Statistical Analysis of First-Order MARMA Processes

In this paper, we consider processes of the MARMA type that can be derived from the classical ARMA processes by replacing summation by the maximum operation. It is assumed that the innovations and the values of the process have the standard Fréchet distribution. For simple MARMA processes of first order, certain numerical characteristics are calculated. Sign tests and rank statistical methods for parameter estimation are developed. The characterization relations that can be used for the identification of models are justified.