Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T07:35:49.005Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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