Polynomial Trend Regression With Long-memory Errors

For a time series generated by polynomial trend with stationary long-memory errors, the ordinary least squares estimator (OLSE) of the trend coefficients is asymptotically normal, provided the error process is linear. The asymptotic distribution may no longer be normal, if the error is in the form of a long-memory linear process passing through certain nonlinear transformations. However, one hardly has sufficient information about the transformation to determine which type of limiting distribution the OLSE converges to and to apply the correct distribution so as to construct valid confidence intervals for the coefficients based on the OLSE. The present paper proposes a modified least squares estimator to bypass this drawback. It is shown that the asymptotic normality can be assured for the modified estimator with mild trade-off of efficiency even when the error is nonlinear and the original limit for the OLSE is non-normal. The estimator performs fairly well when applied to various simulated series and two temperature data sets concerning global warming. Copyright 2005 Blackwell Publishing Ltd.