Non-Stationary Stochastic Processes Estimation

1 Periodically stationary multi-seasonal increments of stochastic sequences

In this chapter, we describe properties of the periodically stationary long memory multiplicative seasonal increments of discrete time stochastic processes defined and studied in [117]. We give a definition of the increment sequence and introduce stochastic sequences with periodically stationary (periodically correlated, cyclostationary) long memory multiplicative seasonal increments. These non-stationary stochastic sequences combine the periodic structure of covariation functions of sequences as well as the integrating pattern. A short review of the spectral theory of these increment sequences is presented.

1.1 Stochastic sequences with periodically stationary generalized ...