阅读|长时间记忆还是结构性断裂？ 股市指数波动的经验证据
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Long memory or structural break?Empirical evidences from indexvolatility in stock market
Yi Luo
Management College, Guangdong Polytechnic Normal University,
Guangzhou, China, and
Yirong Huang
Business School, Sun Yat-sen University, Guangzhou, China
Citation:
Luo, Y. and Huang, Y. (2019), "Long memory or structural break? Empirical evidences from index volatility in stock market", China Finance Review International, Vol. 9 No. 3, pp. 324-337. https://doi.org/10.1108/CFRI-11-2017-0222
摘要 Abstract
The purpose of this paper is to explore whether stock index volatility series exhibit real long memory.The authors employ sequential procedure to test structural break involatility series, and use DFA and 2ELW to estimate long memory parameter for the whole samples andsubsamples, and further apply adaptive FIGARCH (AFIGARCH) to describe long memory and structural break.The empirical results show that stock index volatility series are characterized by long memory andstructural break, and therefore it is appropriate to use AFIGARCH to model stock index volatility process.This study empirically investigates the properties of long memory and structural breakin stock index volatility series. The conclusion has a certain reference value for understanding the propertiesof long memory and structural break in volatility series for academic researchers, market participants andpolicy makers, and for modeling and forecasting future volatility, testing market efficiency, pricing financialassets, constructing quantitative investment strategy and measuring market risk.
Keywords: Stock market, Volatility, Long memory, Structural break, AFIGARCH
实证方法 Empirical methodology
We examine real or spurious long memory through empirical analysis according to the following steps:
• Step 1, we apply the methods including DFA and 2ELW to estimate the long memory parameter for all the whole samples.
• Step 2, we detect the presence of structural breaks with the Bai and Perron and sequential procedure for all the whole samples.
• Step 3, we subdivide the whole sample into several subsamples according to the number and date of structural breaks identified in the above step.
• Step 4, we estimate the long memory parameters with the methods used in the first step for all the subsamples.
• Step 5, we identify the real long memory through comparing the estimated long memory parameters for each volatility series on the whole sample and all the subsamples. If the long memory behavior is observed in the whole sample but not in the subsamples, the observed long memory behavior in the whole sample may be induced by structural break, also called spurious long memory. If the long memorybehavior is observed in the whole sample and subsamples, the observed long memory behavior in the whole sample may be real.
• Step 6, we model the real long memory behavior in volatility series with FIGARCH or adaptive FIGARCH (AFIGARCH). Real long memory behavior can be identified bycomparing the estimate change of fractional differencing order in FIGARCH or AFIGARCH.
实证结果 Empirical results
Data sample and descriptive statistics for SSEC and S&P 500 index
The results of descriptive statistics and basic tests for the return and volatility series of SSEC and S&P500:
Results of structural break tests for SSEC and S&P 500 index
The number and dates of structural breaks in volatility series:
Results of long memory tests for SSEC and S&P 500 index
The estimate of fractional differencingorder and Hurst exponent:
Results of estimating FIGARCH, AGARCH and AFIGARCH for SSEC and S&P 500 index
The GARCH-type estimation and evaluation of SSEC and S&P500 index:
The estimate of conditional volatility and long-term volatility for SSEC:
The estimate of conditional volatilityand long-term volatility for S&P 500:
Results of structural break and long memory parameter estimation for Hang Seng index (HSI), N225 and Financial Time Stock Exchange (FTSE) index
The estimated results of structural break and long memory for HSI, N225 and FTSE index:
结论 Conclusions
This paper investigates the long memory and structural break in the volatility series for stock index. Firstly, we employ the supF type test and sequential procedure to detect the number and dates of structural breaks and divided the whole sample into several subsamples. Second, we employ DFA and 2ELW to estimate fractional differencing order in whole samples and subsamples, and compare all the estimates among samples and between two methods for SSEC and S&P500 volatility series. Finally, we employ AFIGARCH which accounts for the properties of structural breaks and long memory in volatility series to confirm the results presented in previous sections.
The empirical results demonstrate that the volatility series for SSEC and S&P500 index are simultaneously characterized by structural break and long memory, and AFIGARCH is the appropriate model to describe the volatility process for both SSEC and S&P500. Although SSEC volatility series shows more significant long memory than S&P500 volatility series, the similar findings are obtained for them. It is essential to simultaneously account for the properties of long memory and structural break in the volatility series for modeling and forecasting future volatility, testing market efficiency, pricing financial assets, constructing quantitative investment strategy and measuring market risk. In future, we will further apply AFIGARCH to forecast volatility series and compare the forecastingperformance with other volatility models in more detail.
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