The Poisson limit theorem for high extrema of a time series with seasonal component and monotone trend

In this paper we consider Poisson's limit theorem for high extrema of a stationary time series with a monotone trend and an almost periodic component. It is assumed that the distribution function of the time series is maximum stable and the time series satisfies the weak dependence condition. The limit behavior of the random process of high extrema for this model is considered for the first time.