Improving stock market volatility forecasts with complete subset linear and quantile HAR models

Abstract

Volatility forecasting plays an integral role in risk management, investments and security valuation for all assets with uncertain future payoffs. We enrich the literature by presenting computationally intensive variations of the heterogeneous autoregressive (HAR) volatility model: the complete subset linear/quantile regression HAR models, HAR-CSLR and HAR-CSQR. Predictions of 1- to 22-day-ahead volatility of four major market indices (NIKKEI 225, S&P 500, SSEC and STOXX 50) show that both models tend to outperform several benchmark HAR models. Forecasting accuracy improvements tend to stabilize for longer forecasting horizons: e.g., five-day-ahead improvements range from 6.57% (SSEC) to 35.62% (NIKKEI 225) and from 3.99% (STOXX) to 9.54% for mean square error (MSE) and QLIKE loss functions. In terms of MSE, the HAR-CSQR model outperforms several standard benchmark HAR models across all market indices and forecast horizons.