基于结构转换PTTGARCH模型沪深股市波动率的估计

Estimation of volatility of CSI 300 index based on regime switching PTTGARCH model

考虑股市收益率波动存在结构转换特征以及描述波动非线性和非对称特征的幂变换门限GARCH(PTTGARCH)模型,本文提出结构转换PTTGARCH模型.选取沪深300指数日对数收益率作为研究对象,将股指的波动变化分为下跌、上涨和盘整三个状态:选用2013年7月1日至2015年12月17日以及2015年12月18日至2016年1月8日作为样本内和样本外时期:分别应用GARCH,EGARCH,APGARCH,PTTGARCH模型及具有结构转换的相应模型对沪深股市波动率进行估计和预测,利用高频数据得到的已实现波动率作为股指实际波动率的估计.采用平均平方误差(MSE_1,MSE_2),平均绝对误差(MAE_1,MAE_2)对估计与预测的波动率进行评价,并采用模型信度集(MCS)检验比较各模型估计和预测能力.研究结果表明:单状态和具有马尔可夫结构转换PTTGARCH模型在样本内和样本外的拟合和预测结果均更为准确.

Considering the volatility of stock market presenting regime switching as well as nonlinear and asymmetric characteristics which can be described using the power-transformed and threshold （PTT） GARCH model, the paper proposes regime switching PTTGARCH （RS-PTTGARCH） model. The daily log return series of CSI 300 Index are taken as the study example and regimes of volatility of the series are classified into three states： the falling, the rising and the consolidation. The in-sample period is selected from July 1 2013 to Dec. 17 2015 and the out-of-sample period from Dec. 18 2015 to Jan. 8 2016. Estimation and forecasting of the volatility of CSI 300 Index have been performed using GARCH, EGARCH, APGARCH, PTTGARCH, and corresponding models with Markov regime switching, respectively. Per- formance of these models has been evaluated using MSE1, MSE2, MAE1, MAE2, in which the actual volatilities of series are estimated by the realized volatility using high frequency data of the series. Besides, the model confidence set （MCS） test has been used to evaluate the performance of these models. It has been concluded that the PTTGARCH models both with single regime and Markov regime switching outperform the other models in estimation and prediction of the volatilities of the return series within the sample and out-of-sample.