Statistical inference for time-inhomogeneous volatility models
- Mercurio, Danilo
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62M10 62P20
- stochastic volatility model, adaptive estimation, local homogeneity
This paper offers a new approach for estimation and few-step ahead 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 an algorithm which can perform this task and investigate it both from the theoretical point of view and through Monte Carlo simulations. Finally the procedure is applied to some exchange rate data sets 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 based on local constant approximation seems to be slightly superior as far as the out of sample results are taken into consideration.
- Ann. Statist., vol. 12 (2004), no. 2, pp. 577-602