Open Access
December, 1972 On Limit Theorems for Quadratic Functions of Discrete Time Series
E. J. Hannan, C. C. Heyde
Ann. Math. Statist. 43(6): 2058-2066 (December, 1972). DOI: 10.1214/aoms/1177690885


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).


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E. J. Hannan. C. C. Heyde. "On Limit Theorems for Quadratic Functions of Discrete Time Series." Ann. Math. Statist. 43 (6) 2058 - 2066, December, 1972.


Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0254.62057
MathSciNet: MR362779
Digital Object Identifier: 10.1214/aoms/1177690885

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 6 • December, 1972
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