On the asymptotically efficient regression estimates in the case of degenerate spectrum

N. P. Rasulov

Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 324-333

Résumé

Asymptotically efficient regression estimates for the time series $$ \xi(t)=\sum\alpha_j\theta_j(t)+\Delta t,\qquad t=1,2,\dots, $$ are considered under the assumption that the stationary residual $\Delta(t)$ has the spectral density of the form $f(\lambda)=|P(e^{i\lambda})|^2g(\lambda)$, where $g(\lambda)>0$, $P(z)$ is a polynomial with zeroes on the unit circumference $|z|=1$.