Open Access
September, 1982 Autocorrelation, Autoregression and Autoregressive Approximation
Hong-Zhi An, Chen Zhao-Guo, E. J. Hannan
Ann. Statist. 10(3): 926-936 (September, 1982). DOI: 10.1214/aos/1176345882


Theorems are proved relating to the rate of almost sure convergence of autocovariances, and hence autocorrelations, to their true values. These rates are uniform in the lag up to some order $P(T)$, increasing with $T$. The key assumption is that the process is stationary and the best linear predictor is the best predictor. In particular for an ARMA process and $P(T) = O\{(\ln T)^a\}, a < \infty$, the rate is $O\{(\ln \ln T/T)^{1/2}\}$. These results are used to discuss autoregressions and the use of autoregressions to approximate the structure of a more general process by increasing the order of the autoregression with $T$.


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Hong-Zhi An. Chen Zhao-Guo. E. J. Hannan. "Autocorrelation, Autoregression and Autoregressive Approximation." Ann. Statist. 10 (3) 926 - 936, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0512.62087
MathSciNet: MR663443
Digital Object Identifier: 10.1214/aos/1176345882

Primary: 62M10
Secondary: 60F15

Keywords: autocovariance , Autoregression , autoregressive approximation , Law of the iterated logarithm , martingale , method of subsequences , stationary process , strong convergence

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • September, 1982
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