Foundations of time series analysis and prediction theory (Q2754859)

This monograph provides foundations for time series analysis and prediction theory. Special effort is made to motivate the results on the structure and prediction of stationary processes both in the time domain and in the spectral domain, especially to explain, extend and unify in a mathematically coherent manner the diverse developments of the last few decades. NEWLINENEWLINENEWLINEAfter the introduction, Chapter 2 (Time series analysis: one long series), deals with several key results for analyzing dependent data (e.g. elimination and estimation of trend, transformations to orthogonality, forecasting systems). Chapter 3 (Time series analysis: many short series), generalizes the methods developed initially to model the covariance matrix of one long stationary series to model the common covariance matrix of several short nonstationary series or longitudinal data using the Cholesky decomposition. Chapter 4 (Stationary ARMA models), presents classical results on ARMA models (including the functional form of the likelihood function of Gaussian ARMA models). Chapter 5 (Stationary processes), discusses spectral representations of a stationary process and its covariance function, convergence of the natural estimators of the covariance and spectral density functions and basic results of prediction theory. NEWLINENEWLINENEWLINEChapter 6 (Parameterization and prediction), presents a versatile method (based on the regression technique) of parameterizing stationary processes. Chapter 7 (Finite prediction and partial correlations), deals with the linear least squares predictors based on the finite past (e.g., partial correlations and their convergnece, Durbin-Levinson algorithm, connections with the theory of orthogonal polynomials). Chapter 8 (Missing values: past and future), presents, e.g., canonical correlations between past and future, the missing value problem, prediction using incomplete past and intervention analysis. Chapter 9 (Stationary sequences in Hilbert spaces) and Chapter 10 (Stationarity and Hardy spaces) concentrate on mathematics of prediction theory. NEWLINENEWLINENEWLINEThe book is suitable for researchers and advanced students who are interested in the deeper aspects of time series analysis.