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January, 1978 On Consistency in Time Series Analysis
P. M. Robinson
Ann. Statist. 6(1): 215-223 (January, 1978). DOI: 10.1214/aos/1176344080

Abstract

A number of statistics that arise in time series analysis can be represented as the sum of a partial realization of a possibly serially dependent and nonstationary discrete-parameter stochastic process. The almost sure and $L_p, p > 1$, convergence of such statistics is investigated, under various moment conditions. The results are applied to the least squares estimates of multiple regressions.

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P. M. Robinson. "On Consistency in Time Series Analysis." Ann. Statist. 6 (1) 215 - 223, January, 1978. https://doi.org/10.1214/aos/1176344080

Information

Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0374.60041
MathSciNet: MR464378
Digital Object Identifier: 10.1214/aos/1176344080

Subjects:
Primary: 60F15
Secondary: 60G45 , 62M10

Keywords: $L_p$ convergence , Almost sure convergence , martingale inequalities , time series regression

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 1 • January, 1978
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