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Statistical inference for time-inhomogeneous volatility models

Author

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  • Mercurio, Danilo
  • Spokoiny, Vladimir G.

Abstract

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.

Suggested Citation

  • Mercurio, Danilo & Spokoiny, Vladimir G., 2002. "Statistical inference for time-inhomogeneous volatility models," SFB 373 Discussion Papers 2002,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200261
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    Cited by:

    1. Feng, Yuanhua, 2002. "Modelling Different Volatility Components," CoFE Discussion Papers 02/18, University of Konstanz, Center of Finance and Econometrics (CoFE).

    More about this item

    Keywords

    stochastic volatility model; adaptive estimation; local homogeneity;
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