Sequential estimation for time series regression models

Abstract

Sequential procedures are proposed to estimate the regression parameters in a linear regression model with dependent residuals. The error process considered here is a linear process with unknown spectral density. The sequential point estimator for the regression parameters is based on the least-squares estimator and is shown to be asymptotically risk efficient under some natural conditions on the design sequence. Simulation studies are given to evaluate the asymptotic performances of the sequential procedures of the sequential estimator.