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EXACT LOCAL WHITTLE ESTIMATION IN LONG MEMORY TIME SERIES WITH MULTIPLE POLES

Published online by Cambridge University Press:  05 March 2020

Josu Arteche
Josu Arteche*
Affiliation:
University of the Basque Country UPV/EHU
*
Address correspondence to Josu Arteche, Department of Econometrics and Statistics, University of the Basque Country UPV/EHU, Bilbao 48015 Spain; e-mail: josu.arteche@ehu.eus.
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 6 , December 2020 , pp. 1064 - 1098
Copyright
© Cambridge University Press 2020

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Footnotes

*

Research was supported by the Spanish Ministry of Science and Innovation and ERDF grant ECO2016-76884-P, and UPV/EHU Econometrics Research Group, Basque Government grant IT1359-19. The author thanks the Editor, Co-Editor, three anonymous referees, Javier García-Enríquez, Rajendra Bhansali, Carlos Velasco, Javier Hualde, and Tomás del Barrio for useful constructive comments.

References

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