Yellow Cents/bushel

COTTON

Cotton, 1 1/16Str Low - Midl, Memph C/lb

Jo

COCOA

-0.0575

7.4970

2122.24

0.0129 -0.5339 -0.4014 -1.0552

9.5889 11.6165 9.1553 81.4727

4553.14 14668.64 7497.71 1132601.00

12/18/1995 0.0139 5/6/1996 0.0228

0.4691 0.4169

58.1177 8.8347

558513.10 6325.31

0.0002 0.0000

5/6/1996 10/4/2000

0.0201 0.0200

-0.0063 -0.2099

7.6296 8.1933

3902.67 2643.44

S F S F

0.0000 0.0003 0.0002 0.0000

10/4/2000 8/4/2005 8/4/2005 7/22/1998

0.0201 0.0260 0.0230 0.0173

-0.1294 -0.2176 -0.4846 -0.1308

8.3651 13.1021 14.5155 6.5763

2809.40 9112.23 11902.28 2059.51

S F S

0.0000 0.0001 0.0001

7/22/1998 1/19/1998 1/19/1998

0.0151 0.0181 0.0174

-0.1372 -0.1008 -0.1991

5.7846 6.1513 5.7881

1254.01 1661.02 1321.41

F S F S F S F S F

0.0002 0.0003 0.0002 0.0002 0.0001 0.0002 0.0001 0.0001 0.0000

2/1/1989 2/1/1989 9/6/1995 9/6/1995 1/1/1992 1/1/1992 1/5/1979 1/5/1979 1/4/1980

0.0224 0.0232 0.0167 0.0181 0.0243 0.0247 0.0158 0.0166 0.0186

-1.4078 -1.1213 0.0462 -0.2118 0.3599 0.6333 -0.6528 -0.2951 -8.0157

27.9634 27.9481 6.4725 17.6735 9.9281 21.0776 18.0732 7.7562 309.1111

162244.40 161303.70 2463.58 43996.18 11846.29 80185.18 88195.39 8849.89 35188406.00

S

0.0000

1/4/1980

0.0191

-11.8145

566.0923 119000000.00

45

0.0216

of

FTSE/JSE TOP 40 Index - South Africa

0.0004

re

JSE40

F

ro

Hang Seng China Enterprises Index Hong Kong/China

12/18/1995

-p

HSHARES

0.0211 0.0147 0.0138 0.0177

PLATINUM

London Platinum Free Market US$/troy oz

SILVER

Silver, Handy&Harman (NY) cts/troy oz

SOYAOIL

Soya Oil, Crude Decatur Cents/lb

SOYBEAN

Soybeans, No. 1 Yellow C/bushel

WHEAT

Wheat No. 2, Soft Red Cts/bushel

WTI

Crude Oil - WTI Spot Cushing U$$/bbl

11/2/1993 1/3/1979 1/3/1979 1/6/1976

S F S F S F S F S F S

0.0002 0.0001 0.0001 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002

1/6/1976 1/4/1982 1/4/1982 1/3/1979 1/3/1979 1/3/1979 1/3/1979 3/31/1982 3/31/1982 1/3/1986 1/3/1986

lP

0.0370

0.0179

11.7722

14996.12

0.0569 0.0127 0.0130 0.0169

-1.0863 -0.1783 -0.0365 -0.0403

100.5782 10.3750 14.4464 10.9247

1856422.00 19158.50 46044.60 22626.10

0.0170 0.0195 0.0192 0.0151 0.0157 0.0146 0.0150 0.0174 0.0211 0.0242 0.0247

-0.4049 -0.7031 -0.6912 0.1135 0.0422 -0.4820 -0.6162 -0.0369 -0.4564 -0.8473 -0.7832

11.6341 9.7672 11.7075 5.0233 5.2680 7.7580 8.7574 8.5139 14.9893 18.7179 18.8733

27091.82 15102.05 24572.57 1597.49 1985.12 9082.63 13359.70 10647.87 50625.73 77299.83 78688.55

of

Gold, Handy & Harman Base US$/troy oz

11/2/1993

S F S F

0.0001 0.0002 0.0002 0.0002 0.0002

re

GOLD

F

ro

Natural Gas - Henry Hub US$/MMBTU

-p

GAS

Jo

ur na

Notes: a End of the period is 4/7/2014. F/S indicates whether the data are futures or return series. F and S refer to return series and corresponding spot return series, respectively. SD denotes standard deviation. JB refers to the Jarque-Bera test.

46