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 coefficients 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/trigonometric functions by minimising the L2-type criterion. In hypotheses testings of the calibrated and the simple parametric HAR models against the nonparametric TVC-HAR model, the test statistic constructed based on the generalised likelihood ratio method augmented with bootstrap method provides evidence in favour of the nonparametric TVC-HAR model. More importantly, using the fluctuation test developed by Giacomini and Rossi (2010) for forecast evaluation, the nonparametric TVC-HAR model was found to consistently outperform the calibrated TVC-HAR and the simple HAR models in out-of-sample forecasting