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Modeling Nonstationary And Leptokurtic Financial Time Series

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  • Chen, Ying
  • Spokoiny, Vladimir

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.

Suggested Citation

  • Chen, Ying & Spokoiny, Vladimir, 2015. "Modeling Nonstationary And Leptokurtic Financial Time Series," Econometric Theory, Cambridge University Press, vol. 31(4), pages 703-728, August.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:04:p:703-728_00
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    Cited by:

    1. Li, Xinjue & Zboňáková, Lenka & Wang, Weining & Härdle, Wolfgang Karl, 2019. "Combining Penalization and Adaption in High Dimension with Application in Bond Risk Premia Forecasting," IRTG 1792 Discussion Papers 2019-030, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. repec:hum:wpaper:sfb649dp2017-023 is not listed on IDEAS
    3. Hood, Matthew & Malik, Farooq, 2018. "Estimating downside risk in stock returns under structural breaks," International Review of Economics & Finance, Elsevier, vol. 58(C), pages 102-112.
    4. Niels Gillmann & Ostap Okhrin, 2023. "Adaptive local VAR for dynamic economic policy uncertainty spillover," Papers 2302.02808, arXiv.org.
    5. Li, Xinjue & Zbonakova, Lenka & Härdle, Wolfgang Karl, 2017. "Penalized adaptive method in forecasting with large information set and structure change," SFB 649 Discussion Papers 2017-023, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Kong, Xiaolin & Ma, Chaoqun & Ren, Yi-Shuai & Narayan, Seema & Nguyen, Thong Trung & Baltas, Konstantinos, 2023. "Changes in the market structure and risk management of Bitcoin and its forked coins," Research in International Business and Finance, Elsevier, vol. 65(C).

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