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.