Forecasting Realized Volatility Using a Nonnegative Semiparametric Model

Abstract

This paper introduces a parsimonious and yet flexible semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen and Shephard (2001) and Nielsen and Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the distributional and functional form of its error component is partially unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Simulation studies validate the new method and suggest that it works reasonably well in finite samples. The out-of-sample forecasting performance of the proposed model is evaluated against a number of standard models, using data on S&P 500 monthly realized volatilities. Some commonly used loss functions are employed to evaluate the predictive accuracy of the alternative models. It is found that the new model generally generates highly competitive forecasts.

Keywords: Volatility forecasting, Realized volatility, Linear programming estimator, Tukey’s power transformation, Nonlinear nonnegative autoregression, Forecast comparisons

JEL Classification: C22, C51, C52, C53, C58