基于马尔可夫状态转换模型的沪深股市波动率的估计

中国管理科学 ›› 2013, Vol. ›› Issue (2): 42-49.

基于马尔可夫状态转换模型的沪深股市波动率的估计

杨继平, 张春会

北京航空航天大学经济管理学院, 北京 100191

收稿日期:2012-09-10 修回日期:2013-01-24 出版日期:2013-04-30 发布日期:2013-04-25
基金资助:
国家自然科学基金资助项目(70871003,71271011)

Volatility Estimation of Shanghai and Shenzhen Stock Market Based on Markov Regime Switching Models

YANG Ji-ping, ZHANG Chun-hui

School of Economics and Management, Beihang University, Beijing 100191, China

Received:2012-09-10 Revised:2013-01-24 Online:2013-04-30 Published:2013-04-25

摘要/Abstract

摘要： 为了更准确地估计具有结构转换的沪深股市收益率波动特征,本文将沪深股市的波动变化分为上涨、下跌和盘整三个状态,选用2000年1月4日至2011年12月30日的上证综指和深证成指日收益率数据作为样本,2012年1月4日至2012年1月17日的日收益率作为样本外预测,分别应用GARCH和APGARCH模型,以及RS-GARCH和RS-APGARCH模型估计和预测两序列的波动率,最后采用MSE₁、MSE₂和QLIKE对估计和预测出的波动率进行评价。结果表明:单一状态和三种状态下APGARCH模型均比GARCH模型估计和预测的波动率更准确;更进一步带有马尔可夫状态转换的模型估计和预测出的波动率更准确,且误差分布服从正态分布的模型估计和预测的波动率拟合结果优于误差服从t分布的模型。

关键词: 马尔可夫状态转换, APGARCH模型, 波动率

Abstract: In order to get the more accurate estimation of volatility of daily return series of Shanghai and Shenzhen Stock market with regime switching, volatility of these stock index return series are divided into three regime states: rising, falling and consoliclation in the paper. Return series of Shanghai Composite Index and Shenzhen Component Index are chosen as study sample and January 4, 2000 to 2011 December 30 is set as the sample period and January 4, 2012 to January 17, 2012 is set as out of sample period. Then GARCH model, RS-GARCH model, APGARCH model and RS-APGARCH model are applied to estimation and forecasting of volatility of these two return series. Finally MSE₁, MSE₂ and QLIKE are used to evaluate the performance of these models. The results show that APGARCH model is more accurate in estimation and prediction of the volatilities of the series than the GARCH model, models with Markov regime switching are more accurate in estimation and prediction of the volatilities of the series, and the models with normal error distribution are more accurate in estimation and prediction of the volatilities of the series than the models with the error distribution following t-distribution.

Key words: Markov regime switching, APGARCH model, volatility

中图分类号:

F830.91

杨继平, 张春会. 基于马尔可夫状态转换模型的沪深股市波动率的估计[J]. 中国管理科学, 2013, (2): 42-49.

YANG Ji-ping, ZHANG Chun-hui. Volatility Estimation of Shanghai and Shenzhen Stock Market Based on Markov Regime Switching Models[J]. Chinese Journal of Management Science, 2013, (2): 42-49.

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