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VOL. 52 | 2006 Conditional-sum-of-squares estimation of models for stationary time series with long memory


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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62117

Digital Object Identifier: 10.1214/074921706000000996

Primary: 62M10

Rights: Copyright © 2006, Institute of Mathematical Statistics


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