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Econometrics Paper
Conditional-Sum-of-Squares Estimation of Models for Stationary Time Series with Long Memory
Peter M Robinson
September 2006
Paper No' EM/2006/505:
Full Paper (pdf)

Tags: long memory; conditional-sum-of-squares estimation; central limit theorem; almost sure convergence.

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.