Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments
- Boston : De Gruyter, 2024.
- xviii, 292p. : ill. ; 24 cm.
Includes bibliography and index.
The problem of forecasting future values of economic and physical processes, the problem of restoring lost information, cleaning signals or other data observations from noise, is magnified in an information-laden word. Methods of stochastic processes estimation depend on two main factors.The first factor is construction of a model of the process being investigated. The second factor is the available information about the structure of the process under consideration. In this book, we propose results of the investigation of the problem of mean square optimal estimation (extrapolation, interpolation, and filtering) of linear functionals depending on unobserved values of stochastic sequences and processeswith periodically stationary and long memory multiplicative seasonal increments.Formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the functionals are derived in the case of spectral certainty, where spectral structure of the considered sequences and processes are exactly known.