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April 2004 Statistical inference for time-inhomogeneous volatility models
Danilo Mercurio, Vladimir Spokoiny
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Ann. Statist. 32(2): 577-602 (April 2004). DOI: 10.1214/009053604000000102


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.


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Danilo Mercurio. Vladimir Spokoiny. "Statistical inference for time-inhomogeneous volatility models." Ann. Statist. 32 (2) 577 - 602, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1091.62103
MathSciNet: MR2060170
Digital Object Identifier: 10.1214/009053604000000102

Primary: 62M10
Secondary: 62P20

Keywords: adaptive estimation , local homogeneity , stochastic volatility model

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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