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Component-wise Representations of Long-memory Models and Volatility Prediction

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  • Tommaso Proietti

Abstract

Extracting and forecasting the volatility of financial markets is an important empirical problem. The article provides a time series characterization of the volatility components arising when the volatility process is fractionally integrated, through a generalization of the Beveridge–Nelson decomposition, and proposes a new integrated moving average (MA) model, formulated in terms of the fractional lag operator, the FLagIMA model, which allows the series to be decomposed as the sum of a fractional noise and a white noise component. We provide an assessment of the predictive performance of the FLagIMA model in comparison with other popular predictors and two other rival specifications, the fractionally integrated first-order MA model, and a fractional equal root integrated MA model. For statistical inference we show that, under mild regularity conditions, the Whittle pseudo-maximum likelihood estimator of the model parameters is consistent and asymptotically normal, also in the nonstationary case.

Suggested Citation

  • Tommaso Proietti, 2016. "Component-wise Representations of Long-memory Models and Volatility Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 668-692.
    • Handle: RePEc:oup:jfinec:v:14:y:2016:i:4:p:668-692.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbw004
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    References listed on IDEAS

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    1. Engle, Robert F. (ed.), 1995. "ARCH: Selected Readings," OUP Catalogue, Oxford University Press, number 9780198774327.
    2. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 651-676, June.
    3. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    4. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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    Cited by:

    1. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends in unobserved components models," Papers 2005.03988, arXiv.org, revised May 2020.
    2. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    3. Federico Maddanu, 2023. "Forecasting highly persistent time series with bounded spectrum processes," Statistical Papers, Springer, vol. 64(1), pages 285-319, February.
    4. Taylor, Nick, 2017. "Realised variance forecasting under Box-Cox transformations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 770-785.
    5. Proietti, Tommaso & Maddanu, Federico, 2024. "Modelling cycles in climate series: The fractional sinusoidal waveform process," Journal of Econometrics, Elsevier, vol. 239(1).
    6. Uwe Hassler & Marc-Oliver Pohle, 2019. "Forecasting under Long Memory and Nonstationarity," Papers 1910.08202, arXiv.org.
    7. Taylor, Nick, 2017. "Timing strategy performance in the crude oil futures market," Energy Economics, Elsevier, vol. 66(C), pages 480-492.

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