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A Generalised Fractional Differencing Bootstrap for Long Memory Processes

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  • George Kapetanios
  • Fotis Papailias
  • A. M. Robert Taylor

Abstract

A bootstrap methodology suitable for use with stationary and non‐stationary fractionally integrated time series is further developed in this article. The resampling algorithm involves estimating the degree of fractional integration, applying the fractional differencing operator, resampling the resulting approximation to the underlying short memory series and, finally, cumulating to obtain a resample of the original fractionally integrated process. This approach extends existing methods in the literature by allowing for general bootstrap schemes including blockwise bootstraps. Furthermore, we show that it can also be validly used for non‐stationary fractionally integrated processes. We establish asymptotic validity results for the general method and provide simulation evidence which highlights a number of favourable aspects of its finite sample performance, relative to other commonly used bootstrap methods.

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  • George Kapetanios & Fotis Papailias & A. M. Robert Taylor, 2019. "A Generalised Fractional Differencing Bootstrap for Long Memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 467-492, July.
    • Handle: RePEc:bla:jtsera:v:40:y:2019:i:4:p:467-492
    DOI: 10.1111/jtsa.12460
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    Cited by:

    1. Marchese, Malvina & Kyriakou, Ioannis & Tamvakis, Michael & Di Iorio, Francesca, 2020. "Forecasting crude oil and refined products volatilities and correlations: New evidence from fractionally integrated multivariate GARCH models," Energy Economics, Elsevier, vol. 88(C).
    2. Lui, Yiu Lim & Phillips, Peter C.B. & Yu, Jun, 2024. "Robust testing for explosive behavior with strongly dependent errors," Journal of Econometrics, Elsevier, vol. 238(2).
    3. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    4. Arteche González, Jesús María, 2020. "Frequency Domain Local Bootstrap in long memory time series," BILTOKI info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).

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