NoVaS Transformations: Flexible Inference for Volatility Forecasting

In this paper we present several new ¯ndings on the NoVaS transformation approach for volatility forecasting introduced by Politis (2003a,b, 2007). In particular: (a) we present a new method for accurate volatility forecasting using NoVaS ; (b) we introduce a \time- varying" version of NoVaS and show that the NoVaS methodology is applicable in situations where (global) stationarity for returns fails such as the cases of local stationarity and/or structural breaks and/or model uncertainty; (c) we conduct an extensive simulation study on the forecasting ability of the NoVaS approach under a variety of realistic data generating processes (DGP); and (d) we illustrate the forecasting ability of NoVaS on a number of real datasets and compare it to realized and range-based volatility measures. Our empirical results show that the NoVaS -based forecasts lead to a much `tighter' distribution of the forecasting performance measure. Perhaps our most remarkable ¯nding is the robustness of the NoVaS forecasts in the context of structural breaks and/or other non-stationarities of the underlying data. Also striking is that forecasts based on NoVaS invariably outperform those based on the benchmark GARCH(1,1) even when the true DGP is GARCH(1,1) when the sample size is moderately large, e.g. 350 daily observations.