ABSTRACT

This study empirically examines the effects of structural breaks on equity return volatility persistence by using Chinese and Japanese equity index return data. Applying standard GARCH models and two kinds of structural break dummy variables, we derive the following findings. First, we reveal that for both Chinese and Japanese equity index returns, the values of GARCH parameters of standard GARCH models decline when the first structural break dummies are incorporated. Second, our analyses further clarify that for both Chinese and Japanese equity index returns, the values of GARCH parameters of standard GARCH models again decline when different kinds of structural break dummies are incorporated.

Keywords:

GARCH Model, Equity Return Volatility Persistence, Structural Break, Structural Break Dummies

1. Introduction

In economics and finance, structural breaks are recently being much important, while well-known volatility persistence of equity returns is also important in financial time-series modeling (e.g., Narayan et al. [1] ; Chen et al. [2] ; Chatzikonstanti and Venetis [3] ; Tsuji [4] [5] [6] ). In particular, what is the effect of equity returns’ structural breaks on their volatility persistence? Moreover, how are equity returns’ structural breaks related to their volatility persistence? In this paper, to answer these important research questions, we investigate the effects of equity return structural breaks on their volatility persistence by using Chinese and Japanese equity index return data. Incorporating two kinds of structural break dummies into the standard univariate GARCH models, this paper derives the following interesting findings. 1) First, this study reveals that for both Chinese and Japanese equity index returns, the values of GARCH parameters of standard GARCH models decline when the first structural break dummies are incorporated. 2) Second, our analyses further clarify that for both Chinese and Japanese equity index returns, the values of GARCH parameters of standard GARCH models again decline when different kinds of structural break dummies are incorporated.

As we document later, these interesting findings are very robust; and thus, the findings from our research are highly useful and valuable for economic and financial modeling of various kinds of time-series. Hence, our results derived in this paper make an important contribution to the research in the fields of economics and finance. Regarding the rest of this paper, Section 2 reviews recent related research; in Section 3, our data and variables are explained; and in Section 4, our methodology is documented. After that, Section 5 explains our main empirical results and finally, Section 6 concludes the paper.

2. Literature Review

This section reviews recent literature employing structural break analyses very concisely. First, Narayan et al. [1] tested structural breaks in the US, the UK, and Japanese equity prices, and they suggested that the structural breaks have slowed down the growth rates of the US, the UK, and Japanese equity markets. Chen et al. [2] examined the effect of structural breaks on the linkage of spot?futures oil prices, and they suggested that the structural breaks caused some effects on the issues of cointegrating relations, market efficiency, arbitrage, causalities, and oil futures volatility forecasting performance.

Using stock market data, Chatzikonstanti and Venetis [3] investigated whether the observed long memory characteristic of equity returns is spurious and whether it is explained by the presence of structural breaks; and they suggested that once the structural breaks are considered, the equity return volatility persistence was eliminated. Güloğlu et al. [7] examined the volatility spillovers among five Latin American equity markets, and they suggested that when the structural breaks of variances are taken into consideration, volatility spillover effects among the five equity markets were not strong.

Recently, Smith [8] estimated the US equity premium from economic fundamentals under structural breaks, and they found that the US equity premium fell from 8.16% in 1951 to 1.15% in 1985. Using the US equity market data, Hood and Malik [9] suggested that their out-of-sample tests incorporating both time-varying nature and structural breaks in volatility yielded more accurate Value-at-Risk forecasts than several alternative benchmark methods.

As the above brief literature review shows, recent studies advocated the importance of structural breaks. Hence, this study quantitatively examines Chinese and Japanese equity returns by taking structural breaks into account and employing two kinds of structural break dummy variables in the following sections.

3. Data and Variables

In this section, we explain our main variables. All data we use in this study are from Thomson Reuters. Our first variable is LRCHI, denoting daily log returns of the Shanghai A-share index in China; our second variable is LRTPX, denoting daily log returns of the Tokyo Stock Price Index (TOPIX) in Japan. Our sample period as to these two percentage log returns spans from January 4, 2000 to August 2, 2018.

Figure 1 plots the price evolution of the Shanghai A-share index and the TOPIX from January 3, 2000 to August 2, 2018. Further, Table 1 exhibits the summary statistics of the above Chinese and Japanese equity index returns. Table 1 indicates that for both returns, their mean values are almost zero, their values of skewness are negative, and their values of kurtosis are clearly higher than the value of three for normal distributions.

4. Methods

We next explain our methodology. In this study, we use the standard GARCH model and two kinds of structural break dummy variables. Namely, for Chinese and Japanese equity returns, we estimate the standard GARCH model without and with two kinds of dummy variables that capture structural breaks for each equity index return.

We construct two structural break dummies after detecting structural break points by ICSS algorithm. The identified break point numbers and time periods are exhibited in Table 2. As this table shows, for both LRCHI and LRTPX, there are 11 break points.

We first employ Ewing and Malik [10] -type structural break dummies and denote the structural break dummy variables for LRCHI as CDUM1 (k), and those for LRTPX as JDUM1 (j), where k = 1, …, 11 and j = 1, …, 11. For example, CDUM1 (1) takes one from the first structural break point (December 8, 2006) onwards and zero elsewhere; and JDUM1 (1) takes one from the first structural break point (November 29, 2002) onwards and zero elsewhere. Further, we denote our second structural break dummy variables for LRCHI as

Notes. SD denotes the standard deviation value. Max. and Min. denote maximum and minimum values, respectively.

Notes. Break points and time periods are detected by ICSS algorithm. The sample period is from January 4, 2000 to August 2, 2018.

CDUM2 (m), and those for LRTPX as JDUM2 (n), where m = 1, …, 11 and n = 1, …, 11. Specifically, CDUM2 (1) takes one for January 4, 2000 to December 7, 2006, and zero elsewhere; while JDUM2 (1) takes one for January 4, 2000 to November 28, 2002, and zero elsewhere.

5. Results

This section documents the main points of our empirical results. First, Table 3 displays the estimation results of standard GARCH models with no structural break dummy for Chinese and Japanese equity index returns. As Panel A of Table 3 indicates, for LRCHI, it is noted that the GARCH parameter takes a high value of 0.9384, and as Panel B of Table 3 indicates, for LRTPX, we also note that the GARCH parameter takes a high value of 0.8773.

Next, Table 4 displays the estimation results of standard GARCH models with Ewing and Malik [10] -type structural break dummies for Chinese and Japanese equity returns. As Panel A of Table 4 indicates, for LRCHI, the GARCH parameter takes 0.8538, and this value is rather lower than 0.9384, where structural breaks are ignored. In addition, as Panel B of Table 4 indicates, for LRTPX, the GARCH parameter takes 0.8072, and this value is clearly lower than 0.8773, where structural breaks are ignored.

Furthermore, Table 5 displays the estimation results of standard GARCH models with different structural break dummies for Chinese and Japanese equity returns. As Panel A of Table 5 indicates, for LRCHI, the GARCH parameter takes 0.8538, and this value is again rather lower than 0.9384, where structural breaks are ignored. In addition, as Panel B of Table 5 indicates, for LRTPX, the GARCH parameter takes 0.8072, and this value is again clearly lower than 0.8773, where structural breaks are ignored.

Notes. In this table, C: constant term; A: ARCH parameter; G: GARCH parameter. *** and ** indicate the statistical significance of the estimates at the 1% and 5% levels, respectively.

Notes. In this table, C: constant term; A: ARCH parameter; G: GARCH parameter. ***, **, and * indicate the statistical significance of the estimates at the 1%, 5%, and 10% levels, respectively.

As above, regarding our main concern of this study: the changes in the values of volatility persistence parameters of GARCH models, they always decrease when we take structural breaks into consideration. These results can be found for both Chinese and Japanese equity index returns regardless of types of dummy variables; thus, we emphasize that the above results are highly robust. Hence, from our results, we understand that when structural breaks are ignored, volatility persistence of international equity returns may be overestimated in, at least, univariate GARCH models.

Notes. In this table, C: constant term; A: ARCH parameter; G: GARCH parameter. ***, **, and * indicate the statistical significance of the estimates at the 1%, 5%, and 10% levels, respectively.

6. Conclusions

This study empirically examined the effects of structural breaks on equity return volatility persistence by using Chinese and Japanese equity index return data. Using standard GARCH models and two kinds of structural break dummy variables, we derived the following findings. First, this study found that for both Chinese and Japanese equity index returns, the values of GARCH parameters of standard GARCH models declined when Ewing and Malik [10] -type structural break dummies are incorporated. Second, our analyses further clarified that for both Chinese and Japanese equity index returns, the values of GARCH parameters of standard GARCH models again declined when different kinds of structural break dummies are incorporated.

As above, all our results demonstrated that when structural breaks are ignored, the volatility persistence of international equity returns may be overestimated at least in univariate GARCH models. We note that GARCH models are also important in economics and finance (e.g., Tsuji [11] [12] [13] [14] [15] ); and we consider that the findings from our study are highly valuable for modeling of various kinds of economic and financial time-series since many economic and financial time-series have structural breaks. However, it is also noted that the structural break dummies we used in this study might be somewhat difficult to incorporate into multivariate models directly. Thus, we should recognize the importance of developing suitable and reasonable structural break modeling for multivariate economic and financial time-series, and it is one of our important future works.

Acknowledgements

The author firstly appreciates this journal for its repeated kind article invitation. The author also thanks Joy Deng, Yavonne Zhang, and Jasmyn Chen for their kind editorial assistance to this article. The author further thanks anonymous referees for their constructive and supportive comments on this paper. Furthermore, the author also greatly appreciates the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research and the Chuo University Personal Research Grant for their continuing financial assistance to my research. Finally, I deeply thank all the Editors of this journal for their kind attention to my paper.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

Cite this paper

Tsuji, C. (2018) How Are Structural Breaks Related to Stock Return Volatility Persistence? Evidence from China and Japan. Modern Economy, 9, 1635-1643. https://doi.org/10.4236/me.2018.910102

References