Unlock the complexities of non-stationary stochastic processes with this essential De Gruyter Textbook. Explore advanced estimation techniques for forecasting, data restoration, and signal cleaning in our information-rich world. This comprehensive guide delves into vector stationary increments and periodically stationary multi-seasonal increments, offering solutions for mean-square optimal estimation (extrapolation, interpolation, and filtering). Discover formulas for calculating errors and spectral characteristics when the spectral structure is known. For scenarios with unknown spectral densities, the book presents the robust minimax-estimation method. Essential for researchers and practitioners in econometrics, signal processing, and data science seeking to master the estimation of complex time series.