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Semiparametric Whittle estimation of a cyclical long-memory time series based on generalised exponential models

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  • Masaki Narukawa

Abstract

This paper considers a semiparametric estimation of the memory parameter in a cyclical long-memory time series, which exhibits a strong dependence on cyclical behaviour, using the Whittle likelihood based on generalised exponential (GEXP) models. The proposed estimation is included in the so-called broadband or global method and uses information from the spectral density at all frequencies. We establish the consistency and the asymptotic normality of the estimated memory parameter for a linear process and thus do not require Gaussianity. A simulation study conducted using Monte Carlo experiments shows that the proposed estimation works well compared to other existing semiparametric estimations. Moreover, we provide an empirical application of the proposed estimation, applying it to the growth rate of Japan's industrial production index and detecting its cyclical persistence.

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  • Masaki Narukawa, 2016. "Semiparametric Whittle estimation of a cyclical long-memory time series based on generalised exponential models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 272-295, June.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:272-295
    DOI: 10.1080/10485252.2016.1163350
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    Cited by:

    1. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.

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