Probability theory and mathematical statistics

On the existence of stationary sequences of $M$-orthogonal random variables with specified covariances

I. S. Borisov

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: Necessary and sufficient conditions are studied for a covariance matrix of finite size to be interpreted as a covariance matrix of a finite segment of an infinite stationary sequence of random variables.

Keywords: stationary sequence, $m$-dependent random variables, covariance matrix.

UDC: 519.21

MSC: 60G10

Received September 29, 2024, published November 1, 2024

DOI: 10.33048/semi.2024.21.064