Non-Stationary Stochastic Processes Estimation

5 Filtering of sequences with periodically stationary increments

In this chapter, we deal with the filtering problem for stochastic sequences with periodically stationary long memory multi-seasonal increments based on observations of the sequence with a periodically stationary noise sequence. The problem is investigated with the help of representation of the considered sequences in the form of a multidimensional stochastic sequence with stationary GM increments and a multidimensional stationary noise sequence.

5.1 Hilbert space projection method of filtering

5.1.1 Filtering of multidimensional stochastic sequences with stationary GM increment

Consider a multidimensional stochastic sequence $\overrightarrow{\mathit{\xi }}\mathrm{(}\mathit{m}\mathrm{)}$ with stationary GM increments constructed ...