Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors. (English) Zbl 0727.62087

Summary: The least squares invariant quadratic estimator of an unknown covariance function of a stochastic process is defined and a sufficient condition for consistency of this estimator is derived. The mean value of the observed process is assumed to fulfil a linear regression model. A sufficient condition for consistency of the least squares estimator of the regression parameters is derived, too.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J05 Linear regression; mixed models
Full Text: DOI EuDML


[1] T. W. Anderson J. B. Taylor: Strong consistency of least squares estimates in normal linear regression. Ann. Stat. 4 (1976), 788-790. · Zbl 0339.62039 · doi:10.1214/aos/1176343552
[2] E. Z. Demidenko: Linear and nonlinear regression. (Russian) Finansy i statistika, Moscow 1981.
[3] E. J. Hannan: Rates of convergence for time series regression. Advances Appl.. Prob. 10 (197S), 740-743. · Zbl 0394.62068 · doi:10.2307/1426656
[4] V. Solo: Strong consistency of least squares estimators in regression with correlated disturbances. Ann. Stat. 9 (1981), 689-693. · Zbl 0477.62048 · doi:10.1214/aos/1176345476
[5] F. Štulajter: Estimators in random processes. (Slovak). Alfa, Bratislava 1989.
[6] R. Thrum J. Kleffe: Inequalities for moments of quadratic forms with applications to almost sure convergence. Math. Oper. Stat. Ser. Stat. 14 (1983), 211 - 216. · Zbl 0545.60027 · doi:10.1080/02331888308801697
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.