ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 65,   1   (1996)
pp.   129-139

ON VARIANCE-COVARIANCE COMPONENTS ESTIMATION IN LINEAR MODELS WITH AR(1) DISTURBANCES
V. WITKOVSKY

Abstract.  Estimation of the autoregressive coefficient $\varrho$ in linear models with first-order autoregressive disturbances has been broadly studied in the literature. Based on C.R. Rao's MINQE-theory, Aza\is et al. (1993) gave a new general approach for computing locally optimum estimators of variance-covariance components in models with non-linear structure of the variance-covariance matrix. As a special case, in the linear model with AR(1) errors, we discuss a new algorithm for computing locally optimum quadratic plus constant invariant estimators of the parameters $\varrho$ and $\sigma^2$, respectively. Moreover, simple iteration of this estimation procedure gives a maximum likelihood estimates of both, the first order parameters, and the variance-covariance components.

AMS subject classification.  62J10, 62F30
Keywords.  Autoregressive disturbances, variance-covariance components, minimum norm quadratic estimation, maximum likelihood estimation, Fisher scoring algorithm, MINQE(I), LMINQE(I), AR(1), MLE, FSA