The Invariant Quadratic Estimators, the Maximum Likelihood Estimator (MLE) and Restricted Maximum Likelihood Estimator (REML) of variances in an orthogonal Finite Discrete Spectrum Linear Regression Model (FDSLRM) are derived and the problems of unbiasedness and consistency of these estimators are investigated. Copyright Springer-Verlag 2004Time series, finite discrete spectrum linear regression model, invariant quadratic estimators of variance components, maximum likelihood estimation, restricted maximum likelihood estimation,
Predictions in time series using multivariate regression models are studied with respect to their mean squared errors. Two new methods of prediction are proposed: the simple one and the method based on the kriging theory. The mean squared errors of these predictions are computed and it is shown that the ®rst one can be regarded as a special case of the kriging approach.Keywords. Multivariate regression model; best linear unbiased predictor; mean squared error of predictor.
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