Non-Stationary Stochastic Processes Estimation

4 Interpolation of sequences with periodically stationary increments observed with or without noise

In this chapter we deal with the interpolation problem for stochastic sequences with periodically stationary long memory multi-seasonal increments. Estimates are based on observations of the sequence with a periodically stationary noise sequence.

To describe the problem precisely consider a stochastic sequence $\mathit{\vartheta }\mathrm{(}\mathit{m}\mathrm{)}$ with periodically stationary GM increments and a periodically stationary noise sequence $\mathit{\eta }\mathrm{(}\mathit{m}\mathrm{)}$ uncorrelated with $\mathit{\vartheta }\mathrm{(}\mathit{m}\mathrm{)}$. Consider a multidimensional stochastic sequence with stationary GM increments $\overrightarrow{\mathit{\xi }}\mathrm{(}\mathit{m}\mathrm{)}$ generated by transformation (1.2) and a multidimensional stationary stochastic sequence $\overrightarrow{\mathit{\eta }}\mathrm{(}\mathit{m}\mathrm{)}$ uncorrelated with the sequence $\overrightarrow{\mathit{\xi }}\mathrm{(}$