Preface to the Second EditionPreface to the First EditionCHAPTER 1 Stationary Time Series 1.1 Examples of Time Series 1.2 Stochastic Processes 1.3 Stationarity and Strict Stationarity 1.4 The Estimation and Elimination of Trend and Seasonal Components !.5 The Autocovariance Function of a Stationary Process 1.6 The Multivariate Normal Distribution 1.7 Applications of Kolmogorov's Theorem ProblemsCHAPTER 2 Hilbert Spaces 2.1 Inner-Product Spaces and Their Properties 2.2 Hilbert Spaces 2.3 The Projection Theorem 2.4 Orthonormal Sets 2.5 Projection in R 2.6 Linear Regression and the General Linear Model 2.7 Mean Square Convergence, Conditional Expectation and Best Linear Prediction in L2(t, P) 2.8 Fourier Series 2.9 Hilbert Space Isomorphisms 2.10* The Completeness of L2 (D, ,, P) 2.11* Complementary Results for Fourier Series ProblemsCHAPTER 3 Stationary ARMA Processes 3.1 Causal and Invertible ARMA Processes 3.2 Moving Average Processes of Infinite Order 3.3 Computing the Autocovariance Function of an ARMA(p, q) Process 3.4 The Partial Autocgrrelation Function 3.5 The Autocovariance Generating Function 3.6* Homogeneous Linear Difference Equations with Constant Coefficients ProblemsCHAPTER 4 The Spectral Representation of a Stationary Process 4.1 Complex-Valued Stationary Time Series 4.2 The Spectral Distribution of a Linear Combination of Sinusoids 4.3 Herglotz's Theorem 4.4 Spectral Densities and ARMA Processes 4.5* Circulants and Their Eigenvalues 4.6* Orthogonal Increment Processes on [- n, n] 4.7* Integration with Respect to an Orthogonal Increment Process 4.8* The Spectral Representation 4.9* Inversion Formulae 4.10* Time-lnvariant Linear Filters 4.11* Properties of the Fourier Approximation hn to I(v,w) ProblemsCHAPTER 5 Prediction of Stationary Processes 5.1 The Prediction Etuations in the Time Domain 5.2 Recursive Methols for Computing Best Linear Predictors 5.3 Recursive Prediction of an ARMA(p, q) Process 5.4 Prediction of a Stationary Gaussian Process; Prediction Bounds 5.5 Prediction of a Causal lnvertible ARMA Process in Terms ofXj,-��