Summary: A multiple time series regression model with trending regressors has residuals that are believed to be not only serially dependent but nonstationary. Assuming the residuals can be decomposed as a stationary autoregressive process of known order multiplied by an unknown time- varying scale factor, we propose estimators of the regression coefficients and show them to be as efficient as estimators based on known scale factors.
Our estimators have features in common with adaptive estimators proposed by R. J. Carroll [Ann. Stat. 10, 1224-1233 (1982; Zbl 0571.62058)] and E. J. Hannan [Proc. Symp. Time Ser. Anal., Brown Univ. 1962, 17-37 (1963; Zbl 0209.204)] for different regression problems, involving respectively independent residuals with heteroskedasticity of unknown type, and stationary residuals with unknown serial dependence structure.