NoVaS Transformations: Flexible Inference for Volatility Forecasting

Abstract

In this paper we contribute several new results on the NoVaS transformation approach for volatility forecasting introduced by Politis (2003a,b, 2007). In particular: (a) we introduce an alternative target distribution (uniform); (b) we present a new method for volatility forecasting using NoVaS ; (c) we show that the NoVaS methodology is applicable in situations where (global) stationarity fails such as the cases of local stationarity and/or structural breaks; (d) we show how to apply the NoVaS ideas in the case of returns with asymmetric distribution; and finally (e) we discuss the application of NoVaS to the problem of estimating value at risk (VaR). The NoVaS methodology allows for a flexible approach to inference and has immediate applications in the context of short time series and series that exhibit local behavior (e.g. breaks, regime switching etc.) We conduct an extensive simulation study on the predictive ability of the NoVaS approach and find that NoVaS forecasts lead to a much ÔtighterÕ distribution of the forecasting performance measure for all data generating processes. This is especially relevant in the context of volatility predictions for risk management. We further illustrate the use of NoVaS for a number of real datasets and compare the forecasting performance of NoVaS -based volatility forecasts with realized and range-based volatility measures.ARCH, GARCH, local stationarity, structural breaks, VaR, volatility.