Statistical inference for time-inhomogeneous volatility models

This paper offers a new approach for estimation and forecasting of the volatility of financial time series. No assumption is made about the parametric form of the processes, on the contrary we only suppose that the volatility can be approximated by a constant over some interval. In such a framework the main problem consists in filtering this interval of time homogeneity, then the estimate of the volatility can be simply obtained by local averaging. We construct a locally adaptive volatility estimate (LA VE) which can perform this task and investigate it both from the theoretical point of view and through Monte Carlo simulations. Finally the LAVE procedure is applied to a data set of nine exchange rates and a comparison with a standard GARCH model is also provided. Both models appear to be able of explaining many of the features of the data, nevertheless the new approach seems to be superior GARCH method as far' as the out of sample results are taken into consideration.