On Estimating Time Series Parameters Using Sample Autocorrelations
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1983 · Volume 45 · Issue 1
DOI: 10.1111/j.2517-6161.1983.tb01237.x
Abstract
Consider a scalar linear process {xt} whose spectral density isσ2k(λ,θ0) where σ2is the innovation variance and. We introduce a class of estimators of θ0based only on the sample autocorrelations. These estimators are shown to be consistent and asymptotically normally distributed with a covariance matrix which is independent of the distributions of the innovations. A lower bound to the asymptotic covariances of these estimators is derived and is shown to be achieved by the least-squares estimator. We also consider the extent to which these results generalize to the multivariate case. In particular, we present a multivariate generalization of the main result presented by Kabaila (1980).
Keywords
time series, estimation efficiency, least squares, sample autocorrelations
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