The Annals of Statistics

On Consistency in Time Series Analysis

P. M. Robinson

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 6, Number 1 (1978), 215-223.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344080

Digital Object Identifier
doi:10.1214/aos/1176344080

Mathematical Reviews number (MathSciNet)
MR464378

Zentralblatt MATH identifier
0374.60041

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G45

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

Citation

Robinson, P. M. On Consistency in Time Series Analysis. Ann. Statist. 6 (1978), no. 1, 215--223. doi:10.1214/aos/1176344080. https://projecteuclid.org/euclid.aos/1176344080


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