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July, 1995 On the Almost Sure Convergence of Series of Stationary and Related Nonstationary Variables
Christian Houdre
Ann. Probab. 23(3): 1204-1218 (July, 1995). DOI: 10.1214/aop/1176988180

Abstract

Let $\{X_n\}$ be, for example, a weakly stationary sequence or a lacunary system with finite $p$th moment, $1 \leq p \leq 2$, and let $\{a_n\}$ be a sequence of scalars. We obtain here conditions which ensure the almost sure convergence of the series $\sum a_nX_n$. When $\{X_n\}$ is an orthonormal sequence, the classical Rademacher-Menchov theorem is recovered. This is then applied to study the strong consistency of least squares estimates in multiple regression models.

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Christian Houdre. "On the Almost Sure Convergence of Series of Stationary and Related Nonstationary Variables." Ann. Probab. 23 (3) 1204 - 1218, July, 1995. https://doi.org/10.1214/aop/1176988180

Information

Published: July, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0839.60034
MathSciNet: MR1349168
Digital Object Identifier: 10.1214/aop/1176988180

Subjects:
Primary: 60F15
Secondary: 60E07 , 60G10 , 60G12

Keywords: $S \alpha S$ harmonizable sequences , $S_p$-systems , Almost sure convergence , least squares , Mixing , multiple regression , Rademacher-Menchov theorem , series , stationary Markov chains , Stationary sequences , strong consistency , Weak dependence

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 3 • July, 1995
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