This paper introduces a new specification for the heterogeneous autoregressive (HAR) model for the realized volatility of S&P 500 index returns. In this modelling framework, the coefficients of the HAR are allowed to be time-varying with unspecified functional forms. The local linear method with the cross-validation (CV) bandwidth selection is applied to estimate the time-varying coefficient HAR (TVC-HAR) model, and a bootstrap method is used to construct the point-wise confidence bands for the coefficient functions. Furthermore, the asymptotic distribution of the proposed local linear estimators of the TVC-HAR model is established under some mild conditions. The results of the simulation study show that the local linear estimator with CV bandwidth selection has favorable finite sample properties. The outcomes of the conditional predictive ability test indicate that the proposed nonparametric TVC-HAR model outperforms the parametric HAR and its extension to HAR with jumps and/or GARCH in terms of multi-step out-of-sample forecasting, in particular in the post-2003 crisis and 2007 GFC periods, during which financial market volatilities were unduly high.

This paper introduces a new speci…cation for the heterogeneous autoregressive (HAR) model for the realized volatility of S&P500 index returns. In this new model, the coe¢ cients 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 con…dence intervals for the time varying coef-…cient functions. In addition, the estimated nonparametric TVC-HAR was calibrated by …tting parametric polynomial functions by minimising the L 2-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 nonparametric TVC-HAR model consistently outperforms its calibrated counterpart as well as the simple HAR and the HAR-GARCH models in out-of-sample forecasting.