Do oil price asymmetric effects on the stock market persist in multiple time horizons?

Applied Energy xxx (2016) xxx–xxx

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Do oil price asymmetric effects on the stock market persist in multiple time horizons? Shupei Huang, Haizhong An ⇑, Xiangyun Gao, Xiaoqi Sun School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources, Beijing 100083, China Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China

h i g h l i g h t s
There are no asymmetric effects of oil prices on stock return across the multiscale.
Oil price increase and decrease both have significant influence on stock returns.
The effect on stock returns of oil price changes is greater than the exchange rate.
The responses of the stock market to the oil price changes increase in the long term.

a r t i c l e

i n f o

Article history: Received 17 August 2015 Received in revised form 13 November 2015 Accepted 30 November 2015 Available online xxxx Keywords: Oil price Stock Asymmetric effects Multiscale

a b s t r a c t The oil price could exert asymmetric effects on the stock market. Does this effect persist in various time horizons? To answer this multiscale puzzle, we combine the wavelet transform and the vector autoregression model to examine the dynamic relations between the oil price increase or decrease and stock returns at various time horizons. This paper finds evidence that for each time horizon, both the oil price increase and decrease have significant effects on the stock returns; in addition, the stock market has a reverse influence on the oil price. Further examination proves that the response amplitude of the stock market to the oil price changes ascends as the time horizon lengthens and the response direction varies across different time horizons. Moreover, compared with the exchange rate, the oil price changes could exert a greater effect on the stock market. Overall, based on the influence direction and the extent of the oil price increase and decrease vary with the time scale, there is no persistent asymmetric effect of the oil price on the stock market across time scales. However, the impacts in the longer time horizons deserve more attention from the policy-makers and investors. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Dramatic crude oil price increases could depress national economies and lead to recessions [1]; however, minimal evidence proves that an oil price decrease could foster economic booms. This phenomenon is academically defined as the asymmetric effect of oil price shocks [2–4]. Because the stock market is generally considered as the bellwether of the economy and their linkage builds upon the interest rate, inflation, bonds and cash flow [5], a large body of literature examines whether the asymmetric effect of the

⇑ Corresponding author at: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China. Tel.: +86 10 8232 3783; fax: +86 10 8232 1783. E-mail address: [email protected] (H. An).

oil price is also exists in stock markets. Sadorsky proves the asymmetric effect of oil prices on the stock market using the vector auto-regress model [6], and then Basher and Sadorsky confirm these phenomena for emerging countries [7]. Recently, Salisu and Oloko pronounced a significant own asymmetric impact during the world economic slowdown period [8]. In contrast, Cong et al., find minimal evidence for an asymmetric effect on the aggregated stock index [9]. The works by Nandha et al., and Park et al. confirm that no asymmetric issues with larger data sample size, and they recommend to hedge the oil price risk [10]. Obviously, it is difficult to derive a consistent conclusion for the asymmetric issue with increasing literature [8,11–18]. Because of the reputedly complicated oil and stock markets as well as the influences of many exogenous factors, such as policy changes, new technology improvement and environmental concerns, the oil–stock issue is

http://dx.doi.org/10.1016/j.apenergy.2015.11.094 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Huang S et al. Do oil price asymmetric effects on the stock market persist in multiple time horizons?. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.11.094

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highly complex and difficult to attain conclusive results [19,20]. Therefore, by involving more nonlinear considerations, Ramos and Veiga show evidence that the asymmetric effect is solely significant for oil-importing when the distinction among countries and oil volatility are considered [21]; this proves that more elaborated examinations involving nonlinear factors could offer more convincing results. However, in addition to these obvious nonlinear factors, there remains an important hidden factor for considering the asymmetric effect of oil price changes. As we know, there are a variety of stakeholders with markedly different investment horizons [22]. The investors who prefer long-term trading rely in part on the trend analysis at quarterly and yearly time horizons. In monthly and weekly time horizons, the investors often rely on a computational finance strategy. The daily and intra-daily frequency is the ideal choice for speculators [23]. Thus, the markets combine all investors from various time horizons, which means that all the investment classes may exert different influences on the entire market [24]. Moreover, a strand of literature provides a convincing evidence for multiscale characteristics of the relationships between the oil price and stock market such as the study by Jammazi [19], Khalfaoui et al. [25], Reboredo and Rivera-Castro [26] and our previous research [27]. However, the existing literature that focuses on the oil–stock interaction examines this nexus in a general manner and ignores the asymmetry effect of the oil price, which may omit crucial and specific reference information for the stakeholders in the markets. Therefore, whether the asymmetric effect of the oil price persists in multiple time horizons remains a nascent problem. Encountering this issue in multiple time horizons, we choose the wavelet transform to attain a multiscale analysis. The economic and financial research of the past decade provides evidence of the effectiveness and efficiency of the wavelet [28–30]. The researches proved that there are multiscale features in the stock markets [31–34], energy commodity markets [35–39] and their interactions [22,27,40]. Hence, using a wavelet transform, we can examine whether the asymmetric effect of the oil price on the stock market exists across various time horizons, which has been a gap in the literature. Based on the analysis in different time horizons, we can answer the following questions: Could the oil price increase and decrease cause changes in the stock market across different time horizons? Does the stock market respond to the oil price increase or decrease in the same direction, and do these response directions persist across time horizons? With the objective of exploring the asymmetric puzzle across various time horizons, we combine novel and traditional approaches, the wavelet transform and the vector autoregression model (VAR). First, we use dummy variables to separate the oil price time series into an increase and a decrease series. Second, we implement the wavelets to decompose the oil price increase/decrease series and stock returns into various time horizons. Third, we construct the VAR model involving the oil price changes and stock return variables for each time horizon. Finally, the analysis examines the asymmetric puzzle for each time horizon using the Granger causality test, the impulse response function and variance decomposition.

2. Methodology and data To test the asymmetric effects of oil price variations on the stock market in multiple time horizons, we first need to transform the original time series into different time horizons with the discrete wavelet transform. Based on the decomposition results, we construct the multiple variables vector autoregression model to explore the dynamic interaction between the oil price and the stock index.

2.1. Discrete wavelet transform First, the Haar à trous wavelet transform is used to decompose the oil price changes and stock index in different time scales. Generally, in the existing economical literature using the discrete wavelet transform, most have adopted the maximal overlap discrete wavelet transform (MODWT) [38,41]. However, MODWT has a boundary effect that could omit information at the beginning or end of the time series. The Haar à trous wavelet transform (HTW) solves the boundary effect and effectively retains the information by abandoning the sampling and interpolating processes [42]. In addition, for the wavelet transform always needs to find a balance between the time and scale because in the high frequency band, the time resolution is better, and in the low frequency band, the frequency resolution is better. The Haar à trous wavelet transform (HTW) has a better tradeoff between the most desirable wavelets’ properties (time alignment of the Haar and non-decimation of the à trous), which could retain the entire information of the original time series effectively and also offer precise construction and observation [43]. In detail, the Haar à trous wavelet transform can be represented as an equation involving a series of wavelet coefficients and scale coefficients. First, given the scale, coefficient ci+1 is defined as follows:

ciþ1 ðkÞ ¼

þ1 X

hðlÞci ðk þ 2i lÞ

ð1Þ

l¼1

where h(⁄) is the filter (1/2, 1/2). Then the wavelet coefficient di can be obtained from the difference in the successive scale coefficients:

di ðkÞ ¼ ci1 ðkÞ  ci ðkÞ

ð2Þ

Finally, the original time series is composed into j scales, namely D1, D2, D3,. . ., Dj and Aj. Among these scales, D1, D2, D3, . . ., Dj represent the details of the changes in the time series. The HTW of one time series can be represented as follows:

XðkÞ ¼ cj ðkÞ þ

J X dj ðkÞ

ð3Þ

j¼1

Hence, according to the decomposition of the HTW, we can obtain the wavelet and scale coefficients for different scales, which reveal richer fluctuation information at each scale. 2.2. Econometric model Based on the wavelet decomposition results, we establish a multiple vector auto-regression model to further explore the dynamic relation between the oil price changes and stock market. Furthermore, the impulse response function uncovers the direction of the response of the stock index to oil price changes, and the variance decomposition can estimate the level of impact of oil price changes. 2.2.1. Vector auto-regression model Sims [44] presented the vector auto regression model (VAR) for the dynamic analysis of the economic system. The VAR model treats all of the variables as endogenous, and evaluates the estimation of the dynamic interaction between the economic variables. The VAR model can be expressed as follows:

yt ¼ U1 yt1 þ    þ Up ytp þ et ; t ¼ 1; 2; . . . ; T

ð4Þ

where yt is a k-dimensional endogenous variables column vector, p is the lag length, and T is the number of samples.

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S. Huang et al. / Applied Energy xxx (2016) xxx–xxx

In addition, the Granger causality test is used after the VAR model estimation to examine the causality direction between the oil price and the sector stock index. 2.2.2. Impulse response function (IRF) In our study, we use the IRF to determine when the oil price changes increase by one standard deviation at time 0 and the response of the stock index at time 0 and in several periods after. The IRF can be expressed as follows: First, given the VAR model,

yt ¼ ðIk þ H1 L þ H1 L2 þ   Þet ; t ¼ 1; 2; . . . ; T

ð5Þ

ðqÞ

However, calculating hij when s = 1 is excessively complex. If ðqÞ

the model satisfies the stationary conditions, hij would decrease in a geometrical progression as q increases. Therefore, using the limiting number of s can yield the approximate contribution ratio of the variance:

Ps1 RVCj!i ðsÞ ¼ P

ðqÞ 2 q¼0 ðhij Þ

k j¼1

nP

rjj

ðqÞ 2 s1 q¼0 ðhij Þ

rjj

o ; i; j ¼ 1; 2; . . . ; k

ð13Þ

2.3. Data description

and yit, the variable i is

yit ¼

k X ð0Þ ð1Þ ð2Þ ð3Þ ðhij ejt þ hij ejt1 þ hij ejt2 þ hij ejt3 þ   Þ; t ¼ 1; 2; . . . ; T j¼1

ð6Þ We introduce one standard deviation at time 0 to y1; therefore,



e1t ¼

1; t ¼ 0 0;

ð7Þ

t–0

Thus, eit = 0, t = 1, 2, . . . T, i – 1. response of yj to y1 is as follows:

yit ¼

Accordingly,

the

impulse

k X ð0Þ ð1Þ ð2Þ ð3Þ ðhij ejt þ hij ejt1 þ hij ejt2 þ hij ejt3 þ   Þ; t ¼ 1; 2; . . . ; T j¼1

ð8Þ The factor located in row i, column j of matrix Hq can be expressed as follows: ðqÞ

hij ¼

@ yi;tþq ; q ¼ 0; 1; . . . ; N; t ¼ 1; 2; . . . ; T @ ejt

ð9Þ

The foregoing equation, as a function of q, describes the impulse response of variable i when we introduce a disturbance j of one standard deviation at time t and the response of yi,t+q. 2.2.3. Variance decomposition (VD) Although the impulse response function describes the impact of a variable on the system, variance decomposition (VD) is a useful tool for examining the contribution of each variable to the change in a given variable. According to Eq. (8), the variance can be calculated provided that ej has no correlation. Thus, we have the following equation: ð0Þ

E½ðhij ¼

2

ð3Þ ejt þ hijð1Þ ejt1 þ hð2Þ ij ejt2 þ hij ejt3 þ   Þ 

1 X

ðqÞ 2

ðhij Þ

rjj ; i; j ¼ 1; 2; . . . ; T

ð10Þ

q¼0

Supposing that the covariance matrix R of the disturbance is diagonal, the variance of yi is the sum of the aforementioned items.

varðyi Þ ¼

( k 1 X X j¼1

)

ðqÞ 2

ðhij Þ

; i ¼ 1; 2; . . . ; k

ð11Þ

q¼0

The variance of yi can be decomposed into k types of separated disturbance effects. To calculate the contribution of each disturbance to the variance, the following equation can be used:

P1 RVCj!i ð1Þ ¼

ðqÞ 2 q¼0 ðhij Þ

varðyi Þ

i; j ¼ 1; 2; . . . ; k

rjj

P1 ¼P

k j¼1

ðqÞ 2 q¼0 ðhij Þ

nP 1

rjj

ðqÞ 2 q¼0 ðhij Þ

rjj

To investigate the asymmetric impact of crude oil prices on the stock market in different time horizons, we also involve the interest rate and exchange rate in the empirical study based on Fama’s results that the inflation and international economic activities also could exert influence on the stock market [45]. Concerning the international crude oil price, we select the European Brent oil price as a proxy variable. The Shanghai composition index is used to represent the Chinese stock market, and the Shanghai interbank offer rate is considered as a representative of the interest rate. Regarding the exchange rate, we adopt the US dollar against the RMB exchange rate. In addition, the data sample period is from October 2006 to December of 2014 and the data frequency is daily. We adopt the common data point shared by these four variables; we attain 1868 data point for each series. The basic statistical description of the original data is demonstrated in Table 1. The Brent oil price (oil) is extracted from the Energy Information Administration (EIA). The Shanghai composition index (shci) is from the wind database. The Shanghai interbank offer rate (shior) and the exchange rate (er) are from the People’s Bank of China and the Federal Reserve Bank, respectively. We use the logarithmic transformation to all of the dataset as Xt = log(st/st1). Then carrying out stationary test for the logarithmic series, we found these series are I(1) (The details could be seen in Appendix Table A1). Hence, we test co-integrated relationship among them; the results show that there exists co-integrated relationship. 2.3.1. Oil price variables To test the asymmetric impact of the oil price on the stock market in different time horizons, the non-linear changes in the oil prices need to be defined. In accordance with Hamilton’s pioneering work, using a dummy variable can distinguish the positive oil price changes from negative ones. Through comparing the oil price at time point t with the that from time point t  1, the real oil price increase or decrease can be obtained. The non-linear transformation can be defined as follows:

oilpt ¼ maxð0; lnðoilt Þ  lnðoilt1 ÞÞ

ð14Þ

oilnt ¼ minð0; lnðoilt Þ  lnðoilt1 ÞÞ

ð15Þ

The real oil price changes could solely capture the daily oil price changes; there is minimal consideration regarding the history changes. Hence, we introduce the net oil price increase (decrease) to explore dramatic oil price changes involving history informa-

Table 1 The statistical description of the original data.

o; ð12Þ

oil shci er shibor

Mean

Std. Dev.

Min

Max

91.80 2747.62 6.69 2.40

23.01 836.21 0.50 1.09

33.73 1706.70 6.04 0.80

143.95 6092.06 7.92 13.44

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S. Huang et al. / Applied Energy xxx (2016) xxx–xxx

tion. Hamilton proposed the initial measure [46] in which the monthly oil price is used as the sample data and compared the current oil price over the previous year. In this paper, our dataset uses daily frequency. Therefore, we improve the measures and define the net oil price increase (nopi) at the time point t as follows:

nopit ¼ maxð0; lnðoilt Þ  ln½maxðoilt1 ; :::; oiltp ÞÞ;

p ¼ 1; 2; :::; 31 ð16Þ

where nopi can be obtained from the amount that the current oil price exceeds the maximum value over the previous month. With this measure, the nopi will remain a small value when the oil price continues to escalate; if the oil price increases dramatically, the nopi will achieve a high value. Using the nopi, it is easy to identify the exogenous oil price shocks [47]. Therefore, we define the net oil price decrease (nopd) at the time point t as follows:

nopdt ¼ minð0; lnðoilt Þ  ln½maxðoilt1 ; :::; oiltp ÞÞ;

p ¼ 1; 2; :::; 31 ð17Þ

where the nopd is generally negative, excluding the peak values’ time point of the last month. In addition to the oil price changes, the oil price volatility could exert an influence on the stock markets through its effect on the oil price changes [46]. Thus, we also explore the impact of the oil price volatility, which will aid us in determining the uncertainty of the oil price changes. Based on the daily frequency dataset and in accordance with Andersen et al. [48], the monthly oil price volatility volt can be calculated as the average of the squared first log differences of the daily spot crude oil price:

v olt ¼

st X 2 ðlog ðoilt;dþ1 =oilt;d Þ Þ=st

ð18Þ

d¼1

where oilt,d is the Brent oil price of d day in month t, and st is the number of the trading days of month t. 3. Empirical results and discussion 3.1. Decomposition into multiple time horizons We define two types of oil price changes as real oil price increases (decreases) and net oil price increases (decreases) as well as the oil price volatility. For each type of non-linear transformation, we use the dummy variables to differentiate oil price changes and implement the Haar à trous wavelet transform to decompose the original time series of the Brent oil price, the Shanghai composition index, the interest rate and the exchange rate into 6 scales. These 6 scales cover the time horizons of 4 days, 8 days, 16 days, 32 days, 64 days and 128 days. 3.2. Unit root test The VAR model is implemented to explore the oil–stock nexus. Initially, a unit root test should be used to examine the statistical properties of the time series that are used in the VAR model with real oil price changes and net oil prices changes. We select the Augmented Dickey–Fuller test (ADF), the Phillips and Perron test (PP) [49] and the Kwiatkowski–Phillips–Schmidt–Shin test (KPSS) [50] to obtain robust results. The null hypothesis of the ADF and PP tests is that the examined time series has a unit root, whereas the null hypothesis of the KPSS test is that the series is stationary. For all the sub-series in each scale, the null hypothesis of ADF and PP that the series has a unit root is rejected at the 1% level, and the hypothesis of KPSS is not rejected at the 1% level; this demonstrates that all of the examined sub-series are stationary and could be used to construct the VAR model directly (see Table 2)

We also test the impact of the oil price volatility on the Chinese stock market. The volatility of the oil price is in the monthly frequency; therefore, the Shanghai composition index, the exchange rate and the interest rate are also sampled at a monthly frequency. All of the sub-series are stationary in scales 1, 2 and 3. However, in scales 4, 5 and 6, the sub-series such as volatility of the oil price, the interest rate and the exchange rate are I(1). Hence, we construct the VAR model directly from scale 1 to scale 3 and conduct a Johansen–Juselius cointegration test [51] for the series from scale 4 to scale 6. The results indicate that there are cointegration relations among variables in scale 4, scale 5 and scale 6 (because of the limited space, refer to the details in Appendix A). 3.3. Asymmetric effects of oil price shocks 3.3.1. Granger causality test The Granger causality test is used first to examine the interactions between the oil price changes and the stock market. The Granger causality test is based on the VAR model with variables placed in the following order: first log difference of real oil price increases and decreases (net oil price increases and decreases); the first log difference of the exchange rate and the first log difference of the interest rate. The Granger causality test results of the real oil price changes and net oil prices change are shown in Tables 3 and 4, respectively. The real oil price increase and decrease as well as the exchange rate have bidirectional Granger causality relations with the Shanghai composition index through all the scales; this means that the changes that occur in any market could be used as a warning signal that there will be changes in the other market. In addition, these results also demonstrate that the oil price increases and decreases both have a significant influence on the Chinese stock market. For the policy-makers, when the oil prices or exchange rate changes they should focus more on the stock markets because there will be oscillation afterward. For the financial investors, these types of bidirectional relations could be used to hedge the market risk. However, the real oil price changes only consider the oil price changes in a relevant short period. Thus, the guidance information will be more useful for the short-term investors. However, the interest rate does not have a statistically significant Granger causality relation except in scale 6. Concerning the net oil price changes, similar to the situation of the real oil price changes, the net oil price increase and decrease as well as the exchange rate all run a bidirectional Granger causality relation with the Shanghai composition index at the 10% level in all scales. However, the interest rate has a bidirectional Granger causality relation solely with the Shanghai composition index in scale 6. Because the net oil price changes consider the dramatic oil price changes with the history information, based on these bidirectional Granger causality relationships when the oil price changes substantially, the policy-makers and investors are supposed to be more cautious for the stock market fluctuations. In summary, through check the granger relationship between the oil price changes and stock market using real oil price changes and net oil price changes, we confirm that both the oil price increase and decrease could influence the Chinese stock market through all the time scales. However, for the asymmetric effect of the oil price, we need to identify the response direction of the stock market to the oil price change. 3.3.2. Impulse response to the oil price changes Based on the VAR model (oil price changes, er, and shior), the impulse response function could offer refined insight into the response of the stock index to oil price shocks in terms of the response amplitude and direction. In Fig. 1, the upper two rows are the responses of the Shanghai composition index to the real

Please cite this article in press as: Huang S et al. Do oil price asymmetric effects on the stock market persist in multiple time horizons?. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.11.094

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S. Huang et al. / Applied Energy xxx (2016) xxx–xxx Table 2 The unit root test results for the daily oil price changes series. ADF

PP

C

C&T

KPSS

C

C&T

C

C&T

TS

p value

TS

p value

TS

p value

TS

p value

TS

TS

Scale 1 (4 days)

oiln oilp nopi nopd shci er shior

9.2420 11.5110 9.8030 6.3870 4.6440 4.0070 8.3990

0.0000a 0.0000a 0.0000a 0.0000a 0.0001a 0.0014a 0.0000a

9.2430 11.5180 9.8050 6.4250 4.6020 4.5690 8.3980

0.0000a 0.0000a 0.0000a 0.0000a 0.0010a 0.0012a 0.0000a

291.3570 305.7820 199.1770 44.9610 45.4270 52.3470 56.0900

0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a

291.2750 305.7780 199.1050 44.9980 45.4060 52.0700 56.0730

0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a

0.0152 0.0175 0.0147 0.0732 0.1410 0.8400 0.0195

0.0140 0.0138 0.0138 0.0483 0.1380 0.0955 0.0165

Scale 2 (8 days)

oiln oilp nopi nopd shci er shior

8.6420 10.8330 9.1100 6.6030 4.5580 4.1450 8.3320

0.0000a 0.0000a 0.0000a 0.0000a 0.0002a 0.0008a 0.0000a

8.6440 10.8410 9.1120 6.6420 4.5140 4.7240 8.3300

0.0000a 0.0000a 0.0000a 0.0000a 0.0014a 0.0006a 0.0000a

59.6670 61.9150 41.2150 15.4750 18.2880 23.2810 17.0410

0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a

59.6470 61.8950 41.1840 15.4590 18.2720 22.3210 17.0270

0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a

0.0319 0.0261 0.0155 0.0701 0.1410 0.8530 0.0196

0.0289 0.0158 0.0139 0.0472 0.1380 0.0961 0.0169

Scale 3 (16 days)

oiln oilp nopi nopd shci er shior

8.1490 10.2670 8.5010 6.5340 3.9430 3.6940 7.9690

0.0000a 0.0000a 0.0000a 0.0000a 0.0017a 0.0042a 0.0000a

8.1520 10.2760 8.5030 6.5730 3.8900 4.2570 7.9670

0.0000a 0.0000a 0.0000a 0.0000a 0.0125b 0.0037a 0.0000a

17.8680 16.7690 11.3090 6.4410 6.8520 8.2790 6.5360

0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a

17.8500 16.7550 11.2960 6.4310 6.8470 8.1820 6.5300

0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a

0.0256 0.0359 0.0167 0.0619 0.1420 0.8680 0.0215

0.0241 0.0194 0.0139 0.0439 0.1360 0.0962 0.0175

Scale 4 (32 days)

oiln oilp nopi nopd shci er shior

8.2530 9.7140 6.9820 4.9400 3.7150 3.0920 7.5340

0.0000a 0.0000a 0.0000a 0.0000a 0.0039a 0.0271b 0.0000a

8.2550 9.7310 6.9850 4.9820 3.6600 3.6800 7.5330

0.0000a 0.0000a 0.0000a 0.0002a 0.0252b 0.0237b 0.0000a

8.6350 8.5810 5.9080 4.8620 4.3040 4.2320 4.9580

0.0000a 0.0000a 0.0000a 0.0000a 0.0004a 0.0006a 0.0000a

8.6300 8.5710 5.9020 4.8600 4.2980 4.5520 4.9550

0.0000a 0.0000a 0.0000a 0.0004a 0.0032a 0.0012a 0.0002a

0.0352 0.0706 0.0191 0.0655 0.1440 0.8630 0.0211

0.0334 0.0264 0.0145 0.0465 0.1370 0.0969 0.0194

Scale 5 (64 days)

oiln oilp nopi nopd shci er shior

6.7780 8.6240 5.5950 4.0900 2.7070 2.5450 5.7980

0.0000a 0.0000a 0.0000a 0.0010a 0.0728b 0.1049 0.0000a

6.7760 8.6560 5.6000 4.1260 2.6350 3.1350 5.7980

0.0000a 0.0000a 0.0000a 0.0058a 0.2639 0.0982c 0.0000a

6.6950 7.5680 4.6790 4.2520 3.6710 3.2700 4.7790

0.0000a 0.0000a 0.0001a 0.0005a 0.0045a 0.0163b 0.0001a

6.6910 7.5580 4.6780 4.2600 3.6460 3.7900 4.7770

0.0000a 0.0000a 0.0008a 0.0036a 0.0262b 0.0171b 0.0005a

0.0603 0.1220 0.0236 0.0493 0.1510 0.8290 0.0246

0.0605 0.0389 0.0154 0.0402 0.1370 0.0993 0.0244

Scale 6 (128 days)

oiln oilp nopi nopd shci er shior

4.9310 6.0530 7.1150 6.9600 2.7180 3.6520 7.1030

0.0000a 0.0000a 0.0000a 0.0000a 0.0711c 0.0048a 0.0000a

4.9120 6.0710 7.1330 7.0990 2.6330 4.4420 7.1050

0.0003a 0.0000a 0.0000a 0.0000a 0.2649 0.0019a 0.0000a

5.8230 7.1880 5.1510 6.2230 3.3430 3.1360 5.2910

0.0000a 0.0000a 0.0000a 0.0000a 0.0131b 0.0240b 0.0000a

5.8180 7.2450 5.1560 6.2210 3.3230 3.6590 5.2900

0.0000a 0.0000a 0.0001a 0.0000a 0.0625c 0.0252b 0.0001a

0.0690 0.1740 0.0325 0.0595 0.1740 0.7940 0.0352

0.0640 0.0570 0.0170 0.0247 0.1390 0.1050 0.3550

Notes: TS – test statistic; C – constant; T – trend. a Denotes rejection of the null hypothesis of a unit root at the 1% level of significance. b Denotes rejection of the null hypothesis of a unit root at the 5% level of significance. c Denotes rejection of the null hypothesis of a unit root at the 10% level of significance.

oil price increase from scale 1 to scale 6, and the two rows at the bottom are the responses of the Shanghai composition index to the real oil price decrease from scale 1 to scale 6. We fix the period as 100 days. The response amplitude of the Shanghai composition index grows as the time horizons lengthen; the response of the stock market in the long time horizons deserves more focus based on its variation across time scales. Concerning the response direction, the real oil price changes cause the Shanghai composition index to fluctuate sizably and persistently in the previous 50 days and then gradually become zero in scales 1–4. Hence, we infer that in the short term, the stock market fluctuations are mainly because the stakeholders are concerned with energy price changes and exhibit behaviors according to their anticipations. In scales 5 and 6, the cumulative response of the Shanghai composition index is positive to the real oil price increase and negative to the real oil price decrease. Hence, the real oil price increase and decrease both could cause shocks to the Chinese stock market; however, their impacts

are in opposite directions. In the long term, the oil price increase transmits their effect to the stock markets mainly through the entity economy and the transmission takes a period of time. Specifically, there are different types of companies and factories, for instance, factories in the oil refinery industry and companies in transport industry; the oil price changes have different influences on these. Therefore, the oil price impacts on the entire market depend on the offset situation between these different effects. According to our results, in the medium and long term, the oil price increase could cause a boom in the stock market, whereas the oil price decrease will depress the stock market. Hence, in the short run, the fluctuations of the stock market are mainly because of the dealing behavior and the market anticipation; the stock market could adjust this type of fluctuations to the equilibrium status based on its own market mechanism. However, in the long run, the oil price changes could also enhance their effect on the stock market through the entity economy mechanism; therefore policy-makers could adjust their fiscal and monetary policy to

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Table 3 The unit root test for the monthly oil price volatility series. ADF

PP

C

C&T

KPSS

C

C&T

C

C&T

TS

p value

TS

p value

TS

p value

TS

p value

TS

TS

Scale 1 (4 months)

vol shci er shior

4.733 5.584 4.529 4.783

0.000a 0.000a 0.000a 0.000a

4.713 5.579 4.677 4.746

0.001a 0.000a 0.001a 0.001a

15.425 17.925 28.377 20.334

0.000a 0.000a 0.000a 0.000a

15.331 17.895 29.308 20.223

0.000a 0.000a 0.000a 0.000a

0.045 0.098 0.091 0.072

0.043 0.047 0.048 0.051

Scale 2 (8 months)

vol shci er shior

4.296 5.534 4.207 4.653

0.001a 0.000a 0.001a 0.000a

4.277 5.539 4.400 4.639

0.003a 0.000a 0.002a 0.001a

5.916 5.667 7.715 5.447

0.000a 0.000a 0.000a 0.000a

5.874 5.640 7.758 5.400

0.000a 0.000a 0.000a 0.000a

0.047 0.097 0.097 0.051

0.046 0.043 0.047 0.045

Scale 3 (16 months)

vol shci er shior

5.086 3.956 3.449 5.361

0.000a 0.002a 0.009a 0.000a

5.095 3.985 3.667 5.322

0.000a 0.009a 0.025b 0.000a

3.121 2.918 3.420 3.110

0.025b 0.043b 0.010a 0.026b

3.103 2.935 3.407 3.074

0.105 0.151 0.051c 0.113

0.052 0.073 0.074 0.042

0.044 0.034 0.039 0.039

Scale 4 (32 months)

vol shci er shior

2.959 3.960 6.219 3.408

0.039b 0.002a 0.000a 0.011b

2.988 4.017 6.796 3.366

0.136 0.008a 0.000a 0.056c

2.846 3.106 2.906 2.779

0.052c 0.026b 0.045b 0.061c

2.852 3.149 2.922 2.749

0.178 0.095c 0.155 0.216

0.081 0.070 0.060 0.053

0.054 0.033 0.039 0.049

Scale 5 (64 months)

vol shci Dshci er Der shior Dshior

2.956 2.126 6.639 2.993

0.039b 0.234 0.000a 0.036b

3.139 2.439 6.605 3.318

0.097c 0.359 0.000a 0.063c

3.507

0.039b

2.036 2.510 6.629 2.264 8.617 2.109 7.405

0.582 0.323 0.000a 0.454 0.000a 0.541 0.000a

0.093 0.054 0.046 0.065

0.008a

0.299 0.177 0.000a 0.200 0.000a 0.245 0.000a

0.212 0.223 0.046 0.099

3.500

1.972 2.284 6.663 2.218 8.619 2.099 7.436

0.077

0.076

vol Dvol shci Dshci er Der shior Dshior

1.794 3.124 0.687 2.664 2.043 8.612 2.144 2.664

0.383 0.028b 0.850 0.084c 0.268 0.000a 0.227 0.084c

2.249 3.099 2.575 7.447 2.154 8.710 2.177 7.524

0.463 0.113 0.292 0.000a 0.516 0.000a 0.503 0.000a

1.186

0.000a

0.202

0.736 0.000a 0.417 0.000a 0.493 0.000a

0.820 0.001a 0.433 0.000a 0.747 0.000a 0.787 0.000a

0.626

1.045 7.453 1.727 8.645 1.581 7.453

1.527 4.719 2.302 7.424 1.710 8.735 1.613 7.424

0.723

0.151

0.223

0.214

0.253

0.192

Scale 6 (128 months)

Notes: TS – test statistic; C – constant; T – trend. a Denotes rejection of the null hypothesis of a unit root at the 1% level of significance. b Denotes rejection of the null hypothesis of a unit root at the 5% level of significance. c Denotes rejection of the null hypothesis of a unit root at the 10% level of significance.

Table 4 The Granger causality test results for the VAR model involving the real oil price changes (variable order: oilp, oiln, er, shior, shci). Dependent

shci oilp shci oiln shci er shci shior

Independent

oilp shci oiln shci er shci shior shci

chi-sq (prob) Scale 1 (4 days)

Scale 2 (8 days)

Scale 3 (16 days)

Scale 4 (32 days)

Scale 5 (64 days)

Scale 6 (128 days)

99.539 84.861 83.577 107.760 81.589 99.007 39.990 34.778

100.920 90.096 82.321 112.190 81.819 103.960 50.165 34.218

101.650 103.980 85.057 121.410 78.131 99.117 49.050 34.313

103.910 101.420 86.581 111.080 90.644 102.890 55.062 37.333

120.270 89.235 92.550 124.890 99.207 108.960 54.913 47.020

121.080 120.570 103.030 151.040 102.170 138.340 62.553 86.176

0.000 0.002 0.002 0.000 0.003 0.000 0.844 0.950

0.000 0.000 0.003 0.000 0.003 0.000 0.467 0.957

prevent the markets from worsening, particularly when the oil price decreases. Additionally, the investors could use this information for portfolio design and hedging strategies. Because of the limited space, we summarize the response direction of the Shanghai composition index to the net oil price changes in Table 5. The net oil price distinguishes the substantial oil price changes; generally, these types of oil price changes are caused by exogenous factors, for instance international political events. Thus, this type of oil price changes could pass their effect through the path of entity economy and the international cash flow. The Chinese stock market response to the net oil price changes fluctuates from scale 1 to scale 4. When the scale lengthens, the response direction of the stock market to the net oil price changes becomes

0.000 0.000 0.001 0.000 0.007 0.000 0.511 0.956

0.000 0.000 0.001 0.000 0.000 0.000 0.289 0.907

0.000 0.001 0.000 0.000 0.000 0.000 0.294 0.594

0.000 0.000 0.000 0.000 0.000 0.000 0.110 0.001

positive in scale 5 and then changes to negative in scale 6. Hence, we confirm that the oil price increase and decrease both could lead to the fluctuation of the Chinese stock market. Hence, similar to the situation of the real oil price changes, for scales 1–4, the net oil price changes just trigger the nonstationary of the stock markets, which could be handled by the stock market’s own mechanism. Additionally, in the long-term horizons, the response direction of the stock market becomes much more complex with the effect transmit from the multiple path. In the medium time horizons (scales 4 and 5), the stock market responds to the net oil price in a positive manner and then transforms to a negative manner in the long term (scale 6). Therefore, when the international oil price changes dramatically, it is necessary for the policy-makers and

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Fig. 1. Real oil price change shocks to stock returns. Orthogonalized impulse response function of stock returns to a real price increase and decrease from scale 1 to scale 6.

Table 5 The Granger causality test results for the VAR model involving the net oil price changes (variable order: nopi, nopd, er, shior, shci). Dependent

shci nopi shci nopd shci ex shci shi

Independent

nopi shci nopd shci ex shci shi shci

chi-sq prob Scale 1 (4 days)

Scale 2 (8 days)

Scale 3 (16 days)

Scale 4 (32 days)

Scale 5 (64 days)

Scale 6 (128 days)

66.667 66.949 82.550 124.370 81.349 93.242 40.81 36.48

74.805 69.562 87.642 125.190 82.541 98.941 52.137 33.986

70.293 76.505 83.038 130.450 78.163 95.896 52.998 32.2

86.623 84.574 90.906 124.980 90.314 98.435 64.519 34.129

80.053 84.465 135.690 154.700 66.849 91.830 108.96 48.197

134.050 90.779 132.280 185.200 89.784 138.410 97.891 75.405

0.058 0.055 0.003 0.000 0.003 0.000 0.82 0.924

0.013 0.035 0.001 0.000 0.003 0.000 0.391 0.96

0.031 0.009 0.002 0.000 0.007 0.000 0.359 0.976

0.001 0.002 0.000 0.000 0.000 0.000 0.081 0.958

0.004 0.002 0.000 0.000 0.056 0.000 0.000 0.546

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.012

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Table 6 Statistically significant impulse responses of stock returns to net oil price changes.

Shock to nopi Shock to nopd

Scale 1 (4 days)

Scale 2 (8 days)

Scale 3 (16 days)

Scale 4 (32 days)

Scale 5 (64 days)

Scale 6 (128 days)

F F

F F

F F

P F

P P

N N

Table 7 The Granger causality test results for the VAR model involving the oil price volatility (variable order: vol, er, shior, and shci). Dependent

Independent

chi-sq (prob) Scale 1 (4 months)

shci vol shci er shci shior

vol shci er shci shior shci

8.732 66.364 14.336 9.487 7.272 7.869

Scale 2 (8 months) 0.272 0.000 0.046 0.220 0.401 0.344

Table 8 Variance decomposition results of the stock returns because of the real oil price changes and exchange rate.

Scale Scale Scale Scale Scale Scale

1 2 3 4 5 6

(4 days) (8 days) (16 days) (32 days) (64 days) (128 days)

oilp

oiln

ex

oilp/ex

oiln/ex

oilp/oiln

0.052 0.058 0.041 0.062 0.035 0.055

0.046 0.038 0.048 0.047 0.077 0.074

0.044 0.038 0.040 0.042 0.028 0.026

1.181 1.517 1.020 1.498 1.254 2.138

1.038 0.985 1.202 1.123 2.798 2.908

1.138 1.539 0.849 1.334 0.448 0.735

Table 9 Variance decomposition results of the stock returns due to the net oil price changes and the exchange rate.

Scale Scale Scale Scale Scale Scale

1 2 3 4 5 6

(4 days) (8 days) (16 days) (32 days) (64 days) (128 days)

nopi

nopd

ex

nopi/ex

nopd/ex

nopi/nopd

0.038 0.050 0.035 0.048 0.053 0.095

0.040 0.059 0.064 0.060 0.081 0.076

0.045 0.043 0.043 0.047 0.038 0.022

0.862 1.164 0.809 1.033 1.373 4.378

0.888 1.379 1.488 1.288 2.114 3.494

0.971 0.844 0.543 0.802 0.649 3.494

investors to take corresponding activities to the depression of the stock market in the long run. According to the Granger causality test and impulse response function results, we find that the oil price increase and decrease both could cause shocks to the Chinese stock market. Specifically, in the short time horizon, the Chinese stock market responds to the oil price changes in a weak and fluctuating manner. When the time horizons lengthen, the real oil price increases and decreases have opposite effects, whereas the net oil price increases and decreases exert the same effect on the Chinese stock markets.

3.4. Effects of oil price volatility In this paper, we also explore whether the uncertainty caused by the oil price volatility has an impact on the Chinese stock market. The oil price volatility could reflect the uncertainty of the crude oil market and the future return [9]. The oil price volatility index is defined in a monthly frequency; therefore, the wavelet decomposition results cover 6 scales as 4 months, 8 months, 16 months, 32 months, 64 months and 128 months. Based on the unit

8.899 59.162 6.905 15.009 4.670 9.352

Scale 3 (16 months) 0.260 0.000 0.439 0.036 0.700 0.228

9.609 51.652 32.821 13.866 6.498 11.181

0.212 0.000 0.000 0.054 0.483 0.131

root test, we construct a new VAR model that includes the oil price volatility, the exchange rate, the interest rate and stock returns in scales 1, 2 and 3. The Granger causality test results are shown in Table 6. The oil price volatility has no Granger cause for the Shanghai composition index from scale 1 to scale 3, which means that the uncertainty of the oil price shocks could not affect the stock market in the short term. However, the Shanghai composition index is the Granger causality reason for oil price volatility from scale 1 to scale 3, which may be caused by the increasing volume of imported crude oil; China could exert more influence on the international oil market through a huge imported volume (see Table 7) The exchange rate could Granger cause the Shanghai composition index in scale 1, whereas an inverse relation was found in scale 2; in addition, the relation between the exchange rate and the Shanghai composition index becomes bidirectional in scale 3. No significant relation could be found between the Shanghai composition index and the interest rate. In summary, the oil price volatility has no significant relation with the Shanghai composition index in the short term (scales 1– 3). In the long term (scales 4–6), there are cointegration relations between the oil price volatility and the Chinese stock market. This result is in line with the analysis of the real and net oil price changes. Hence, we can infer that the Chinese stock market could adjust itself in the short term; however, in the long term the oil price changes and uncertainty could exert their impact on the stock market.

3.5. A comparison of oil price and exchange rate shocks We use the variance composition to compare the relative importance of the oil price changes and the interest rate (exchange rate) based on quantitatively measuring the contributions of variables to the changes in the Shanghai composition index over a period of 100 days. The contribution of the real oil price increase ranges from 0.035 to 0.062, whereas the contribution of the real oil price decrease presents an increase trend from 0.046 in scale 1 to 0.074 in scale 6. The contribution of the exchange rate decreases from 0.44 in scale 1 to 0.026 in scale 6. Through comparison of the contribution of the real oil price and the exchange rate using their ratios, we find that the real oil price changes have more influence than the exchange rate in nearly every scale. Additionally, the relative importance between the real oil price increase and decrease is varies across scales. Hence, the policy-makers and investors should

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S. Huang et al. / Applied Energy xxx (2016) xxx–xxx Table A1 The unit root test results for the daily oil price changes series. ADF

PP

C

oil shci er shior Doil Dshci Der Dshior

C&T

KPSS C

C&T

TS

p value

TS

p value

TS

C p value

TS

p value

TS

TS

2.9310 2.3170 2.6200 2.2360 3.8590 4.2900 7.2640 3.9770

0.0419 0.1665 0.0889 0.1933 0.0024 0.0005 0.0000 0.0095

2.8410 2.7240 1.7390 2.7570 3.9770 4.2250 4.6580 7.2660

0.1823 0.2262 0.7334 0.2133 0.0095 0.0041 0.0008 0.0000

2.1430 2.1430 3.0990 4.3020 42.6900 44.8860 52.2920 43.9420

0.2277 0.2278 0.0266 0.0004 0.0000 0.0000 0.0000 0.0000

1.6860 2.8490 1.3860 5.0970 42.5750 44.8580 52.0260 43.9460

0.7568 0.1795 0.8650 0.0001 0.0000 0.0000 0.0000 0.0000

1.3600 1.4400 3.4100 1.3100 0.0758 0.1570 0.0826 0.0259

0.1640 0.0886 0.4480 0.2980 0.1920 0.1630 0.6770 0.0355

Table A2 The integration test results for oil price volatility, exchange rate, interest rate and stock return in scale 4 (32 months). Hypothesized No. of CE(s)

Eigenvalue

Trace statistic

0.05 Critical value

Prob.**

None* At most 1* At most 2* At most 3*

0.363558 0.255791 0.107608 0.058951

86.65913 44.18407 16.41332 5.711446

47.85613 29.79707 15.49471 3.841466

0.0000 0.0006 0.0363 0.0168

Trace test indicates 4 cointegrating eqn(s) at the 0.05 level. * Denotes rejection of the hypothesis at the 0.05 level. ** MacKinnon–Haug–Michelis (1999) p-values.

C&T

contribution decreases as the scale lengthens. In most the scales, the contribution percentage of the net oil price changes is larger than that of the exchange, scales 5 and 6 in particular. The relevant contribution from the net oil price increase is smaller than the decrease nearly throughout scales 1–5; however, in scale 6, net oil price increase is 3 times larger (see Table 9). In summary, we find that the real and net oil price changes have a greater influence on the Chinese stock market, and the relative importance of the oil price increase and decrease varies across different scales. 4. Conclusions

Table A3 The integration test results for oil price volatility, exchange rate, interest rate and stock return in scale 5 (64 months). Hypothesized No. of CE(s)

Eigenvalue

Trace statistic

0.05 Critical value

Prob.**

None* At most 1* At most 2* At most 3

0.383606 0.287205 0.149677 0.035515

95.94866 50.46492 18.64015 3.399086

47.85613 29.79707 15.49471 3.841466

0.0000 0.0001 0.0162 0.0652

Trace test indicates 3 cointegrating eqn(s) at the 0.05 level. * Denotes rejection of the hypothesis at the 0.05 level. ** MacKinnon–Haug–Michelis (1999) p-values.

Table A4 The integration test results for oil price volatility, exchange rate, interest rate and stock return in scale 6 (128 months). Hypothesized No. of CE(s)

Eigenvalue

Trace statistic

0.05 Critical value

Prob.**

None * At most 1* At most 2* At most 3*

0.392320 0.294562 0.146389 0.054976

99.81559 52.99361 20.19358 5.315234

47.85613 29.79707 15.49471 3.841466

0.0000 0.0000 0.0091 0.0211

Trace test indicates 4 cointegrating eqn(s) at the 0.05 level. * Denotes rejection of the hypothesis at the 0.05 level. ** MacKinnon–Haug–Michelis (1999) p-values.

decrease the weight of the exchange rate as the reference information for the stock market, particularly in scales 5 and 6. The contribution of the net oil price and exchange rate to the shocks of the Shanghai composition index is shown in Table 8. The contribution of the net oil price increase is much larger in scale 6 and achieves 0.095 more than in other scales, and the contribution of the net oil price decrease increases to approximately 0.079 in scale 5 and scale 6. Additionally, the exchange rate’s

Because the oil price shocks have an asymmetric effect on the economy and the stock market could sensitively respond to the national economy, there is bitter controversy regarding the oilequity nexus. Specifically, there is a strand of literature to check whether or not the asymmetric effect of the oil price exists in the stock market; however, all of the existing literature considers this issues from the holistic perspective and ignores multiscale phenomena. In this paper, our objective is to examine whether the oil price shocks have an asymmetry effect on the Chinese stock market across different time horizons. Hence, we combine the wavelet transform and VAR model methods to explore the relation between the oil price changes and stock markets involving the exchange rate and the interest rate in multiple time horizons. Based on the Granger causality test, the impulse response function and variance decomposition in different time horizons, we derive the following conclusions: First, the oil price increase and decrease both may impact the Shanghai composition index for all scales; however, their impact varies across the time scales. Hence, we reject the hypothesis that the asymmetric effect of oil price will persist across multiple time scales. In the short term, both the oil price increase and decrease could trigger fluctuations of the stock market through the market anticipation and trading behaviors; the stock market could be capable of generating this market fluctuation by its own mechanism. However, in the medium and long term, the impact of the oil price changes could be enhanced by many factors, such as the entity economy and cash flow. Hence, it is reasonable to focus on the long-term effect of oil price changes, particularly when the oil price changes dramatically. Hence, we conclude that there is no asymmetric effect of the oil price changes on the Chinese stock market because of the significant effects of the oil price increases and decreases on the stock index across the time horizons. However, the mechanism of how the oil price change influences the Chinese stock market in different horizons needs a more detailed description; this will be addressed in further research.

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Please cite this article in press as: Huang S et al. Do oil price asymmetric effects on the stock market persist in multiple time horizons?. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.11.094