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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 22, Fasc. 1,
pages 101 - 113
 

ON HARTMAN’S LAW OF ITERATED LOGARITHM FOR EXPLOSIVE GAUSSIAN AUTOREGRESSIVE PROCESSES

Bernard Bercu
Abderrahmen Touati

Abstract: A law of iterated logarithm is established for the maximum likelihood estimator of the unknown parameter of the explosive Gaussian autoregressive process. Outside the Gaussian case, we show that the law of iterated logarithm does not hold, except for a suitable averaging on the maximum likelihood estimator.

2000 AMS Mathematics Subject Classification: Primary 60G15; Secondary 60F15, 62A10.

Key words and phrases: Autoregressive Gaussian process, law of iterated logarithm, maximum likelihood estimation.

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