Nonlinear time-series analysis of stock volatilities

Abstract

SUMMARY The absolute value of the mean-corrected excess return is used in this paper to measure the volatility of stock returns. We apply various nonlinearity tests available in the literature to show that such volatility series are strongly nonlinear. We then explore the use of threshold autoregressive (TAR) models in describing monthly volatility series. The models built suggest that the volatility series exhibit significant lower-order serial correlations when the volatility is large, indicating certain volatility clustering in stock returns. Out-of-sample forecasts are used to compare the TAR models with linear ARMA models and nonlinear GARCH and EGARCH models. Based on mean squared error and average absolute deviation, the comparisons show that (a) the TAR models consistently outperform the linear ARMA models in multi-step ahead forecasts for large stocks, (b) the TAR models provide better forecasts than the GARCH and EGARCH models also for the volatilities of large stock returns, and (c) the EGARCH model gives the best long-horizon volatility forecasts for small stock returns.