Non-Asymptotic Confidence Estimation of the Autoregressive Process Paremeters in the Case of an Unknown Noise Variance

S. E. Vorobeychikov 1 * A. V. Pupkov 2 **

1Tomsk State University, Tomsk, 634050 Russia

2Tomsk State University, Tomsk,634050 Russia

Correspondence to: *e-mail: sev@mail.tsu.ru
Correspondence to: **e-mail: andrewpupkov@gmail.com

February 6, 2023

Abstract—A non-asymptotic procedure of constructing the confidence region of the parameter of the $p$-th order Gaussian autoregressive process AR(p) in the case of an unknown process noise variance is considered. The confidence estimation procedure is based on the martingale property of the numerator of estimate deviation of the least square technique (LST). The results of numerical modeling are presented.

Keywords: autoregressive processLST estimatesequential estimationnon-asymptotic confidence region

DOI: 10.3103/S8756699023040106