Forecasting Volatility with Time-Varying Coefficient Regressions

Qifeng Zhu,Shan Wu,Miman You

doi:10.1155/2020/3151473

Abstract

We extend the heterogeneous autoregressive- (HAR-) type models by explicitly considering the time variation of coefficients in a Bayesian framework and comprehensively comparing the performances of these time-varying coefficient models and constant coefficient models in forecasting the volatility of the Shanghai Stock Exchange Composite Index (SSEC). The empirical results suggest that time-varying coefficient models do generate more accurate out-of-sample forecasts than the corresponding constant coefficient models. By capturing and studying the time series of time-varying coefficients of the predictors, we find that the coefficients (predictive ability) of heterogeneous volatilities are negatively correlated and the leverage effect is not significant or inverse during certain periods. Portfolio exercises also demonstrate the superiority of time-varying coefficient models.

Highlights

Volatility is the key input variable for risk assessment, asset pricing, and portfolio allocation models. e early classic models are GARCH-type [1,2,3] and stochastic volatility (SV) [4] models, and because of the unavailability of high-frequency data, these models are based on daily or weekly returns. e omission of the informative intraday data makes these parameter volatility models not preferred
We extend the heterogeneous autoregressive- (HAR-)type model by explicitly considering the time variation of coefficients and apply these models in forecasting realized volatility of the Shanghai Stock Exchange Composite Index (SSEC). e empirical results demonstrate that, statistically, the time-varying coefficient models generate more accurate forecasts than the Markov regime switching (MRS) and constant coefficient models
We find that our models are helpful in generating more excess returns and improving the utility of a certain risk aversion investor

Summary

Introduction

Volatility is the key input variable for risk assessment, asset pricing, and portfolio allocation models. e early classic models are GARCH-type [1,2,3] and stochastic volatility (SV) [4] models, and because of the unavailability of high-frequency data, these models are based on daily or weekly returns. e omission of the informative intraday data makes these parameter volatility models not preferred. According to the degree of time variation in coefficients, we compare the performances of 3 types of models, constant-coefficients (CC), MRS, and TVC HAR-type models in volatility forecasting. By investigating the coefficient series of the TVC-HAR-type models, we find that the coefficients (predictive abilities) of heterogeneous volatilities are negatively correlated and the leverage effect is not significant or inverse during specific periods. We use our method to capture the time series of the “leverage parameter” which measures the correlation between price shocks and volatility and found that downside risk increases future volatility of the SSEC on the whole, but the leverage effect is not significant or inverse during certain periods.

Methodology

Empirical Study

Findings

Conclusions