Dependence structures between Chinese stock markets and the international financial market: Evidence from a wavelet-based quantile regression approach

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

Contents lists available at ScienceDirect

North American Journal of Economics and Finance journal homepage: www.elsevier.com/locate/najef

Dependence structures between Chinese stock markets and the international financial market: Evidence from a wavelet-based quantile regression approach Lu Yanga, Shuairu Tianb, Wei Yangc, Mingli Xud, Shigeyuki Hamorie,

⁎

a

School of Finance, Zhongnan University of Economics and Law, 182 Nanhu Avenue, East Lake High-tech Development Zone, Wuhan 430-073, PR China b Research Center of Finance, Shanghai Business School, 2271 West Zhongshan Road, Shanghai 200235, PR China c School of Business, East China University of Science and Technology, 130 Meilong Road, Xuhui District, Shanghai 200-237, PR China d School of Public Administration, South China Normal University, Guangzhou Higher Education Mega Center, Guangzhou 510-006, PR China e Faculty of Economics, Kobe University, 2-1, Rokkodai, Nadaku, Kobe 657-8501, Japan

AR TI CLE I NF O

AB S T R A CT

JEL classification: C32 E44 Q43

In this study, we investigate the dependence structures between six Chinese stock markets and the international financial market including possible safe haven assets and global economic factors under different market conditions and investment horizons. The research is conducted by combining a quantile regression approach with a wavelet decomposition analysis. Although we find little or insignificant dependence under short investment horizons, we detect the strong asymmetric dependence of oil prices and the US dollar index on the six Chinese stock markets in the medium and long terms. Moreover, not only is crude oil not a safe haven, it may damage Chinese stock markets as it increases over the long term, even in bull markets. Meanwhile, appreciation of the US dollar (depreciation of RMB) damages (boosts) Chinese stock markets during bull (bear) market conditions under long investment horizons. Moreover, we find that VIX (volatility index)-related derivatives may serve as good risk management tools under any market condition, while gold is a safe haven asset only during crisis periods.

Keywords: Chinese stock market Wavelet Quantile regression analysis

1. Introduction Understanding how global economic factors influence the performance of Chinese stock markets is an important issue to market participants, particularly during bear and bull markets. Changes in global economic factors affect economic growth in China and therefore Chinese stock markets. By considering different market conditions, we can thus describe the changes in dependence structures and spillovers across assets, which is crucial information for constructing portfolios and making financial decisions (Ciner, Gurdgiev, & Lucey, 2013). With the development of the stock markets in China, Chinese investors can purchase a variety of assets. Indeed, six stock markets are available to satisfy different types of investors. First, the main markets (the Shanghai A and Shenzhen A share markets; termed SHA and SZA hereafter) consist of large companies that aim to provide investors with relatively stable dividend incomes. One

⁎

Corresponding author. E-mail addresses: [email protected] (L. Yang), [email protected] (S. Tian), [email protected] (W. Yang), [email protected] (M. Xu), [email protected] (S. Hamori). https://doi.org/10.1016/j.najef.2018.02.005 Received 13 February 2017; Received in revised form 31 January 2018; Accepted 6 February 2018 1062-9408/ © 2018 Elsevier Inc. All rights reserved.

Please cite this article as: Yang, L., North American Journal of Economics and Finance (2018), https://doi.org/10.1016/j.najef.2018.02.005

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

difference between these two markets is that most state-owned corporations are listed on the Shanghai A share market, while private corporations are listed on the Shenzhen A share market. Second, the corresponding B share markets (SHB and SZB) are suitable investment vehicles for both local and foreign investors. Third, the small enterprise market (SEM) was established in May 2004 for enterprises that do not qualify for the main market. Finally, to encourage the development of high-tech enterprises, the Chinese government launched the growth enterprise market (GEM) in September 2009, which has fewer listing requirements than the SEM. Therefore, the SEM and GEM are riskier than the main markets. This study investigates how global economic factors affect these six Chinese stock markets under different market conditions and in different investment horizons. First, separating these markets allows us to capture the landscape of the dependence structures between them and global economic factors based on their characteristics. Second, by separating time into different investment horizons, we can provide useful information for speculators (e.g., hedge funds and market makers), arbitrageurs, and long-term investors (e.g., institutional investors and bankers). In addition, this study aims to identify the safe haven assets suitable for Chinese investors since the “flight to quality” phenomenon also occurs in China (Caballero & Krishnamurthy, 2008; Baur & Lucey, 2010; Baur & McDermott, 2010). Following Mensi, Hammoudeh, Reboredo, and Nguyen (2014), we combine a quantile regression (QR) approach with a wavelet decomposition analysis. The QR approach allows us to investigate dependence at the different quantiles including the states of downturn (lower quantiles), normality (intermediate quantiles), and upturn (upper quantiles) markets. The wavelet analysis allows us to capture the whole picture of the dependence structure based on the different investment horizons studied herein. The remainder of this article is structured as follows. Section 2 provides a brief literature review. Section 3 presents the methodology. Section 4 describes the data and descriptive statistics. Section 5 presents the empirical results. Section 6 concludes the paper and discusses the implications of the findings. 2. Literature review Three types of fundamental theory can explain the interactions between local and international stock markets. Firstly, the degree of economic integration has increased significantly over recent decades. During the globalization of the international economy, international stock markets have become more integrated (Chen, Roll, & Ross, 1986), with numerous studies providing evidence by employing different approaches (Broadstock & Filis, 2014; Li, Zhang, & Gao, 2015; Vithessonthi & Kumarasinghe, 2016). Secondly, financial contagion may occur, which is when stock markets slump in one country and this causes a decline in the stock market in another country. Therefore, the comovement among different stock markets in this category cannot be explained by economic fundamentals. Other researches propose that two factors may explain the irregular comovement among stock markets, namely informational and institutional factors (see also Neaime, 2016; Wang, Xie, Lin, & Stanley, 2017). Further, Wang et al. (2017) state that financial contagion occurs dependent on the recipient country as well as the timescale. Finally, stock market characteristics themselves also affect the comovement among markets, such as industry similarity, volatility, and market size (Banz, 1981; Bekaert & Harvey, 1997; Bracker, Docking, & Koch, 1999). Since then, various factors have been introduced to investigate the reasons driving comovements among stock markets, including gold prices, oil prices, interest rates, and exchange rates (Mensi et al., 2014; Chiang & Chen, 2016; Chen & Chiang, 2016). Further, numerous studies discuss the relationship between Chinese stock markets and other financial markets (Li & Zou, 2008; Panchenko & Wu, 2009; Chan, Treepongkaruna, Brooks, & Gray, 2011; Hammoudeh, Nguyen, Reboredo, & Wen, 2014; Broadstock & Filis, 2014; Li et al., 2015). Most authors investigate dependence structures by combining two markets such as bond–stock, oil–stock, and gold–stock. For example, Li and Zou (2008) find that the T-bond market and bond–stock correlations in China bear more of the brunt of the macroeconomic contractions. Hammoudeh et al. (2014) provide evidence that commodity futures are a desirable asset class for portfolio diversification. Although these studies investigate pairs of stock markets and other financial markets in detail, they fail to incorporate other macroeconomic factors into their analyses (Mensi et al., 2014; Chiang & Chen, 2016; Chen & Chiang, 2016). For example, Chiang and Chen (2016) show that returns from emerging stock markets are determined by domestic as well as global economic factors and that a better macroeconomic climate and an improvement in liquidity help explain Chinese stock returns. Indeed, few researchers discuss the changes in the relationship between global economic factors and Chinese stock markets under different market conditions and investment horizons. We thus employ a wavelet-based QR approach to bridge this gap in the literature. 3. Methodology 3.1. QR analysis Although correlation coefficients are widely used to measure the statistical relationships between variables, they only discuss symmetric linear associations without any consideration of dependence structures. To model dependence structures between financial time series, a more sophisticated statistical tool should thus be employed. By adopting the combination of wavelet analysis and QR, this study is capable of investigating the structure of complex dependence across different time horizons. Since its introduction by Koenker and Bassett (1978), QR has been widely employed to model dependence structures. Compared with traditional regressions, it provides a more accurate landscape to analyze the effect on the dependent variable from conditional

2

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 1 Descriptive statistics of stock market index returns.

Mean Maximum Minimum Std. Dev. Skewness Kurtosis J-B Statistics Observations

SHA

SHB

SZA

SZB

SEM

GEM

0.0213 9.0332 −9.2608 0.0182 −0.5935 6.5616 1421.78 2421

0.0486 9.3672 −9.8893 0.0210 −0.5246 7.9497 2582.48 2421

0.0618 8.5078 −8.9255 0.0204 −0.7260 5.2688 731.965 2421

0.0528 8.9075 −9.1304 0.0173 −0.5935 7.1735 1899.27 2421

0.0454 9.2697 −9.8704 0.0204 −0.6322 5.2919 691.181 2421

0.0516 6.9144 −9.3319 0.0220 −0.5497 4.6153 243.403 1530

Note: SHA, SHB, SZA, SZB, SEM, and GEM denote the Shanghai A share market, Shanghai B share market, Shenzhen A share market, Shenzhen B share market, small enterprise market, and growth enterprise market, respectively. The sample period of the GEM is from June 2, 2010 to September 14, 2016. Table 2 Descriptive statistics of macroeconomic variable returns.

Mean Maximum Minimum Std. Dev. Skewness Kurtosis J-B Statistics Observations

IR

VIX

USD

GOLD

WTI

2.50E−03 0.1610 −0.2109 0.0097 −0.8512 147.4379 2104779. 2421

0.0195 0.4557 −0.4263 0.078779 0.471126 6.6027 1398.863 2421

4.01E−03 0.0595 −0.0306 0.0054 0.3755 10.7950 6186.342 2421

0.0344 0.0687 −0.1016 0.0123 −0.4221 8.4093 3023.598 2421

−0.0132 0.2128 −0.1965 0.0261 0.0908 9.3819 4111.927 2421

Note: J-B statistics are significant in all cases. IR denotes the three-month repurchase rate, VIX denotes the volatility index, USD denotes the US dollar index, Gold denotes the Gold Bullion LBM price, and WTI denotes the Crude Oil-WTI Spot Cushing price. Table 3 Spearman correlations of sample returns.

SHA SHB SZA SZB SEM GEM

IR

VIX

USD

GOLD

WTI

−0.042(0.038) −0.041(0.041) −0.060(0.003) −0.045(0.028) −0.070(0.001) −0.079(0.002)

−0.108(0.000) −0.108(0.000) −0.090(0.000) −0.101(0.000) −0.091(0.000) −0.078(0.002)

−0.050(0.013) −0.049(0.016) −0.047(0.022) −0.058(0.004) −0.041(0.042) 0.019(0.468)

0.055(0.006) 0.034(0.091) 0.056(0.006) 0.026(0.188) 0.052(0.011) 0.059(0.021)

0.097(0.000) 0.108(0.000) 0.787(0.000) 0.099(0.000) 0.077(0.000) 0.058(0.023)

Note: The numbers in parentheses are p-values. IR, VIX, USD, Gold, and WTI denote the three-month repurchase rate, volatility index, US dollar index, Gold Bullion LBM price, and Crude Oil-WTI Spot Cushing price, respectively.

variables (see Koenker, 2005) in consideration of the quantiles of the conditional distribution of the dependent variable1. The same as copula functions, QR not only measures the average or linear dependence between variables, but also examines both upper and lower tail dependence (Baur, 2013; Chuang, Kuan, & Lin, 2009; Lee & Li, 2012). Compared with the copula functions relating the quantile of both the dependent variable and the conditional variables, QR instead relates the quantile of the dependent variable to the conditional variables directly. Let y be a dependent variable that is assumed to be linearly dependent on x. The τ th conditional quantile function of y is thus specified as follows:

Q y (τ|x ) = inf{b|Fy (b|x ) ⩾ τ } =

∑

βk (τ ) xk = x ′β (τ )

(1)

k

where the conditional distribution function of y given x is denoted by Fy (b|x ) , while the degree of dependence between vector x and the τ th conditional quantile of y is measured by the QR coefficient β (τ ) . Conditional dependence is confirmed when x includes exogenous variables. Dependence is unconditional when no exogenous variables are added to x. The complete dependence structure of y is measured by the values of β (τ ) (τ ∈ [0,1]) . Specifically, the dependence of y is determined by a specific explanatory variable in vector x under three situations. In the first case, the values of β (τ ) do not change for different values of τ , which indicates the constant value of dependence. In the second case, an increasing (decreasing) value of β (τ ) comes with the value of τ , which implies a monotonically increasing (decreasing) value of dependence. In the final case, the values of β (τ ) are similar (dissimilar) for low and high quantiles, indicating symmetric (asymmetric) dependence (see Koenker (2005)). 1

For a further analysis of QR, see Koenker (2005) and Koenker and Hallock (2001).

3

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Fig. 1. Plots of the wavelet decomposed results of the Shanghai B-share market index in different scale bands.

We can estimate the coefficients β (τ ) for a given τ by minimizing the weighted absolute deviations between y and x, given by T

β ̂(τ ) = argmin ∑ (τ −1{yt

< xt β (τ )} )|yt −x t′ β (τ )|

(2)

t=1

where 1{yt < xt β (τ )} is the usual indicator function. Following the suggestion of Koenker and D’Orey (1987), the problem is solved by using the linear programming algorithm. Moreover, the pair bootstrapping procedure proposed by Buchinsky (1995) is employed to estimate the standard errors for the estimated coefficients. This procedure is used because it provides standard errors that are asymptotically valid under the heteroscedasticity and misspecifications of the QR function. 3.2. Wavelet theory In time series analysis, wavelet theory is a comparatively new and powerful tool to generate a data structure that contains segments of various lengths. Compared with the Fourier transform, which requires that the time series under study be periodic and assumes that scales do not evolve over time (Kim & Baek, 2013), one advantage of wavelet analysis is that it can decompose a time series into more elementary functions that contain information on a series (high or low scale) (Aguiar-Conraria, Azevedo, & Soares,

Fig. 2. Plots of the wavelet decomposed results of the Shenzhen A-share market index in different scale bands.

4

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Fig. 3. Plots of the wavelet decomposed results of the Shenzhen B-share market index in different scale bands.

2008; Roueff & Von Sachs, 2011). Based on the different scales of the time series, we can then draw useful information on the signal (raw data). To begin with, we consider a signal in terms of wavelets. Based on different normalization rules, two types of wavelets are defined, namely father wavelets ϕ and mother wavelets φ . The father wavelet integrates to one, while the mother wavelet integrates to zero:

∫ ϕ (t ) = 1

(3)

∫ φ (t ) = 0

(4)

The smooth and low-frequency parts of a signal are described by father wavelet, while the detail and high-frequency components are illustrated by the mother wavelet.

Fig. 4. Plots of the wavelet decomposed results of the small enterprise market index in different scale bands.

5

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Fig. 5. Plots of the wavelet decomposed results of the growth enterprise market index in different scale bands.

Fig. 6. Plots of the wavelet decomposed results of the three-month repurchase rate in different scale bands.

By using a resolution matched to its scale, the wavelet analysis can transform any function y(t) in L2 () (space for square summable functions) into different frequency components. Therefore, a sequence of projections onto the father and mother wavelets generated from ϕ and φ through scaling and translation can be constructed as follows: j

ϕj,k (t ) = 2− 2 ϕ (2−j t −k )

(5)

j

φj,k (t ) = 2− 2 φ (2−j t −k )

(6)

where j = 1,⋯,J is the scaling parameter in a J-level decomposition and k is a translation parameter. With the development of time

6

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Fig. 7. Plots of the wavelet decomposed results of the volatility index in different scale bands.

Fig. 8. Plots of the wavelet decomposed results of the US dollar index in different scale bands.

series analysis, a number of wavelet families have been introduced, namely the Haar, Daublets, Symmlets, and Coiflets (Daubechies, 1992). Thus, any wavelet representation of the signal y (t ) 2in L 2 () can be written as

y (t) =

∑ k

sJ ,k ϕJ ,k (t ) +

∑ k

dJ ,k φJ ,k (t ) +

∑

dJ − 1,k φJ − 1,k (t ) + ··· ∑ d1,k φ1,k (t ) k

k

(7)

In this representation, J is the number of multi-resolution components, sJ ,k are the smooth coefficients capturing the trend, and dJ ,k are the detail coefficients representing increasing finer scale deviations from the smooth trend. These are defined by 2

In this paper, y (t ) denotes all the raw data employed.

7

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Fig. 9. Plots of the wavelet decomposed results of the Gold Bullion LBM price in different scale bands.

Fig. 10. Plots of the wavelet decomposed results of the Crude Oil-WTI Spot Cushing price in different scale bands.

sJ ,k =

∫ y (t ) ϕJ ,k (t ) dt

(8)

dJ ,k =

∫ y (t ) φJ ,k (t ) dt

(9)

The magnitude of these coefficients measures the contribution of the corresponding wavelet function relative to the total signal. The scale factor 2 j is also called the dilation factor, while the translation parameter 2 jk refers to the location parameter. The larger the index, j the scale factor 2 j and thus the function become wider and more spread out. As the functions ϕJ ,k (t ) and φJ ,k (t ) widen, their translation parameter 2 jk also rises correspondingly. With a multi-resolution decomposition3, the decomposed signals can be described as follows: 3

See Mallat (1989), Hardin, Kessler, and Massopust (1992), and Baggett, Medina, and Merrill (1999) for details.

8

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 4 QR estimates under the wavelet decomposition for SHA. Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

Panel A: raw series Raw C IR VIX USD GOLD WTI PseudoR2

−0.030*** 0.028 −0.062*** −0.191 0.037 −0.013 0.023

−0.020*** −0.063** −0.038*** −0.162 0.039 0.043* 0.021

−0.008*** −0.085*** −0.016*** −0.076 0.050 0.033* 0.010

0.001*** −0.079** −0.007* −0.000 0.059** 0.036** 0.007

0.009*** −0.059 −0.016*** 0.106 0.102*** 0.057** 0.009

0.020*** −0.119 −0.018* −0.069 0.051 0.010 0.007

0.027*** −0.159** −0.012 −0.184 0.034 0.025 0.013

Panel B: wavelet series D1 C IR VIX USD GOLD WTI PseudoR2

−2.002*** −0.129 −0.009 0.092 −0.014 0.079 0.006

−1.403*** −0.054 −0.000 0.146 0.063 0.057** 0.003

−0.657*** −0.087** 0.004 0.059 0.070* 0.040** 0.006

−0.020 −0.105*** 0.008 −0.044 0.052 0.048*** 0.007

0.620*** −0.162*** 0.006 0.052 0.053* 0.056*** 0.006

1.382*** −0.178*** −0.011 −0.181 0.096* 0.011 0.006

2.013*** −0.106 −0.005 −0.179 0.033* 0.027 0.007

D2

C IR VIX USD GOLD WTI PseudoR2

−1.397*** −0.253* −0.035*** 0.158 0.053 0.103*** 0.027

−0.965*** −0.111 −0.033*** 0.031 0.064 0.050** 0.015

−0.484*** −0.042* −0.031*** 0.003 0.039 0.043* 0.016

0.012 −0.119*** −0.024*** −0.190** 0.028 0.027 0.017

0.467*** −0.077*** −0.030*** −0.194** 0.021 0.029 0.020

0.942*** −0.022 −0.027*** −0.248 −0.012 0.047* 0.021

1.384*** −0.046** −0.045*** −0.208 0.031 0.066** 0.022

D3

C IR VIX USD GOLD WTI PseudoR2

−0.953*** 0.152*** −0.078*** −0.041 −0.055 0.013 0.055

−0.714*** 0.122* −0.067*** −0.052 −0.014 0.013 0.047

−0.370*** −0.021 −0.056*** −0.022 0.001 0.007 0.030

−0.007 −0.070** −0.049*** 0.081 0.031 0.027 0.030

0.349*** −0.053 −0.059*** 0.036 −0.014 0.026 0.035

0.728*** 0.007 −0.074*** 0.185 0.007 0.028 0.047

1.014*** 0.022 −0.089*** 0.067 −0.040 −0.038 0.049

D4

C IR VIX USD GOLD WTI PseudoR2

−0.682*** 0.071 −0.083*** −0.003 0.193* −0.055* 0.045

−0.479*** −0.063 −0.052*** −0.249** 0.170*** 0.027 0.039

−0.239*** −0.127*** −0.058*** 0.007 0.095** 0.028 0.043

0.011 −0.150*** −0.054*** −0.175** 0.053 0.056*** 0.055

0.227*** −0.117*** −0.052*** −0.069 0.107*** 0.011 0.047

0.482*** −0.035 −0.085*** −0.065 0.161** −0.001 0.048

0.700*** −0.040 −0.122*** 0.274 0.250** −0.044*** 0.076

D5

C IR VIX USD GOLD WTI PseudoR2

−0.530*** −0.002 −0.099*** 0.548*** 0.623*** −0.059 0.099

−0.379*** −0.043 −0.046*** 0.144 0.494*** −0.035 0.065

−0.176*** 0.026 −0.015 0.146 0.338 0.068*** 0.041

0.005 0.048* −0.047*** 0.162** 0.370*** 0.063*** 0.059

0.179*** −0.007 −0.052*** 0.378*** 0.542*** 0.031 0.069

0.374*** 0.038 −0.083*** 0.318*** 0.640*** −0.054* 0.029

0.512*** −0.032 −0.076*** 0.301* 0.615*** −0.054 0.114

D6

C IR VIX USD GOLD WTI PseudoR2

−0.358*** −0.201*** −0.157*** 0.261** 0.055 −0.249*** 0.167

−0.302*** −0.210*** −0.158*** 0.185** 0.045 −0.168*** 0.118

−0.152*** −0.166*** −0.110*** −0.067 0.090 0.010 0.080

0.003 −0.044 −0.124*** −0.305** 0.226*** −0.009 0.084

0.142*** −0.087*** −0.096*** −0.222** 0.091* 0.011 0.091

0.280*** −0.040 −0.113*** 0.082 0.386*** 0.014 0.068

0.379*** 0.079 −0.148*** −0.623** 0.214** 0.114** 0.068

D7

C IR VIX USD GOLD WTI PseudoR2

−0.208*** −0.049* −0.146*** −0.122 −0.392*** 0.114*** 0.206

−0.162*** −0.098* −0.133*** −0.490* −0.239*** 0.085** 0.157

−0.080*** −0.049*** −0.129*** −0.786*** 0.062* 0.024** 0.165

−0.002 −0.080*** −0.125*** −0.406*** 0.115*** 0.048*** 0.160

0.085*** −0.138*** −0.134*** 0.504*** 0.180*** 0.119*** 0.154

0.153*** −0.128*** −0.108*** 0.597*** 0.203*** 0.208*** 0.209

0.185*** −0.252*** −0.125*** 1.052*** 0.225*** 0.187*** 0.234

(continued on next page)

9

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 4 (continued) Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

D8

C IR VIX USD GOLD WTI PseudoR2

−0.255*** −0.026*** −0.087*** 2.943*** −0.210** 0.622*** 0.157

−0.227*** −0.069*** −0.112*** 2.488*** 0.013 0.572*** 0.125

−0.088*** −0.182*** −0.263*** −0.381 0.056 0.056 0.061

0.011*** 0.007 −0.223*** −1.355*** −0.292*** −0.211*** 0.110

0.113*** −0.075 −0.196*** −0.728*** 0.252 −0.294** 0.085

0.184*** −0.127*** −0.077 −0.954*** 0.590*** −0.208*** 0.215

0.206*** −0.164*** 0.022 −0.917*** 0.481*** −0.100** 0.305

S

C IR VIX USD GOLD WTI PseudoR2

−0.154*** 0.279*** −0.725*** −0.977*** −0.520*** −0.171 0.478

−0.143*** 0.277*** −0.713*** −1.171*** −0.454*** −0.204* 0.381

−0.080*** 0.059 −0.459*** −1.452*** −0.074* 0.033 0.151

−0.016** −0.156*** −0.087 −0.496 0.101** 0.302*** 0.015

0.133*** −0.582*** 0.844*** 4.817*** 0.679*** 1.359*** 0.118

0.178*** −0.739*** 0.957*** 6.088*** 0.914*** 1.794*** 0.410

0.182*** −0.738*** 0.955*** 6.507 0.955*** 1.875*** 0.486

Note: IR, VIX, USD, GOLD, and WTI denote the three-month repurchase rate, VIX index, US dollar index, gold price, and WTI crude oil price, respectively. q = 0.05 means the lowest quantile (the most severe financial stress period), while q = 0.95 refers to the highest quantile (the highest bull market period). ***, **, and * denote significance at the 1%, 5%, and 1% levels, respectively.

∑

SJ (t ) =

sJ ,k ϕJ ,k (t )

(10)

k

DJ (t ) =

∑

sJ ,k φJ ,k (t )

(11)

k

The functions SJ (t ) and DJ (t ) denote the smooth and detail signals, respectively. They decompose a signal into orthogonal components at different scales. A signal y (t ) can be rewritten as

y (t ) = SJ (t ) + DJ (t ) + DJ − 1 (t ) + ···+DJ (t )

(12)

The highest-level approximation SJ (t ) is the smooth signal, while the detail signals D1 (t ) , D2 (t ) , …, DJ (t ) are associated with oscillations of lengths 2–4, 4–8,…, 2 J −2 J + 14 .4 3.2.1. Discrete wavelet transform (DWT) To obtain the detail signals D1 (t ) , D2 (t ) , …, DJ (t ) , we employ the wavelet filter coefficients to scale g = (g1,0,⋯,g1,L − 1,0,⋯,0)T the raw signal. Assume h1 = (h1,0,⋯,h1,L − 1,0,⋯,0)T as the wavelet filter coefficients of a Daubechies compactly supported wavelet for unit scale (see Daubechies, 1992), zero padded to length N by defining h1,j = 0 . For l > L, certain properties must be satisfied by a wavelet filter that can be found in Tiwari, Dar, and Bhanja (2013). At the same time, assume as the zero padded scaling filter coefficients, defined through g1,l = (−1)l + 1h1,L − l − 1. Meanwhile, let y0 ,⋯,yN − 1 be a time series. The time series can be filtered by using hj5 to obtain the wavelet coefficients on the condition of scales having N⩾ Lj :

1 N ∼ Wj,t = 2 j /2Wj,2 j (t + 1) + 1,⎡(L−2) ⎛1− j ⎞ ⎤ ⩽ t ⩽ ⎡ j −1⎤ (13) ⎝ 2 ⎠⎦ ⎦ ⎣2 ⎣ ∼ ∼ Lj − 1 1 j j where Lj = (2 −1)(L−1) + 1, Wj,t = j /2 ∑ j /2 hj,l x t − 1, t = Lj −1,⋯,N −1. By subsampling every 2 th of the Wj,t coefficients, we can 2 2 ∼ obtain the value of the Wj,t coefficients associated with changes to a scale of length τj = 2 j−1. In other words, the wavelet filter is a necessary way in which to obtain the detail signals D1 (t ) , D2 (t ) , …, DJ (t ) , while the scaling filter is an initial process to scale the raw data with the results of the smoothing signal. 3.2.2. Maximal overlap DWT (MODWT) In this study, we consider the MODWT as an alternative since the wavelet and scaling coefficients in it are not shift-invariant because of their sensitivity to circular shifts. Moreover, in contrast to the limitations of the orthogonal DWT, the MODWT does not require the dyadic length requirement (i.e., a sample size divisible by 2 j ). Therefore, the MODWT is employed with the following expressions:

∼ Wj,t =

Lj − 1

∑

∼ ∼ hj,l Xt′− lmod2N and Vj,t =

L−1

∑

∼ gj,l Xt′− lmod2N

(14) ∼ ∼ ∼ ∼ j/2 j/2 The scaling filters gj and wavelet filters hj are rescaled as gj = gj /2 and hj = hj /2 . The non-decimated wavelet coefficients l=0

l=0

4

For the application of wavelets to economic data, see Yang and Hamori (2015), Yang et al. (2016), and Cai et al. (2017). Both wavelet (high-pass) filter ht and scaling (low-pass) filter gt depend on the type of wavelet transform. Their expressions are illustrated in detail in the next section. 5

10

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 5 QR estimates under the wavelet decomposition for SHB. Scale

Variables

Panel A: raw series Raw C IR VIX USD GOLD WTI PseudoR2 Panel B: wavelet series D1 C

IR ×

10−3

VIX × 10−3 USD ×

D2

10−3

D4

D5

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

−0.034*** 0.050 −0.055*** −0.354 −0.114 0.092** 0.034

−0.020*** −0.047 −0.040*** −0.165 −0.010 0.064 0.021

−0.007*** −0.085*** −0.019*** 0.019 0.076 0.043*** 0.011

0.001*** −0.047*** −0.008 0.010 0.033 0.028** 0.005

0.009*** −0.079** −0.006 −0.007 0.038 0.046** 0.004

0.021*** −0.185*** −0.022** 0.095 −0.021 0.064*** 0.011

0.030*** −0.210 −0.020 −0.019 −0.041 0.095* 0.011

−0.021*** −2.636***

−0.014*** −1.710***

−0.006*** −0.358

−0.000 −0.593

0.006*** −1.141***

0.014*** −1.446***

0.022*** 1.269

0.027

−0.011

0.044

0.049

0.005

−0.097

−0.142*

0.393

0.912

0.831

−0.640

0.513

−3.405***

−2.766

0.233

0.708**

0.178

0.963**

0.224

−1.447**

0.838*** 0.005

0.629 0.003

0.468*** 0.004

0.275** 0.003

0.113 0.004

0.354 0.009

0.500 0.011

C × 10−3

−16.350***

−10.951***

−4.803***

−0.109

4.575***

11.184***

16.734***

IR × 10−3

−1.330

−0.253

0.265

−0.363

−0.365

0.397

1.211

VIX × 10−3 USD

−0.498***

−0.366***

−0.292***

−0.293***

−0.248***

−0.464***

−0.538***

0.005** 0.403

0.002 −0.470

−0.001 −0.083

−0.002*** 0.137

−0.002* −0.140

−0.003* −0.298

−0.001 −0.568

WTI × 10−3 PseudoR2

1.986***

1.241***

0.562***

0.157

0.468**

0.948***

1.820***

0.035

0.019

0.013

0.017

0.015

0.026

0.039

C × 10−3

−10.703***

−8.156***

−3.702***

−0.093

3.440***

7.791***

12.240***

IR × 10−3

1.153

1.442**

−0.297

−0.556*

−0.932***

−0.906

0.211

VIX × 10−3

−0.567***

−0.493***

−0.378***

−0.327***

−0.403***

−0.563***

−0.795***

USD × 10−3

−2.838*

−0.810

1.763

2.352***

1.787*

4.486*

3.645

GOLD × 10−3

−1.780**

−0.761

0.739

0.897**

0.487

0.921

−0.562

WTI × 10−3 PseudoR2

0.281

0.255

0.569**

0.719***

0.710***

0.914*

0.812

0.025

0.024

0.021

0.021

0.023

0.025

0.040

C × 10−3

−8.429***

−5.459***

−2.381***

−0.106

2.395***

5.677***

8.711***

IR × 10−3

1.351

−0.024

−0.628**

−0.772***

−0.873***

−0.930

−0.172

VIX × 10−3

−0.997***

−0.922***

−0.611***

−0.585***

−0.781***

−1.197***

−1.706***

USD × 10−3

9.353***

2.816

0.240

0.067

−0.686

2.955

7.880

GOLD × 10−3

2.336

0.755

0.908**

0.042

−0.016

1.343

1.849

WTI × 10−3 PseudoR2

−0.535

−0.403

0.240

0.291

0.001

0.087

−0.471

0.043

0.034

0.030

0.037

0.036

0.069

0.077

C × 10−3

−6.050***

−4.200***

−2.046***

0.035

2.062***

4.397***

5.730***

IR × 10−3

−1.435**

−0.582

0.129

0.511**

0.264

−0.641

−1.771***

VIX × 10−3 USD

−1.852***

−1.407***

−0.950***

−0.623***

−0.862***

−1.316***

−1.289***

7.481*** 9.386***

3.549** 7.186***

−0.085 4.879***

−0.087 4.533***

−1.177 5.626***

4.392*** 8.926***

4.259*** 8.286***

−1.682*** 0.107

−0.460 0.112

0.683*** 0.092

0.730*** 0.081

0.766*** 0.108

0.246 0.135

0.919*** 0.125

−4.154***

−3.169***

−1.647***

−0.013

1.581***

3.014***

4.227***

−4.526

−2.933

−0.433

***

GOLD × WTI PseudoR2

C × 10−3

−1.601

−1.637

−1.702

−3.932***

−2.062***

−1.723***

−1.491***

−1.285***

−1.200***

−0.878***

−0.709***

0.251

−1.574

−1.870*

−5.956***

−8.090***

−4.779***

0.131

GOLD × 10−3

2.143***

2.311***

2.436***

1.248**

1.849***

3.204***

2.227

WTI × 10−3 PseudoR2

−1.169***

−1.190***

−0.731**

0.284

−0.152

0.603*

1.059**

0.179

0.130

0.114

0.097

0.109

0.115

0.094

C × 10−3

−2.594***

−1.985***

−1.052***

−0.096**

1.094***

2.053***

2.731***

IR × 10−3

−4.705***

−4.339***

−3.067***

−2.910***

−3.554***

−3.330***

−4.671***

VIX × 10−3 GOLD

−0.113

−0.139

−1.711***

−2.713***

−1.676***

−1.603***

−2.068

−0.006*** 3.285***

−0.002*** 3.463***

0.001*** 1.742***

0.002*** 1.271***

0.002*** 0.785***

0.004*** 0.642

0.005 1.231

0.374

0.319

0.252

0.200

0.197

0.302

0.381

IR ×

10−3

VIX × 10−3 USD ×

D7

Q(0.25)

0.003

10−3

D6

Q(0.10)

GOLD × 10−3 WTI × 10−3 PseudoR2

GOLD × 10−3

D3

Q(0.05)

10−3

WTI × 10−3 PseudoR2

***

***

***

***

*

(continued on next page)

11

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 5 (continued) Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

D8

C × 10−3

−2.543***

−2.222***

−0.904***

0.132***

0.890***

2.059***

2.195***

IR × 10−3

−2.360***

−2.811***

−1.852***

0.774*

0.036

−3.142***

−3.205***

−0.861***

−0.890***

−3.565***

−3.242***

−2.453***

−0.601*

−0.894***

0.011*** −7.554***

0.008** −7.624***

−0.001 −0.673

−0.010*** −0.733

−0.017*** −0.950

−0.041*** 0.393

−0.041*** 0.133

WTI × 10−3 PseudoR2

4.223***

4.387***

1.025**

−2.513***

−3.524***

−3.645***

−3.983***

0.238

0.176

0.121

0.157

0.148

0.348

0.470

C × 10−3

−1.219***

−1.138***

−0.849***

0.192**

1.636***

2.046***

2.150***

IR × 10−3

4.363***

4.048***

3.336***

−0.806**

−4.910***

−6.468***

−6.693***

VIX × 10−3 USD

−10.191***

−9.950***

−8.497***

−3.291***

5.885***

7.559***

8.053***

−0.017 −0.693***

−0.015 −0.137

***

***

−0.004*** 0.598

−0.003** 0.514

VIX × USD

10−3

GOLD × 10−3

S

GOLD × 10−3 WTI PseudoR2

***

***

***

−0.014 0.581*

0.001 4.247***

0.043 8.232***

0.059 10.486***

0.066*** 10.619***

−0.003*** 0.262

0.004*** 0.065

0.014*** 0.212

0.019*** 0.409

0.021*** 0.491

Note: IR, VIX, USD, GOLD, and WTI denote the three-month repurchase rate, VIX index, US dollar index, gold price, and WTI crude oil price, respectively. q = 0.05 means the lowest quantile (the most severe financial stress period), while q = 0.95 refers to the highest quantile (the highest bull market period). ***, **, and * denote significance at the 1%, 5%, and 1% levels, respectively.

represent t the differences between the generalized averages of the data on a scale τj = 2 j−1. In addition, we adopt the common extension, refection boundary conditions, to extend the series to length 2N. For example, the unobserved samples X-1, X-2, …, X-N are assigned the observed values at X0, X1, XN-1. Therefore, the extended series Xt′ can be defined as Xt′ = Xt for t = 0, ⋯ N-1, while Xt′ = X2N − t − 1 for t = N, ⋯ , 2N-1. In particular, we employ the MODWT in this study to counter the problem that the DWT can only be applied to sample sizes that are multiples of 2. In addition, the MODWT not only can handle any sample size without introducing phase shifts that would change the location of events over time, but also allows translation-invariant as a shift in the signal without changing the pattern of the wavelet transform coefficients. 4. Sample data and descriptive statistics 4.1. Sample data We use the daily closing stock price index for the six Chinese stock markets described earlier: SHA, SHB, SZA, SZB, SEM, and GEM. In addition, we consider the three-month repurchase rate in China (IR), the US stock market volatility index (VIX), gold prices (GOLD; expressed in US dollars per ounce), West Texas Intermediate crude oil prices (WTI; expressed in US dollars per barrel), and the US dollar index (USD) as the global economic factors. The selected global macroeconomic factors are motivated by their strong linkage to the Chinese economy. For the SHA, SHB, SZA, SZB, and SEM, the daily sample spans October 10, 2006 to September 14, 2016, totaling 2421 daily observations. The sample period for the GEM runs from June 2, 2010 to September 14, 2016, with 1530 observations6. Since the Chinese stock market follows a different trading day from the international financial market, we delete the unmatched trading days to simplify the calculations. All data come from DataStream. 4.2. Statistical and stochastic properties of the data Table 1 provides the descriptive statistics of the return series under study for the Chinese stock market indexes. As shown in this table, the SZB share market shows the lowest volatility, while the GEM shows the highest. Moreover, the skewness values are negative in all cases, indicating that the Chinese stock markets experience bear markets more often. Table 2 summarizes the return series for the global macroeconomic variables. As expected, both the stock market index return series and global macroeconomic variable return series are skewed with high excess kurtosis. This finding implies the presence of high peaks and fat tails. Moreover, the Jarque–Bera test also suggests that the normality of the unconditional distributions is unsuitable for all the series. Table 3 reports the Spearman correlations of the level series between the Chinese stock market indexes and global macroeconomic variables (IR, USD, GOLD, WTI, VIX). We find a significant correlation between the Chinese stock market indexes and global macroeconomic variables with only two exceptions: the SZB–GOLD pair and the GEM–USD pair. The IR has significant and negative correlations with all six Chinese stock markets. The VIX shows significant and negative correlations with the Chinese stock markets, indicating that fear in the US stock market affects the Chinese stock market. These results imply that investors should consider the influence of the VIX when they allocate their assets to ensure they derive diversification benefits and reduce downside risk. 6 The GEM opened on October 23, 2009. It has since played an important role in providing high-tech small and medium-sized enterprises a platform on which to raise equity funding, especially during the recent economic transformation in China.

12

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 6 QR estimates under the wavelet decomposition for SZA. Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

Panel A: raw series Raw C IR VIX USD GOLD WTI PseudoR2

−0.036*** 0.066** −0.056*** −0.228 0.039 0.039 0.016

−0.023*** −0.060 −0.026*** 0.343 0.023 0.030 0.012

−0.009*** −0.122*** −0.014** −0.089 0.066 0.014 0.009

0.002*** −0.112*** −0.005 −0.032 0.064* 0.043* 0.006

0.013*** −0.177*** −0.010* −0.013 0.086** 0.056*** 0.011

0.022*** −0.139 −0.022*** 0.139 0.077 0.059** 0.009

0.030*** −0.222 −0.021 0.158 0.060 0.059** 0.013

Panel B: wavelet series D1 C × 10−3

−21.54***

−15.17***

−7.534***

−0.541*

7.198***

15.32***

23.12***

−2.886

IR ×

10−3

VIX × 10−3 USD GOLD × 10−3

D2

−0.827

−0.071

−0.177

0.804 0.113

1.791 0.153

0.753 0.642

−0.447 0.725*

−1.078 0.527

−1.780 0.751

−1.189 −0.255

***

***

0.111

0.376

***

0.463

0.003

0.006

0.006

0.006

0.005

0.005

C × 10−3

−15.79***

−11.25***

−5.862***

0.140

5.473***

11.95***

16.76***

IR × 10−3

−3.599***

−1.726**

−0.484

−1.268**

−1.042***

−0.375

0.333

VIX × 10−3 USD

−0.290**

−0.351***

−0.299***

−0.234***

−0.208***

−0.386***

−0.545***

0.004*** 0.601

−0.001 0.165

−0.002* 0.431

−0.003*** 0.735*

−0.002* 0.233

−0.002 0.036

−0.002 −0.116

1.226***

0.598**

0.322

0.217

0.280

0.367

0.60

0.021

0.011

0.014

0.017

0.0113

0.012

0.023

−11.38***

−8.907***

−4.612***

−0.153

4.317***

8.895***

11.54***

0.891

1.019**

−0.357

−0.624

−0.847**

−1.587***

−1.155**

−0.676***

−0.601***

−0.441***

−0.431***

−0.457***

−0.677***

−0.598***

−0.062 1.066

−0.862 0.050

−0.107 0.649

1.554 1.096**

0.684 0.372

3.128** 1.385**

3.251 1.512**

WTI × 10−3 PseudoR2

−0.464*

−0.189

0.028

−0.046

0.157

−0.049

−0.856**

0.022

0.024

0.016

0.015

0.017

0.027

0.028

C × 10−3

−7.730***

−5.473***

−2.793***

−0.131

2.562***

5.952***

8.098***

IR × 10−3

0.929

−0.751

−1.309***

−1.746***

−1.010***

0.144

0.419

VIX × 10−3 USD

−0.932***

−0.576***

−0.486***

−0.545***

−0.745***

−1.082***

−1.230***

−0.000 −2.032**

−0.001 −1.629***

−0.003*** 0.568

−0.002* 0.457

−0.001 1.337**

−0.004** 1.079*

−0.007** −0.049

−0.448

0.146

0.017

−0.091

−0.444**

−0.180

−0.462***

0.034

0.027

0.031

0.037

0.039

0.045

0.059

10−3

C×

10−3 10−3

GOLD × 10−3

GOLD × 10−3

WTI × 10−3 PseudoR2

C×

10−3

−6.146

***

−4.650

***

−2.223

***

0.549

0.157

**

0.494

2.050

***

4.346

***

6.120***

−2.028**

−1.291***

−0.817**

−0.589**

−0.780***

−1.050

−3.104***

−1.686***

−1.029***

−0.496***

−0.390***

−0.844***

−1.407***

−1.637***

2.604 8.041***

2.906* 7.642***

0.635 6.242***

2.026** 5.663***

3.682*** 7.160***

3.429** 7.343***

3.417** 8.077***

WTI × 10−3 PseudoR2

−1.602***

−0.862***

−0.112

−0.282

−0.553**

−1.119***

−0.834**

0.121

0.097

0.070

0.070

0.101

0.127

0.127

C × 10−3

−4.387***

−3.471***

−1.753***

−0.079

1.691***

3.325***

4.452***

IR × 10−3

−4.990***

−4.166***

−2.752***

−1.650***

−1.953***

−2.645***

−3.853***

VIX × 10−3 USD

−1.921***

−1.846***

−1.491***

−1.107***

−1.042***

−1.149***

−1.251***

0.011** −0.934

0.008*** 0.454

0.005*** 2.217***

0.002* 2.698***

0.003** 1.198**

0.011*** 2.512*

0.014*** 2.741***

WTI × 10−3 PseudoR2

−0.518

−0.853*

−0.131

0.610*

0.684**

1.743***

2.730***

0.207

0.140

0.107

0.069

0.094

0.096

0.118

C × 10−3

−2.726***

−1.924***

−1.055***

0.060*

0.979***

1.949***

2.851***

IR × 10−3

−4.775***

−4.082***

−2.677***

−3.150***

−3.359***

−3.239***

−4.835***

−0.116

0.256

−0.465

***

−0.932

−0.558

−1.252

−1.421***

0.017*** −0.531

0.005*** −1.697*

0.001 −3.747***

0.006*** 1.610***

0.008*** 3.740***

0.011*** 2.994*

0.020*** 6.026***

2.832***

3.348***

1.718***

1.536***

1.555***

0.650

2.431***

0.276

0.209

0.160

0.166

0.171

0.204

IR × 10−3 VIX × USD

10−3

GOLD × 10−3

GOLD × 10−3

D7

−1.965

0.064

0.452

VIX × USD

D6

−1.518

0.041

***

0.002

IR × 10−3

D5

−1.243

0.065

***

0.040

WTI × 10−3 PseudoR2

D4

−1.198

0.010

**

WTI × 10−3 PseudoR2

GOLD ×

D3

−1.427

−0.035

***

VIX × USD

10−3

GOLD × 10−3

WTI × 10−3 PseudoR2

***

***

***

0.251 (continued on next page)

13

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 6 (continued) Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

D8

C × 10−3

−2.513***

−2.242***

−0.861***

0.097***

1.289***

1.882***

2.080***

IR × 10−3

−2.383***

−2.469***

−4.254***

−0.626

−3.134***

−3.127***

−3.742***

−2.078***

−2.228***

−1.174***

−1.397***

−3.679***

−1.576***

−0.945**

0.007** −9.617***

0.012*** −7.815***

−0.010*** −3.636***

−0.017*** −5.723***

−0.025*** −2.837

−0.023*** 3.319***

−0.019*** 4.944***

WTI × 10−3 PseudoR2

2.027**

3.128***

2.594***

−1.976***

−4.152***

−3.194***

−2.055***

0.252

0.200

0.113

0.117

0.108

0.307

0.460

C × 10−3

−1.061***

−0.978***

−0.627***

0.546***

1.894***

2.430***

2.507***

IR × 10−3

4.171***

4.101***

3.400***

−0.811

−5.900***

−7.942***

−8.195***

VIX × 10−3 USD

−7.023***

−7.004***

−4.917***

1.363

7.678***

8.915***

9.224***

−0.024 −7.338***

−0.019 −6.691***

−0.015 −6.195***

0.013 −1.306**

***

0.044 4.695***

***

0.059 6.973***

0.063*** 7.280***

−0.004*** 0.499

−0.003** 0.401

−0.003** 0.203

0.005*** 0.023

0.015*** 0.198

0.020*** 0.371

0.021*** 0.469

VIX × USD

10−3

GOLD × 10−3

S

GOLD × 10−3 WTI PseudoR2

***

***

***

Note: IR, VIX, USD, GOLD, and WTI denote the three-month repurchase rate, VIX index, US dollar index, gold price, and WTI crude oil price, respectively. q = 0.05 means the lowest quantile (the most severe financial stress period), while q = 0.95 refers to the highest quantile (the highest bull market period). ***, **, and * denote significance at the 1%, 5%, and 1% levels, respectively.

Additionally, the USD is significantly negatively correlated with the Chinese stock markets, suggesting a tradeoff between investment in US and Chinese stock markets. However, both GOLD and WTI exhibit positive and significant correlations with all six Chinese stock markets. Although no detailed explanation has thus far been offered for this relationship, numerous studies have found a positive relationship between the Chinese stock market and crude oil prices (e.g., Zhang & Chen, 2011), possibly because the synchronization between Chinese business cycles and global macroeconomic factors (e.g., oil prices) has become a driving force. 5. Empirical results In the first step, we decompose the raw data into eight investment horizons by employing the Daublet basis. Owing to the properties of orthogonality, near symmetry, and compatibility, this approach fits the goal of the present study7. Hereafter, we employ the wavelet transform to decompose Chinese stock markets and macroeconomic factor time series into a set of eight orthogonal components, termed D1 to D88. In particular, D1 denotes 2–4 days, D2 denotes 4–8 days, D3 denotes 8–16 days, D4 denotes 16–32 days, D5 denotes 32–64 days, D6 denotes 64–128 days, D7 denotes 128–256 days, and D8 denotes 256–512 days. Figs. 1–10 plot the different wavelet components of the signal (ranging from D1 to D8) and a trend/smoothed component (S) based on the MODWTs of order J = 8 in the level series. Moreover, MODWTs are suitable to represent a time scale domain in the original series. Methodologically, we first apply the QR approach to the raw data series. Then, we apply the QR approach to the wavelet series to provide further evidence based on the classification of investment horizons above. Following the standard procedure in the QR literature, Tables 4–99 report the numerical results for the seven quantiles from 0.05 to 0.95 (i.e., the most severe financial stress period, bear market, stable market, bull market, and highest quantile or the highest bull market). In the remainder of this section, we analyze the markets by using different subsets of the independent variables. 5.1. Comovements between Chinese stock markets and the IR As shown in Panel A of Tables 4–9, the parameters of the IR from the 0.25 to 0.75 quantiles are negative and significant. Further, on the upper tail, these parameters are significantly negative for the SHA, SEM, and GEM. However, we find no significant estimates for the lower tail between the IR and Chinese stock markets. These results suggest that Chinese stock markets are more sensitive to positive interest rate shocks than to negative ones. Moreover, while interest rates may serve as a useful tool during normal market conditions, they become useless during extreme market conditions, especially bear markets. The results in Panel B of Tables 4–9 show that the IR has a stronger relationship with Chinese stock markets in longer-term investment horizons (D5–D8) than in D1–D4, especially in the tails. These results suggest that interest rates are a useful tool for adjusting asset prices in the long term regardless of the prevailing market conditions. However, they still have a limited effect on the Chinese stock market in the short term, especially in bear markets. To sum up, interest rates have a negative relationship with all six Chinese stock markets during normal market conditions and 7 Daublet wavelets proposed by and named after Ingrid Daubechies are the first orthogonal wavelets with compact support (zero outside a finite interval) such as near symmetry and various widths. Owing to their data properties, they are also chosen for this study. The detail coefficients (Ds) are the increasing finer scale deviations from the smooth trend. 8 The use of eight components exhausts all the data points. At the eighth component, we have 256–512 days, whereas the total observations are 2421 days only. Thus, any further decomposition would have been meaningless. 9 Note that the standard errors are omitted to save space.

14

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 7 QR estimates under the wavelet decomposition for SZB. Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

Panel A: raw series Raw C IR VIX USD GOLD WTI PseudoR2

−0.030*** 0.061 −0.045*** −0.099 0.026 0.135*** 0.035

−0.018*** −0.001 −0.020* −0.127 0.024 0.060 0.018

−0.007*** −0.116** −0.018*** −0.042 0.034 0.038* 0.007

0.001*** −0.046 −0.008* −0.071 −0.001 0.018 0.003

0.009*** −0.081*** −0.007 −0.104 0.024 0.013 0.006

0.018*** −0.077 −0.015* −0.019 0.019 0.049 0.007

0.025*** −0.051 −0.023** 0.010 −0.014 0.056** 0.014

Panel B: wavelet series D1 C × 10−3

−17.949***

−12.923***

−5.868***

−0.365*

5.724***

12.960***

19.152***

−1.584

−2.193

−2.770***

−0.441

−0.227

−1.299

−1.018

VIX × 10−3

0.025

0.123*

0.079*

0.044

0.041

0.051

0.003

USD × 10−3

0.269

0.553

0.596

−0.617

0.201

0.010

−1.448

GOLD × 10−3

−0.772

0.269

0.143

0.275

0.584*

−0.057

−0.811

WTI × PseudoR2

0.636*

0.543**

0.202

0.184

0.279

0.443***

0.415

0.006

0.004

0.004

0.002

0.005

0.005

0.007

C × 10−3

−13.776***

−9.665***

−4.152***

−0.076

4.287***

9.685***

13.924***

IR ×

10−3

10−3

D2

D3

D4

D5

***

***

IR × 10−3

0.316

−0.128

−0.277

−0.410

−0.056

0.515

−0.132

−0.400***

−0.344***

−0.286***

−0.189***

−0.281***

−0.323***

−0.500***

USD × 10−3

1.872

0.247

−1.257*

−2.079**

−2.267***

−1.632

−1.083

GOLD × 10−3

0.107

−0.346

−0.352

−0.297

−0.576

−0.144

−0.685

WTI × 10−3 PseudoR2

1.010***

0.902**

0.276

0.268*

0.266

0.629***

1.323***

0.023

0.022

0.016

0.014

0.016

0.021

0.031

C × 10−3

−9.603***

−6.951***

−3.233***

−0.084

3.065***

7.142***

10.421***

IR × 10−3

1.196***

0.333

−0.815*

−1.228***

−0.933***

−0.440

0.468

VIX × 10−3

−0.655***

−0.603***

−0.460***

−0.424***

−0.455***

−0.696***

−0.807***

USD × 10−3

−1.754*

−0.953

0.817

0.004

0.911

3.409**

3.149**

GOLD × 10−3

−1.107*

−0.805

0.106

0.265

0.387

0.308

0.128

WTI × 10−3 PseudoR2

0.050

0.147

0.648***

0.406**

0.540**

0.757**

0.662**

0.051

0.037

0.032

0.032

0.033

0.044

0.062

C × 10−3

−7.223***

−4.888***

−2.437***

−0.101

2.468***

5.097***

7.560***

IR × 10−3

−0.572

−0.854***

−0.481***

−1.328***

−1.296***

−0.965**

0.140

VIX × 10−3

−1.160***

−0.796***

−0.497***

−0.550***

−0.720***

−0.952***

−0.968***

USD × 10−3

5.566***

1.371

−2.840***

−2.631***

−1.721*

−0.440

3.583

GOLD × 10−3

−1.523***

−1.053**

−0.747**

0.714

0.805

1.312

1.419

WTI × 10−3 PseudoR2

−0.727

−0.436

0.168

0.308

0.105

−0.084

−0.162

0.045

0.038

0.038

0.042

0.050

0.052

0.051

C × 10−3

−4.200***

−3.109***

−1563***

−0.012

1.606***

3.292***

4.050***

IR × 10−3

−1.633***

−0.686***

−0.130

0.290*

−0.408*

−0.431**

−1.089

−0.906

−0.965

−0.929

−0.963

−0.933

−0.792***

−0.752***

10−3

***

***

***

***

***

USD × 10−3

0.002

−0.002*

−0.004***

−0.004***

−0.003***

−0.002

−0.001

GOLD × 10−3

−5.195***

−4.181***

−3.373***

3.310***

3.664***

3.434***

3.777***

WTI × 10−3 PseudoR2

−0.029

0.045

0.598***

0.144

0.295

0.231

0.461*

0.095

0.111

0.123

0.126

0.131

0.156

C×

−3.487

10−3

IR × 10−3 VIX ×

10−3

USD × 10−3 GOLD ×

10−3

WTI × 10−3 PseudoR2 D7

***

VIX × 10−3

VIX ×

D6

***

C×

IR × 10−3 VIX ×

10−3

USD × 10−3 GOLD ×

−1.269

0.044

1.317

−2.400***

−0.859***

−1.474***

−0.473**

−0.864**

−1.168**

−1.859

−1.644

−1.219

***

10−3

WTI × 10−3 PseudoR2

***

***

***

2.426

***

3.300***

−1.322

−1.174

−1.104

−1.363***

−6.464***

−5.924***

−5.376***

−9.674***

−7.408***

−8.722***

−6.984***

0.539

0.708

3.830***

1.792***

3.179***

1.518**

1.814**

−0.724***

−0.651**

−0.565***

−0.386

0.210

0.213

−0.100

0.203

0.159

0.150

0.150

0.157

0.172

−2.560

10−3

−2.940

0.149

−2.269***

***

***

***

***

***

0.166

−0.933

0.033

0.971

−2.705***

−2.126***

−1.414***

−1.640***

−1.760***

−2.396***

−3.95***

−1.898***

−1.379***

−1.959***

−2.532***

−2.462***

−2.383***

−1.971***

−0.063

−7.833***

−9.893***

−7.113***

−0.868

6.939***

9.605***

−5.722***

−2.912***

−0.617*

0.208

2.256***

3.348***

1.654***

0.146

0.878

1.050***

0.493***

−0.238**

−0.401***

0.044

0.220

0.229

0.248

0.193

0.222

0.280

0.344

***

−1.782

***

***

***

***

1.692

***

2.328***

(continued on next page)

15

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 7 (continued) Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

D8

C × 10−3

−2.074***

−1.941***

−1.046***

0.213***

0.901***

1.559***

1.799***

IR × 10−3

−1.133***

−1.402***

−1.385***

0.156

−0.261

−1.761***

−2.837***

−4.581***

−4.418***

−4.526***

−3.660***

−2.305***

−2.816***

−2.501***

−0.003 −0.010*** −0.158

−0.004 −0.011*** 0.164

−0.005 −0.006*** −0.290

−0.007*** −0.003*** −1.661***

−0.013*** −0.003*** −1.701***

−0.033*** −0.004*** −3.596***

−0.032*** −0.005*** −2.770***

VIX × USD GOLD

10−3

WTI × 10−3 PseudoR2 S

C

IR × 10−3 VIX × 10−3 USD GOLD × 10−3 WTI PseudoR2

0.377

0.265

0.165

0.194

0.219

0.364

0.463

−0.811*** 5.241***

−0.779*** 5.308***

−0.557*** 4.739***

0.521*** 0.145

1.761*** −3.675***

2.120*** −4.938***

2.201*** −4.980***

−10.229***

−10.320***

−9.362***

−5.420***

2.187***

4.294***

4.344***

−0.011*** −5.207***

−0.011*** −5.237***

−0.011*** −4.594***

0.005 −0.021

0.031*** 4.008***

0.045*** 5.903***

0.042*** 5.525***

−0.005*** 0.612

−0.005*** 0.540

−0.006*** 0.320

0.003*** 0.112

0.012*** 0.141

0.016*** 0.320

0.015*** 0.378

Note: IR, VIX, USD, GOLD, and WTI denote the three-month repurchase rate, VIX index, US dollar index, gold price, and WTI crude oil price, respectively. q = 0.05 means the lowest quantile (the most severe financial stress period), while q = 0.95 refers to the highest quantile (the highest bull market period). ***, **, and * denote significance at the 1%, 5%, and 1% levels, respectively.

over shorter investment horizons. However, they play an important role in determining asset prices over long-term investment horizons regardless of the market conditions. Therefore, in the short term, investors need pay little attention to a sudden decrease in interest rates. By contrast, considering adjustments in the IR is crucial for investors over the long term. Overall, interest rates are of great significance for investment decisions on portfolio design and asset allocation for all Chinese investors over long investment horizons. 5.2. Comovements between Chinese stock markets and the VIX The relationship between Chinese stock markets and the VIX (which measures fear in the US stock market) is typically negative and asymmetric across different market conditions. That said, as highlighted in Panel A of Tables 4–9, SHA and SHB show no upper tail dependence, while the other markets show negative relationships with the VIX. These results confirm that the Chinese stock markets would be unable to protect investment during periods of high financial stress. In shorter investment horizons, especially D1, we find no relation between Chinese stock markets and the VIX under any market conditions. However, the significance of the results for all markets increases in D2 and D3, with negative relationships between Chinese stock markets and the VIX in most cases. The only exception is SZB. These results indicate that the stress in the US equity market affects the Chinese stock market. Indeed, even short-term traders must consider the stress in the US equity market except when making overnight transactions. For the medium- and long-term investment horizons, the VIX is negatively linked to Chinese stock markets with an increasing coefficient value regardless of the market conditions. Hence, the VIX increases its impact on Chinese stock markets as the investment horizons lengthen. Moreover, VIX-based contracts may also serve as a risk hedge tool when designing portfolios and asset allocations. 5.3. Comovements between Chinese stock markets and the USD According to Panel A of Tables 4–9, although there is no significant dependence in the main markets (SHA, SHB, SZA, SZB), a positive relationship in the upper tail is observed between the SEM and GEM (i.e., high-risk markets) and the USD. This asymmetric dependence indicates that the appreciation of the US dollar (depreciation of RMB) boosts high-risk markets during bull conditions. For the short investment horizons, the parameters are not significant. As the investment horizon lengthens, the number of significant cases increases. Generally, we observe positive estimates between Chinese stock markets and the USD for medium-term investment horizons under all market conditions. However, this relationship changes in D8 to a negative one for the upper tail, while the lower tail remains positive. The asymmetric dependence structure thus suggests that the appreciation of the US dollar (depreciation of RMB) damages the Chinese stock market during bull conditions but boosts it during bear conditions under long investment horizons (Chen & Chiang, 2016). Overall, the dependence structure between Chinese stock markets and the USD is complex. In the short term, there seems to be no significant relationship, while the relationship becomes positive in the medium term under all market conditions. Lastly, in the long term, the relationship in the lower (upper) tail is positive (negative). 5.4. Comovements between Chinese stock and commodity markets Panel A in Tables 4–9 highlights the strong positive relationship between the gold market and GEM under normal market conditions. Nguyen, Bhatti, Komorníková, and Komorník (2016) show that gold can only be a safe haven asset during market crashes in 16

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 8 QR estimates under the wavelet decomposition for the SEM. Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

Panel A: raw series Raw C IR VIX USD GOLD WTI PseudoR2

−0.035*** 0.045 −0.055*** −0.163 0.084 0.002 0.012

−0.024*** −0.036 −0.029*** −0.167 0.038 0.015 0.011

−0.009*** −0.142*** −0.019** −0.072 0.063 0.018 0.009

0.002*** −0.125*** −0.009 −0.083 0.055 0.037 0.008

0.012*** −0.179*** −0.012* 0.019 0.076* 0.048 0.009

0.023*** −0.170* −0.015** 0.201** 0.060 0.084*** 0.013

0.030*** −0.292*** −0.016** 0.140* 0.075 0.046* 0.016

Panel B: wavelet series D1 C × 10−3

−20.717***

−15.442***

−7.939***

−0.520*

7.266***

15.471***

22.96*** −0.005

−2.220

−2.704

−1.369

−1.648

−1.113

−2.083

VIX × 10−3

−0.039

0.070

0.034

−0.006

0.026

−0.016

−0.100

USD × 10−3

−0.953

0.955

1.066

0.052

−0.583

−2.610*

−1.505

GOLD × 10−3

−0.226

−0.223

0.769*

0.704*

0.608

0.266

−0.645

WTI × PseudoR2

0.180

0.498**

0.428**

0.487**

0.195

0.186

0.101

0.002

0.004

0.006

0.005

0.002

0.004

0.002

C × 10−3

−16.396***

−11.757***

−6.059***

−0.009

5.689***

11.800***

17.016***

IR ×

10−3

10−3

D2

D3

−1.197

−1.547

−0.616

−1.386***

−0.857*

−0.704

0.244

−0.462***

−0.308***

−0.218***

−0.199***

−0.181***

−0.302**

−0.428***

USD × 10−3

4.236**

0.125

−1.362

−2.597***

−1.481

−3.781**

−2.941

GOLD × 10−3

0.925

0.720

0.389

0.776

0.522

−0.032

0.566

WTI × 10−3 PseudoR2

1.038***

0.296

0.194

0.272

0.385*

0.426

0.488

0.020

0.008

0.009

0.014

0.012

0.012

0.022

C × 10−3

−11.696***

−8.673***

−4.678***

−0.101

4.424***

8.849***

11.904***

IR × 10−3

0.465

0.826*

−0.115

−1.013**

−0.964

−1.443***

−1.802***

VIX × 10−3

−0.644***

−0.589***

−0.440***

−0.444***

−0.464***

−0.565***

−0.775***

2.245

−1.107

−0.205

0.747

1.522

3.999**

5.170***

GOLD × 10−3

−1.509**

0.365

0.503

0.320

0.347

1.103

1.638

WTI × 10−3 PseudoR2

−0.615

−0.434**

0.160

0.199

0.162

0.065

−0.226

0.025

0.026

0.017

0.014

0.015

0.027

0.038

C × 10−3

−7.436***

−5.421***

−2.858***

−0.074

2.678***

5.803***

7.983***

10−3

IR × 10−3

−0.265

−1.313***

−1.875***

−2.110***

−1.735***

−0.304

0.089

VIX × 10−3

−0.779***

−0.512***

−0.513***

−0.482***

−0.647***

−0.874***

−1.156***

USD × 10−3

0.942

0.991

−2.897***

−2.717**

−0.062

−2.291*

−3.498*

−0.174

0.219

0.904

1.127

WTI × 10−3 PseudoR2

−0.023

0.355

0.126

−0.100

−0.135

0.246*

0.033

0.028

0.032

0.038

0.034

0.047

0.061

C × 10−3

−5.962***

−4.383***

−2.191***

0.112

2.056***

4.219***

5.743***

IR × 10−3

−3.281***

−1.780***

−1.318***

−0.643**

−1.050***

−1.443***

−3.184***

−1.812

−1.254

***

−0.792

−0.635

−0.906

−1.578

−1.656***

0.003* −6.315***

0.004*** 6.057***

0.003*** 6.376***

0.005*** 6.894***

0.003* 7.226*** −0.575*

VIX × USD

10−3

10−3

***

−0.972

*

***

***

***

**

0.532 −0.205

***

0.003* −6.353***

−0.772

−0.414

0.092

−0.523**

−0.512*

−0.553*

0.130

0.105

0.085

0.083

0.102

0.124

0.132

−3.994***

−3.072***

−1.746***

0.011

1.620***

3.267***

4.029***

−4.255***

−4.347***

−3.848***

−2.848***

−2.986***

−3.971***

−5.036***

−1.765***

−1.633***

−1.493***

−1.022***

−0.960***

−1.177***

−1.069***

USD × 10−3

7.335***

3.205*

1.452

0.719

2.646**

6.653***

8.275***

GOLD × 10−3

0.561

−0.288

0.423

1.069**

0.026

1.377*

1.656**

−0.174

−0.599

−1.420

−0.384

0.175

0.955

0.233

0.187

0.128

0.100

0.107

0.153

0.191

−2.608***

−1.969***

−1.058***

0.005

1.015***

2.049***

2.754***

IR × 10−3

−4.371***

−4.426***

−3.157***

−3.393

−3.826***

−3.530***

−4.770***

VIX × 10−3 USD GOLD

−0.316

−0.104

−0.443***

−1.242***

−0.851***

−1.573***

−1.615***

***

***

GOLD ×

10−3

C×

10−3

IR × 10−3 VIX ×

10−3

10−3

WTI × PseudoR2 D7

−1.816

*

0.001 −5.910***

WTI × 10−3 PseudoR2 D6

***

IR × 10−3

GOLD ×

D5

***

VIX × 10−3

USD ×

D4

*

C×

10−3

WTI × 10−3 PseudoR2

***

***

***

***

**

1.582***

***

0.015 0.002** 2.465***

0.011 0.006*** 2.473***

0.004 0.006*** 1.620***

0.012 0.003*** 1.640***

0.010 0.004*** 1.613***

0.016 0.006*** 1.004**

0.021*** 0.008*** 1.556

0.299

0.252

0.204

0.188

0.199

0.267

0.337 (continued on next page)

17

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 8 (continued) Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

D8

C × 10−3

−2.121***

−1.887***

−0.997***

IR × 10−3

−2.222***

−2.225***

−3.388***

0.039

1.182***

1.78***

1.922***

−1.955***

−3.643***

−3.306***

−1.830***

−2.069***

−3.666***

−1.819***

−1.429***

−4.463***

−3.568***

0.017*** −2.523***

−3.802***

0.019*** −0.333

0.001 −1.431

−0.013*** −2.273

−0.023*** −3.989***

−0.022*** 1.497

−0.025*** 0.865

WTI × 10−3 PseudoR2

3.032***

3.580***

2.134***

−0.880

4.105***

−4.377***

−4.799***

0.266

0.240

0.119

0.108

0.096

0.309

0.482

C × 10−3

−1.006***

−0.967***

−0.772***

0.446***

1.541***

2.023***

2.110***

IR × 10−3

5.304***

5.154***

4.308***

−0.272

−4.143***

−5.903***

−6.224***

VIX × 10−3 USD

−5.636***

−5.426***

−4.596***

0.506

5.267***

6.427***

6.850***

***

−0.006 −7.433***

***

−0.006 −7.226***

−0.005*** 0.462

−0.005*** 0.369

VIX × USD

10−3

GOLD × 10−3

S

GOLD × 10−3 WTI PseudoR2

−0.006 −6.355***

***

0.025 −0.293

***

0.041 5.007***

***

0.057 7.039***

0.059*** 7.379***

−0.004*** 0.203

0.007*** 0.056

0.013*** 0.182

0.017*** 0.325

0.018*** 0.423

**

Note: IR, VIX, USD, GOLD, and WTI denote the three-month repurchase rate, VIX index, US dollar index, gold price, and WTI crude oil price, respectively. q = 0.05 means the lowest quantile (the most severe financial stress period), while q = 0.95 refers to the highest quantile (the highest bull market period). ***, **, and * denote significance at the 1%, 5%, and 1% levels, respectively.

certain countries, indicating that it may not be a perfect hedge tool in the financial market. For the other Chinese stock markets, there is no significant relationship with GOLD. Further, although the dependence between WTI and the Chinese stock market is positive, this relationship depends on the market conditions (e.g., upper tail dependence with WTI for the other markets). In particular, tail dependences with the crude oil market are observed for both SHB and SZB. These results indicate that a rise in oil prices improves the performance of Chinese stock markets, especially during tranquil periods. In other words, both markets are more positively integrated with each other in bull markets. For investment horizons under one year, as shown in Panel B of Tables 4–9, we find no significant relationship between GOLD and Chinese stock markets except for the GEM. However, as the investment horizon increases, gold behaves as a safe haven asset during crisis periods since there is a negative relationship between GOLD and Chinese stock markets (Ciner et al., 2013). By contrast, the dependence with Chinese stock markets turns positive as the market conditions improve. Moreover, the positive average and tail dependence the Chinese stock markets and WTI is also observed for GOLD; however, the level of significance is sensitive to bear, tranquil, and bull market conditions. In contrast to GOLD, as the investment horizon increases, crude oil cannot be considered to be a diversification tool for Chinese stock markets during crisis periods since a positive relationship between the crude oil market and Chinese stock markets is observed. In the long term, we observe negative (positive) tail dependence with gold assets in bear (bull) markets. Moreover, the dependence between WTI and Chinese stock markets turns negative as market conditions improve. In sum, for investment horizons of less than one year, gold may not serve as a risk hedge asset; however, it behaves more as a safe haven asset for the Chinese stock market as investment horizons increase. The case for WTI is contrary to that for GOLD. Overall, the results indicate that gold assets can still be a risk hedge asset during crisis periods, while an increase in crude oil prices damages Chinese stock markets, even under bull conditions, in the long term. 5.5. Robustness check In this section, we employ the Wald robustness test (see Koenker & Bassett, 1982) to check the stability of the results classified by investment horizon by applying nonparametric regression analysis, which is capable of checking parameter heterogeneity across any two quantiles. The coefficients for each quantile have the same slope (are significantly different) is the null (alternative) hypothesis assumes. Table 10 reports the results of these heterogeneity tests with different quantiles. To simplify the presentation of the results, only the empirical results for the lowest quantile (q = 0.05) against the highest quantile (q = 0.95) and for the medium quantile (q = 0.5) against the highest quantile are provided. According to Table 10, the null hypothesis is rejected for the homogeneity of parameters regardless of the quantile. The results provide evidence that the estimated coefficients are time-varying. To sum up, we can state that the dynamic relationship between the Chinese stock market and global economic factors exists as a result of different market conditions and time horizons. 6. Conclusion This study examines the dependence between six Chinese stock markets (SHA, SHB, SZA, SZB, SEM, GEM) and the international financial market including possible safe haven assets and global economic factors by implementing a combined QR–wavelet

18

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 9 QR estimates under the wavelet decomposition for the GEM. Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

Panel A: raw series Raw C IR VIX USD GOLD WTI PseudoR2

−0.038*** −0.377 −0.078*** 0.458 0.114 −0.019 0.029

−0.026*** −0.125 −0.045** 0.349 0.289** −0.002 0.016

−0.011*** −0.183** −0.011 0.128 0.150*** 0.025 0.007

0.002*** −0.160** −0.001 0.005 0.120** 0.073** 0.010

0.014*** −0.079 −0.012 0.326** 0.185*** 0.062* 0.009

0.026*** −0.106*** −0.006 0.425** 0.155 0.074** 0.013

0.035*** −0.165*** −0.035** 0.463** 0.115 −0.032 0.015

Panel B: wavelet series D1 C × 10−3

−22.504***

−16.652***

−8.374***

−0.224

8.480***

17.812***

24.603***

−4.779

−2.921

−1.186

−2.806

−3.180

−2.053

−0.287

0.048

0.001

−0.075

0.021

−0.033

−0.093

−0.450***

IR ×

10−3

VIX × 10−3 USD

0.001 1.520***

0.001 0.245

0.002 0.371

0.004 0.440

WTI × 10−3 PseudoR2

0.761

0.144

0.155

0.379

0.277

0.282

−0.545

0.011

0.007

0.007

0.008

0.005

0.003

0.014

C × 10−3

−18.185***

−13.243***

−6.653***

−0.037

6.542***

13.752***

18.295***

IR × 10−3

−2.317***

−1.092

−0.856**

−0.019

−0.020

−0.585

1.822***

VIX × 10−3 USD GOLD

−0.432**

−0.267*

−0.226**

−0.239**

−0.152

−0.243

−0.426**

0.006*** 0.058 0.468

0.003* 0.001 −0.017

0.009 0.002*** −0.038

−0.001 0.002*** 0.034

−0.001 0.001* 0.700*

0.001 0.001 0.817

0.002 0.001 0.951*

0.016

0.006

0.009

0.011

0.009

0.005

0.019

C × 10−3

−12.471***

−9.621***

−5.068***

−0.183

5.105***

10.291***

13.384***

IR × 10−3

−0.022

0.480

−0.084

−0.554

−0.774

−1.747

−1.817***

VIX × 10−3

−0.511**

−0.383***

−0.111

−0.157*

−0.178*

−0.734***

−0.858***

WTI × 10−3 PseudoR2

D5

0.458

0.339

3.556**

2.735

6.412***

3.254

0.002* 0.027

0.003*** 0.321

0.002*** 0.683*

0.003*** 0.704

0.003*** −0.285

0.004*** −1.089

0.014

0.016

0.015

0.012

0.013

0.031

0.051

−7.930

−5.761

−0.115

3.138

−2.269***

−1.586***

−1.050***

−1.260***

−1.149***

−0.775*

−0.790

VIX × 10−3

−0.914***

−0.665***

−0.431***

−0.556***

−0.848***

−1.141***

−1.630***

USD × 10−3

−1.271

−1.235

−0.659

0.442

1.447

0.981

−2.014

GOLD × 10−3

1.756

0.666

0.186

1.030*

0.908

1.145

1.567

WTI × 10−3 PseudoR2

−1.584**

−1.273**

−1.911***

−1.582***

−1.989***

−2.486***

−1.686***

0.069

0.039

0.029

0.027

0.044

0.058

0.099

C×

10−3

VIX × USD GOLD

10−3

WTI × 10−3 PseudoR2

***

***

−3.249

***

6.185

***

8.695***

−6.430

−4.736

−0.102

2.280

−2.865**

−2.562***

−2.188***

−2.056***

−1.958***

−2.950***

−4.276***

−1.740***

−1.616***

−0.767***

−0.742***

−0.604***

−1.277***

−2.048***

0.003 0.001 −0.745

−0.003 0.001 −1.187*

0.005*** 0.002* 0.393

0.006*** 0.004*** −0.975***

0.010*** 0.002*** −1.372***

0.009*** 0.003*** −2.369***

0.004 0.001 −2.400***

***

***

−2.215

***

***

***

4.452

***

6.636***

0.106

0.074

0.065

0.072

0.080

0.088

0.131

C × 10−3

−4.172***

−3.335***

−1.801***

0.102

1.800***

3.235***

4.710***

IR × 10−3

−3.036***

−2.308***

−1.739***

−1.017***

−0.617*

−0.802*

−2.200*

VIX × 10−3 USD GOLD

−1.564***

−1.123***

−0.009

0.288

0.226

−1.022***

−0.953**

0.007*** −0.005*** −3.032***

0.012*** −0.007*** −4.840***

0.013*** 0.007*** −5.519***

0.010*** 0.006*** −4.820***

0.009*** 0.006*** −5.427***

0.015*** 0.006*** −4.931***

0.031*** 0.011*** −3.646**

WTI × 10−3 PseudoR2 D7

−1.655 0.003*** −0.277

IR × 10−3

C×

10−3

IR × 10−3

D6

***

0.003 1.430**

USD × 10−3 GOLD

D4

**

***

0.003 0.924

WTI × 10−3 PseudoR2 D3

*

***

0.004 −1.044

GOLD × 10−3

D2

***

0.158

0.176

0.139

0.122

0.143

0.087

0.085

C × 10−3

−3.180***

−2.021***

−1.221***

−0.115

1.383***

2.455***

2.954***

IR × 10−3

1.601***

0.095

−0.519**

−2.354***

−3.069***

−2.640***

−1.261

VIX × 10−3 USD

−2.165***

−1.715***

−0.924***

−0.621***

−1.413***

−2.546***

−2.878***

−0.024*** 9.684***

0.001 8.635***

0.010*** 6.671***

0.016*** 9.501***

0.022*** 8.273***

0.036*** 9.550***

0.036*** 9.686***

−5.681***

−4.838***

−4.881***

−3.887***

−5.591***

−6.543***

−6.425***

0.413

0.301

0.189

0.141

0.196

0.289

0.418

GOLD × 10−3

WTI × 10−3 PseudoR2

(continued on next page)

19

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Table 9 (continued) Scale

Variables

Q(0.05)

Q(0.10)

Q(0.25)

Q(0.50)

Q(0.75)

Q(0.90)

Q(0.95)

D8

C × 10−3

−0.826***

−0.665***

−0.364***

0.058***

0.464***

0.732***

0.783***

IR × 10−3

−0.577*

−0.863***

−1.774***

−1.777***

−1.586***

−1.967***

−2.137***

−2.214***

−1.857***

−1.048***

−0.418***

−0.187

−0.073

−0.025

USD × 10−3

−10.918***

−10.903***

−15.398***

−10.118***

−4.635***

−2.257***

−2.152***

GOLD × 10−3

−7.951***

−8.466***

−9.057***

−6.645***

−5.015***

−5.891***

−6.071***

WTI × 10−3 PseudoR2

−7.624***

−7.561***

−6.550***

−4.864***

−3.584***

−2.372***

−2.183***

0.725

0.691

0.653

0.585

0.584

0.628

0.640

−3.195***

−3.396***

−3.582***

−1.858***

−0.659***

0.307***

0.533***

−8.241***

−7.618***

−6.042***

−2.389***

−2.122***

−2.218***

−2.409***

6.222***

6.406***

6.410***

4.967***

5.079***

4.914***

5.127***

−0.011*** −0.034*** −0.964**

−0.009* −0.039*** −2.755***

0.011** −0.048*** −3.748***

0.006*** 0.034*** −6.226***

−0.005** 0.022*** −4.649***

−0.018*** 0.012*** −3.632***

−0.018*** 0.010*** −2.599***

0.453

0.450

0.463

0.547

0.589

0.558

0.547

VIX ×

S

C×

10−3

10−3

IR × 10−3 VIX × USD GOLD

10−3

WTI × 10−3 PseudoR2

Note: IR, VIX, USD, GOLD, and WTI denote the three-month repurchase rate, VIX index, US dollar index, gold price, and WTI crude oil price, respectively. q = 0.05 means the lowest quantile (the most severe financial stress period), while q = 0.95 refers to the highest quantile (the highest bull market period). ***, **, and * denote significance at the 1%, 5%, and 1% levels, respectively. Table 10 Heterogeneity tests (Wald tests) for the equality of the slopes. SHA

SHB

SZA

SZB

SEM

GEM

tau1 = c(0.05.0.95) Raw 12.95(0.024) D1 1.363(0.928) D2 6.737(0.241) D3 7.067(0.216) D4 6.514(0.259) D5 1.945(0.857) D6 129.09(0.000) D7 160.28(0.000) D8 268.72(0.000) S 25124(0.000)

4.914(0.426) 24.27(0.002) 9.328(0.096) 3.493(0.625) 10.16(0.071) 30.48(0.000) 55.47(0.000) 40.19(0.000) 1122.1(0.000) 21093(0.000)

6.793(0.237) 2.087(0.837) 75.44(0.000) 11.22(0.047) 5.671(0.339) 3.958(0.553) 59.52(0.000) 63.94(0.000) 1929.2(0.000) 19556(0.000)

15.11(0.001) 19.87(0.001) 6.962(0.224) 20.24(0.001) 4.975(0.247) 7.439(0.189) 33.42 (0.000) 67.85 (0.000) 727.1(0.000) 15175(0.000)

15.41(0.008) 0.411(0.995) 6.965(0.223) 11.54(0.042) 7.550(0.182) 1.441(0.919) 42.51(0.000) 49.47(0.000) 1428.5(0.000) 14796(0.000)

18.56(0.004) 1.227(0.802) 5.127(0.241) 5.554(0.446) 8.151(0.212) 2.811(0.812) 44.88(0.000) 58.55(0.000) 1478.1(0.000) 14877(0.000)

Tau2 = c(0. 5.0.95) Raw 22.17(0.014) D1 5.274(0.872) D2 53.61(0.001) D3 51.35(0.000) D4 57.34(0.000) D5 66.19(0.001) D6 242.39(0.000) D7 463.65(0.001) D8 1125.7(0.001) S 25398(0.000)

33.22(0.000) 34.38(0.002) 110.87(0.000) 50.10(0.000) 110.87(0.000) 271.75(0.000) 195.08(0.000) 701.64(0.000) 2592.1(0.000) 21994(0.000)

35.38(0.000) 8.806(0.551) 109.24(0.000) 19.13(0.039) 93.23(0.000) 197.99(0.000) 109.24(0.000) 330.01(0.000) 2180.4(0.000) 20047(0.000)

61.88(0.000) 58.09(0.000) 32.70(0.000) 119.37(0.000) 97.13(0.000) 77.09(0.000) 75.37(0.000) 356.99(0.000) 1258.9(0.000) 16505(0.000)

46.11(0.000) 5.261(0.873) 33.52(0.000) 36.36(0.000) 55.52(0.000) 168.96(0.000) 100.81(0.000) 272.43(0.000) 1750.4(0.000) 15956(0.000)

26.46(0.000) 4.2131(0.523) 30.22(0.000) 44.46(0.000) 50.05(0.000) 134.16(0.000) 151.88(0.000) 244.63(0.000) 1548.2(0.000) 14,484 (0.000)

Note: This table presents the estimation results of the Wald test for the equality of slopes (0.05 against the 0.5 and 0.95 quantiles). The p-values are in parentheses. The bold type indicates statistical significance at the 5% level.

approach. In addition, we analyze different market conditions and investment horizons to compare and contrast our empirical evidence and report a number of important findings. For the IR, the empirical evidence first shows a negative relationship with Chinese stock markets during normal market conditions for shorter investment horizons. However, its importance increases in the long term regardless of the market conditions. Second, although there is little evidence in the short term for the VIX, we find that it is negatively linked to Chinese stock markets with increasing coefficient values for longer investment horizons, regardless of the market conditions. Third, the dependence structure between Chinese stock markets and the USD index is complex. In the short term, there seems to be no significant relationship, while the relationship turns positive under medium-term investment horizons in all market conditions. Lastly, the asymmetric dependence structure for the USD (i.e., lower tail dependence is positive, while upper is negative in the long term) suggests that the appreciation of the US dollar (depreciation of RMB) damages (boosts) Chinese stock markets during bull (bear) market conditions under long investment horizons.

20

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Moreover, in contrast to the literature, we find that gold cannot serve a strong hedge of Chinese stock markets in the short term. However, as the investment horizons lengthen, gold becomes a safe haven asset for Chinese stock markets, especially during crisis periods. On the contrary, not only is crude oil not a safe haven, it may damage Chinese stock markets as it increases over the long term, even in bull markets. Some important policy and economic implications can be derived from the presented findings. By considering the relationship with global macroeconomic factors, investors can gain diversification benefits and additional returns from their portfolios without increasing risk by diversifying into different asset classes. Specifically, the identification of the dependence structures between the Chinese stock and crude oil markets can provide useful information for portfolio managers and policymakers. Indeed, Chinese stock markets are positively related to oil prices during crisis periods, while negatively related to oil prices during tranquil periods in the long term. This result shows that oil assets can serve as a diversification tool during crises, while oil shocks damage the Chinese stock market in bull conditions. Therefore, investors should consider this information when constructing their portfolios, while policymakers should pay attention to oil shocks when Chinese stock markets are buoyant. Moreover, policymakers should be prudent in discerning the effects of oil price changes on the Chinese economy since China is becoming heavily dependent on overseas oil supplies. Overall, they should use the information presented herein related to gold prices, interest rates, the VIX, and the USD when making their risk management and portfolio diversification decisions. Acknowledgments We are grateful to an anonymous referee for helpful comments and suggestions. This research is supported by the Project of National Natural Science Funds for Young Scholars (Grant No. 71601185/71403294), the Key Project of the Ministry of Education of China in Philosophy and Social Sciences under Grant 16JZD016, and JSPS KAKENHI Grant Number (A) 17H00983. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.najef.2018.02. 005. References Aguiar-Conraria, L., Azevedo, N., & Soares, M. J. (2008). Using wavelets to decompose the time–frequency effects of monetary policy. Physica A, 387(12), 2863–2878. Baggett, L. W., Medina, H. A., & Merrill, K. D. (1999). Generalized multi–resolution analyses and a construction procedure for all wavelet sets in Rn. Journal of Fourier Analysis and Applications, 5, 563–573. Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3–18. Baur, D. G. (2013). The structure and degree of dependence: A quantile regression approach. Journal of Banking & Finance, 37, 786–798. Baur, D., & Lucey, B. (2010). Is gold a hedge or safe haven? An analysis of stocks bonds and gold. Financial Review, 45, 217–229. Baur, D. G., & McDermott, T. K. (2010). Is gold a safe haven? International evidence. Journal of Banking & Finance, 34, 1886–1898. Bekaert, G., & Harvey, C. R. (1997). Emerging equity market volatility. Journal of Financial Economics, 43, 29–77. Bracker, K., Docking, D. S., & Koch, P. D. (1999). Economic determinants of evolution in international stock market integration. Journal of Empirical Finance, 6, 1–27. Broadstock, D. C., & Filis, G. (2014). Oil price shocks and stock market returns: New evidence from the United States and China. Journal of International Financial Markets, Institutions and Money, 33, 417–433. Buchinsky, M. (1995). Estimating the asymptotic covariance matrix for quantile regression models: A Monte Carlo study. Journal of Econometrics, 68, 303–338. Caballero, R. J., & Krishnamurthy, A. (2008). Collective risk management in a flight to quality episode. The Journal of Finance, 63, 2195–2230. Cai, X. J., Tian, S., Yuan, N., & Hamori, S. (2017). Interdependence between oil and East Asian stock markets: Evidence from wavelet coherence analysis. Journal of International Financial Markets, Institutions & Money, 48, 206–223. Chan, K. F., Treepongkaruna, S., Brooks, R., & Gray, S. (2011). Asset market linkages: Evidence from financial, commodity and real estate assets. Journal of Banking & Finance, 35, 1415–1426. Chen, N. F., Roll, R., & Ross, S. A. (1986). Economic forces and the stock markets. Journal of Business, 59, 383–403. Chen, X., & Chiang, T. C. (2016). Stock returns and economic forces: An empirical investigation of Chinese markets. Global Finance Journal, 30, 45–65. Chiang, T. C., & Chen, X. (2016). Stock returns and economic fundamentals in an emerging market: An empirical investigation of domestic and global market forces. International Review of Economics & Finance, 43, 107–120. Ciner, C., Gurdgiev, C., & Lucey, B. (2013). Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates. International Review of Financial Analysis, 29, 202–211. Chuang, C. C., Kuan, C. M., & Lin, H. Y. (2009). Causality in quantiles and dynamic stock return–volume relations. Journal of Banking & Finance, 33, 1351–1360. Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia: SIAM. Hammoudeh, S., Nguyen, D. K., Reboredo, J. C., & Wen, X. (2014). Dependence of stock and commodity futures markets in China: Implications for portfolio investment. Emerging Markets Review, 21, 183–200. Hardin, D. P., Kessler, B., & Massopust, P. R. (1992). Multiresolution analyses based on fractal functions. Journal of Approximation Theory, 71, 104–120. Kim, H. S., & Baek, J. (2013). Assessing dynamics of crude oil import demand in Korea. Economic. Modelling, 35, 260–263. Koenker, R. (2005). Quantile regression. New York, Cambridge University Press: Econometric Society Monograph Series. Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46, 33–50. Koenker, R., & Bassett, G. (1982). Robust tests for heteroscedasticity based on regression quantiles. Econometrica, 50, 43–61. Koenker, R., & D’Orey, V. (1987). Algorithm AS 229: Computing regression quantiles. Journal of the Royal Statistical Society. Series C (Applied Statistics), 36, 383–393. Koenker, R., & Hallock, K. F. (2001). Quantile regression. Journal of Economic Perspectives, 15, 143–156. Lee, B. S., & Li, M.-Y. L. (2012). Diversification and risk–adjusted performance: A quantile regression approach. Journal of Banking & Finance, 36, 2157–2173. Li, X. M., Zhang, B., & Gao, R. (2015). Economic policy uncertainty shocks and stock–bond correlations: Evidence from the US market. Economics Letters, 132, 91–96. Li, X. M., & Zou, L. P. (2008). How do policy and information shocks impact co–movements of China’s T–bond and stock markets? Journal of Banking & Finance, 32, 347–359. Mallat, S. G. (1989). A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Recognition and Machine Intelligence, 11, 674–693. Mensi, W., Hammoudeh, S., Reboredo, J. C., & Nguyen, D. K. (2014). Do global factors impact BRICS stock markets? A quantile regression approach. Emerging Markets Review, 19, 1–17. Neaime, S. (2016). Financial crises and contagion vulnerability of MENA stock markets. Emerging Markets Review, 27, 14–35. Nguyen, M. C., Bhatti, I., Komorníková, M., & Komorník, J. (2016). Gold price and stock markets nexus under mixed–copulas. Economic Modelling, 58, 283–292.

21

North American Journal of Economics and Finance xxx (xxxx) xxx–xxx

L. Yang et al.

Panchenko, V., & Wu, E. (2009). Time-varying market integration and stock and bond return concordance in emerging markets. Journal of Banking & Finance, 33, 1014–1021. Roueff, F., & von Sachs, R. (2011). Locally stationary long memory estimation. Stochastic Processes and their Applications, 121(4), 813–844. Tiwari, A.-K., Dar, A.-B., & Bhanja, N. (2013). Oil price and exchange rates: A wavelet based analysis for India. Economic Modelling, 31, 414–422. Wang, G. J., Xie, C., Lin, M., & Stanley, H. E. (2017). Stock market contagion during the global financial crisis: A multiscale approach. Finance Research Letters, 22, 163–168. Vithessonthi, C., & Kumarasinghe, S. (2016). Financial development, international trade integration, and stock market integration: Evidence from Asia. Journal of Multinational Financial Management, 35, 79–92. Yang, L., & Hamori, S. (2015). Interdependence between the bond markets of CEEC–3 and Germany: A wavelet coherence analysis. North American Journal of Economics and Finance, 32, 124–138. Yang, L., Cai, X.-J., Zhang, H., & Hamori, S. (2016). Interdependence of foreign exchange markets: A wavelet coherence analysis. Economic Modelling, 55, 6–14. Zhang, C., & Chen, X. (2011). The impact of global oil price shocks on China’s stock returns: Evidence from the ARJI(–ht)–EGARCH model. Energy, 36, 6627–6633.

22