Mercurio, Danilo; Spokoiny, Vladimir Statistical inference for time-inhomogeneous volatility models. (English) Zbl 1091.62103 Ann. Stat. 32, No. 2, 577-602 (2004). Summary: This paper offers a new approach for estimating and forecasting 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 of 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 (LAVE) 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 capable of explaining many of the features of the data; nevertheless, the new approach seems to be superior to the GARCH method as far as the out-of-sample results are concerned. Cited in 1 ReviewCited in 42 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M20 Inference from stochastic processes and prediction 65C05 Monte Carlo methods Keywords:stochastic volatility model; adaptive estimation; local homogeneity PDFBibTeX XMLCite \textit{D. Mercurio} and \textit{V. Spokoiny}, Ann. Stat. 32, No. 2, 577--602 (2004; Zbl 1091.62103) Full Text: DOI arXiv References: [1] Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31 307–327. · Zbl 0865.62085 [2] Brodsky, B. and Darkhovsky, B. (1993). Nonparametric Methods in Change-Point Problems . 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