Institute of Mathematical Statistics Lecture Notes - Monograph Series

Conditional-sum-of-squares estimation of models for stationary time series with long memory

P. M. Robinson

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Employing recent results of Robinson (2005) we consider the asymptotic properties of conditional-sum-of-squares (CSS) estimates of parametric models for stationary time series with long memory. CSS estimation has been considered as a rival to Gaussian maximum likelihood and Whittle estimation of time series models. The latter kinds of estimate have been rigorously shown to be asymptotically normally distributed in case of long memory. However, CSS estimates, which should have the same asymptotic distributional properties under similar conditions, have not received comparable treatment: the truncation of the infinite autoregressive representation inherent in CSS estimation has been essentially ignored in proofs of asymptotic normality. Unlike in short memory models it is not straightforward to show the truncation has negligible effect.

Chapter information

Hwai-Chung Ho, Ching-Kang Ing, Tze Leung Lai, eds., Time Series and Related Topics: In Memory of Ching-Zong Wei (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 130-137

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

long memory conditional-sum-of-squares estimation central limit theorem almost sure convergence

Copyright © 2006, Institute of Mathematical Statistics


Robinson, P. M. Conditional-sum-of-squares estimation of models for stationary time series with long memory. Time Series and Related Topics, 130--137, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000996.

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