Abstract
In this paper a generalization of the semi-Pareto autoregressive minification process of the first order is given. The necessary and sufficient condition for stationarity of the process is determined. It is shown that the process is ergodic and uniformly mixing. The joint survival function and the joint density function of the random variables X n+h and X n are determined. The extremes of the random variables X 1, X 2, ..., X n and the geometric extremes of random variables X 1, X 2, ..., X N are derived and their asymptotic distributions are discussed. The estimation of the parameters is discussed and some numerical results are given.
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