Singularities of kernels of linear autoregressive (AR) processes and linear autoregressive--moving-average (ARMA) processes are considered. The paper contains some aspects of the theory of linear stochastic process and discusses a method of estimation and simulation of kernels of linear AR and ARMA processes. Linear stationary AR and ARMA processes, as well as linear AR and ARMA processes with periodic structures are considered. Characteristic functions of linear stationary AR and ARMA processes are presented. Characteristic functions of linear AR and ARMA processes with periodic structures are presented as well.

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