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Strict stationarity, persistence and volatility forecasting in ARCH(∞) processes

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  • Davidson, James
  • Li, Xiaoyu

Abstract

This paper derives a simple sufficient condition for strict stationarity in the ARCH(∞) class of processes with conditional heteroscedasticity. The concept of persistence in these processes is explored, and is the subject of a set of simulations showing how persistence depends on both the pattern of lag coefficients of the ARCH model and the distribution of the driving shocks. The results are used to argue that an alternative to the usual method of ARCH/GARCH volatility forecasting should be considered.

Suggested Citation

  • Davidson, James & Li, Xiaoyu, 2016. "Strict stationarity, persistence and volatility forecasting in ARCH(∞) processes," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 534-547.
    • Handle: RePEc:eee:empfin:v:38:y:2016:i:pb:p:534-547
    DOI: 10.1016/j.jempfin.2015.08.010
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. Douc, Randal & Roueff, François & Soulier, Philippe, 2008. "On the existence of some processes," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 755-761, May.
    3. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    6. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    7. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    8. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    9. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    Cited by:

    1. Hualing Lin & Qiubi Sun & Sheng-Qun Chen, 2020. "Reducing Exchange Rate Risks in International Trade: A Hybrid Forecasting Approach of CEEMDAN and Multilayer LSTM," Sustainability, MDPI, vol. 12(6), pages 1-19, March.

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    More about this item

    Keywords

    GARCH; FIGARCH; Conditional heteroscedasticity; Stationarity; Persistence; Forecasting;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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