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

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

2007-02-26

arxiv.org/abs/math/0702782v1

IMS Lecture Notes Monograph Series 2006, Vol. 52, 130-137

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000996 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000000996

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.

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