Efficient Estimation of Regression Coefficients in Time Series
STANFORD UNIV CA DEPT OF STATISTICS
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Problems of efficient estimation are considered in the model in which the T-component observable random vector y has expected value Z beta, where Z is a T x p matrix of known numbers of rank p or T and beta is a p-component vector of regression coefficients, and nonsingular covariance matrix sigma. The least squares estimate of beta is identical to the Markov or Best Linear Unbiased Estimate if and only if the p columns of Z are linearly independent linear combinations of p linearly independent characteristic vectors of sigma. The proof uses the covariance matrices of the estimates. When the components constitute time series such that sigma corresponds to a stochastic process stationary in the wide sense, the limits of the appropriately normalized covariance matrices of the two estimates are considered as T approaches infinity.
- Statistics and Probability