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

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.

Keywords:

• long memory
• cyclical behaviour
• semiparametric estimation
• exponential models

2010 Mathematics Subject Classification:

• 62M10
• 62G05

Acknowledgments

The author would like to thank anonymous referees for helpful comments and suggestions that have led to improvements in the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported in part by JSPS Grants-in-Aid for Scientific Research [23730209, 15K17038] .