Component-wise Representations of Long-memory Models and Volatility Prediction

Abstract

Extracting and forecasting the volatility of financial markets is an important empirical problem. The article provides a time series characterization of the volatility components arising when the volatility process is fractionally integrated, through a generalization of the Beveridge–Nelson decomposition, and proposes a new integrated moving average (MA) model, formulated in terms of the fractional lag operator, the FLagIMA model, which allows the series to be decomposed as the sum of a fractional noise and a white noise component. We provide an assessment of the predictive performance of the FLagIMA model in comparison with other popular predictors and two other rival specifications, the fractionally integrated first-order MA model, and a fractional equal root integrated MA model. For statistical inference we show that, under mild regularity conditions, the Whittle pseudo-maximum likelihood estimator of the model parameters is consistent and asymptotically normal, also in the nonstationary case.