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An iterated logarithm result for martingales and its application in estimation theory for autoregressive processes

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
C. C. Heyde*
Affiliation:
The Australian National University
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Abstract

The paper begins with an iterated logarithm law of classical Hartman-Wintner form for stationary martingales. This is then used to obtain iterated logarithm results giving information on rates of convergence of estimators of the parameters in a stationary autoregressive process. In the case of an autoregression of small order, detailed rate results for each autocorrelation and for the estimators of all parameters can be obtained. A rate result for the convergence of the sample mean is given in the general case.

Keywords

ITERATED LOGARITHM LAWMARTINGALESTIME SERIES ESTIMATIONAUTOREGRESSIVE PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 146 - 157
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
[2] Hannan, E. J. and Heyde, C. C. (1972) On limit theorems for quadratic functions of discrete time series. Ann. Math. Statist. 43, 2058–2066.Google Scholar
[3] Stout, W. F. (1970) The Hartman-Wintner law of the iterated logarithm for martingales. Ann. Math. Statist. 41, 2158–2160.CrossRefGoogle Scholar