ABSTRACT
The primary interest is in the study of nonstationary processes where the joint distribution of studied time series and/or the modification mechanism may change in time. It begins with the analysis of a nonparametric regression with dependent regression errors, in particular long-memory ones. The chapter discusses classical continuous time processes, including Brownian motion and white noise, and explores learning how to filter a continuous signal from a white noise. It considers a nonstationary discrete-time series and learn how to detrend, deseasonalize and descale it to estimate the spectral density of an underlying stationary time series. The case of missing observations is considered as well. The chapter considers a classical decomposition of amplitude-modulated time series and explains how to deal with a missing mechanism that changes in time. It considers the case of a nonstationary time series with changing in time spectral density. The chapter explores the potential of a controlled design of predictors in a regression.
