The Annals of Mathematical Statistics

On Limit Theorems for Quadratic Functions of Discrete Time Series

E. J. Hannan and C. C. Heyde

Full-text: Open access

Abstract

In this paper it is shown how martingale theorems can be used to appreciably widen the scope of classical inferential results concerning autocorrelations in time series analysis. The object of study is a process which is basically the second-order stationary purely non-deterministic process and contains, in particular, the mixed autoregressive and moving average process. We obtain a strong law and a central limit theorem for the autocorrelations of this process under very general conditions. These results show in particular that, subject to mild regularity conditions, the classical theory of inference for the process in question goes through if the best linear predictor is the best predictor (both in the least squares sense).

Article information

Source
Ann. Math. Statist., Volume 43, Number 6 (1972), 2058-2066.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177690885

Digital Object Identifier
doi:10.1214/aoms/1177690885

Mathematical Reviews number (MathSciNet)
MR362779

Zentralblatt MATH identifier
0254.62057

JSTOR
links.jstor.org

Citation

Hannan, E. J.; Heyde, C. C. On Limit Theorems for Quadratic Functions of Discrete Time Series. Ann. Math. Statist. 43 (1972), no. 6, 2058--2066. doi:10.1214/aoms/1177690885. https://projecteuclid.org/euclid.aoms/1177690885


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