LOG-PERIODOGRAM REGRESSION OF TIME-SERIES WITH LONG-RANGE DEPENDENCE

This paper discusses the estimation of multiple time series models whi ch allow elements of the spectral density matrix to tend to infinity o r zero at zero frequency and be unrestricted elsewhere. A form of log- periodogram regression estimate of differencing and scale parameters i s proposed, which can provide modest efficiency improvements over a pr eviously proposed method (for which no satisfactory theoretical justif ication seems previously available) and further improvements in a mult ivariate context when differencing parameters are a priori equal. Assu ming Gaussianity and additional conditions which seem mild, asymptotic normality of the parameter estimates is established.