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MODELING NONSTATIONARY AND LEPTOKURTIC FINANCIAL TIME SERIES

Published online by Cambridge University Press:  14 October 2014

Ying Chen  and
Vladimir Spokoiny
Ying Chen*
Affiliation:
National University of Singapore
Vladimir Spokoiny
Affiliation:
Weierstrass-Institute and Moscow Institute of Physics and Technology
*
*Address correspondence to Ying Chen. Department of Statistics & Applied Probability. National University of Singapore; e-mail: stacheny@nus.edu.sg.
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Abstract

Financial time series is often assumed to be stationary and has a normal distribution in the literature. Both assumptions are however unrealistic. This paper proposes a new methodology with a focus on volatility estimation that is able to account for nonstationarity and heavy tails simultaneously. In particular, a local exponential smoothing (LES) approach is developed, in which weak estimates with different memory parameters are aggregated in a locally adaptive way. The procedure is fully automatic and the parameters are tuned by a new propagation approach. The extensive and practically oriented numerical results confirm the desired properties of the constructed estimate: it performs stable in a nearly time homogeneous situation and is sensitive to structural shifts. Our main theoretical “oracle” result claims that the aggregated estimate performs as good as the best estimate in the considered family. The results are stated under realistic and unrestrictive assumptions on the model.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 4 , August 2015 , pp. 703 - 728
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

This research was supported by the NUS FRC grant R-155-000-117-112. Vladimir Spokoiny is partially supported by Laboratory for Structural Methods of Data Analysis in Predictive Modeling, MIPT, RF government grant, ag. 11.G34.31.0073. Financial support by the German Research Foundation (DFG) through the Collaborative Research Center 649 “Economic Risk” is gratefully acknowledged.

References

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