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Exact Local Whittle Estimation In Long Memory Time Series With Multiple Poles

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  • Arteche, Josu

Abstract

A generalization of the Exact Local Whittle estimator in Shimotsu and Phillips (2005, Annals of Statistics 33, 1890–1933) is proposed for jointly estimating all the memory parameters in general long memory time series that possibly display standard, seasonal, and/or other cyclical strong persistence. Consistency and asymptotic normality are proven for stationary, nonstationary, and noninvertible series, permitting straightforward standard inference of interesting hypotheses such as the existence of unit roots and equality of memory parameters at some or all seasonal frequencies, which can be used as a prior test for the application of seasonal differencing filters. The effects of unknown deterministic terms are also discussed. Finally, the finite sample performance is analyzed in an extensive Monte Carlo exercise and an application to an U.S. Industrial Production index.

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  • Arteche, Josu, 2020. "Exact Local Whittle Estimation In Long Memory Time Series With Multiple Poles," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1064-1098, December.
    • Handle: RePEc:cup:etheor:v:36:y:2020:i:6:p:1064-1098_3
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    Cited by:

    1. Paul M. Beaumont & Aaron D. Smallwood, 2024. "Conditional sum of squares estimation of k-factor GARMA models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 501-543, September.
    2. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    3. Ergemen, Yunus Emre & Rodríguez-Caballero, C. Vladimir, 2023. "Estimation of a dynamic multi-level factor model with possible long-range dependence," International Journal of Forecasting, Elsevier, vol. 39(1), pages 405-430.
    4. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    5. del Barrio Castro, Tomás & Rachinger, Heiko, 2021. "Aggregation of Seasonal Long-Memory Processes," Econometrics and Statistics, Elsevier, vol. 17(C), pages 95-106.

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