Nonparametric Estimation and Parametric Calibration of Time-Varying Coefficient Realized Volatility Models

This paper introduces a new specification for the heterogeneous autoregressive (HAR) model for the realized volatility of S&P500 index returns. In this new model, the coeffcients of the HAR are allowed to be time-varying with unknown functional forms. We propose a local linear method for estimating this TVC-HAR model as well as a bootstrap method for constructing confidence intervals for the time varying coefficient functions. In addition, the estimated nonparametric TVC-HAR was calibrated by fitting parametric polynomial functions by minimising the L2-type criterion. The calibrated TVC-HAR and the simple HAR models were tested separately against the nonparametric TVC-HAR model. The test statistics constructed based on the generalised likelihood ratio method augmented with bootstrap method provide evidence in favour of calibrated TVC-HAR model. More importantly, the results of conditional predictive ability test developed by Giacomini and White (2006) indicate that the non-parametric TVC-HAR model consistently outperforms its calibrated counterpart as well as the simple HAR and the HAR-GARCH models in out-of-sample forecasting.