In this study, the long memory property in the volatility of Chinese stock markets is examined. For this purpose, we applied two semi-parametric tests (GPH and LW) and the FIGARCH model, to four Chinese market indices: Shanghai A, Shanghai B, Shenzhen A and Shenzhen B. From the results of our analysis, we can conclude that the volatility of Chinese stock markets exhibits long memory features, and that the assumption of non-normality provides better specifications regarding long memory volatility processes.
It is well known that the volatility of financial asset returns often exhibits a long memory property where the autocorrelations of the absolute and squared returns of time series are characterized by a very slow decay [1]. Such a feature is a crucial component of asset risk management, investment portfolios, and the pricing of derivative securities, as its presence is closely connected to the predictability of volatility [2].
Although those working in econometrics became aware of volatility persistence in financial data at the beginning of the 1980s, a parsimonious tool able to analyze the long memory property in the volatility of financial time series has remained out of reach for researchers [3]. One linear measure of the long memory in volatility can be found in the fact that different return transformations, such as absolute returns, or squared returns, display a long memory property [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19] and [20].
Interestingly, this evidence is not consistent with either the generalized ARCH (GARCH) model of Bollerslev [21] or the integrated GARCH (IGARCH) model of Engle and Bollerslev [22]. To overcome this problem, Baillie et al. [23] extended the standard GARCH model with a fractionally integrated process. This approach — the so-called fractionally integrated GARCH (FIGARCH) model — allows fractional orders I(d)I(d) of integration between zero and one, and estimates an intermediate process between GARCH and IGARCH [24], [25], [26], [27] and [28].
The primary aim of this study is to examine the long memory property in the volatility of four Chinese market shares (Shanghai A, Shanghai B, Shenzhen A and Shenzhen B) using three long memory techniques (the GPH test, the local Whittle estimator and FIGARCH model). The Chinese stock market possesses characteristics of a transition economic system and the trading of its shares are recently open to international investors. Due to difference of socialist and capitalist economic systems, the dynamics of the Chinese stock market may exhibit some unique characteristics compared to other mature stock markets. Recently, the Chinese stock market has received great attention from the econophysics community as a new source of empirical studies. For example, the scaling behavior and long range correlations are statistically discovered in stock returns, intertrade durations and the trading volume in the Chinese stock market [29], [30], [31], [32] and [33].
The contribution of this study is three fold. First, some studies have mainly focused on the long memory property in the return series of Chinese market indices [11], [34] and [35]. However, there is (to our best knowledge) still a lack in the research that has examined the long memory property in the volatility of the Chinese stock market. Therefore, our study is an initial attempt to contribute in this neglected research area.
Second, using the three different techniques, our study improves the robustness of statistical results for long memory against short memory in volatility. In particular, we found that the FIGARCH model of Baillie et al. [23] is a useful approach which can capture the long memory property in the volatility of the Chinese stock market.
Third, the non-normal distribution of a financial time series is an important component for enhancing the measurement accuracy of value-at-risk (VaR) in risk and portfolio management [36] and [37]. We found that the FIGARCH model with a Student-tt distribution is suitable to take into account long memory volatility processes and heavy-tailed properties for the Chinese stock market.
The rest of this paper is organized as follows. Section 2 presents the methodology for semi-parametric tests and the FIGARCH model. Section 3 describes the characteristics of the sample data. Section 4 provides the estimation results of semi-parametric tests and the FIGARCH model. The final section summarizes the most relevant conclusions.
This study examined the long memory property in the volatility of Chinese stock markets. For this purpose, we applied two semi-parametric tests (GPH test and the LW estimator) and the FIGARCH model to four Chinese market indices: Shanghai A, Shanghai B, Shenzhen A, and Shenzhen B. Our analysis provides several important conclusions in modeling the long memory in volatility.
First, the estimates from the GPH test and the LW estimator support the Taylor effect in absolute and squared returns, implying that the long memory property exists in the volatility of four Chinese stock markets. Second, the FIGARCH model is better equipped to capture the long memory volatility process than the GARCH and IGARCH models. In particular, the FIGARCH (1,d,0)(1,d,0) model is found to provide a good representation of four Chinese stock returns. Finally, the Student-tt distribution outperforms the normal one in capturing leptokurtosis in residuals.
Overall, it is concluded that the volatility in four Chinese stock markets reveals a long memory feature. In addition, the assumption of non-normality provides better specifications when modeling long memory volatility processes.
