Preface to the Second Edition
Preface to the First Edition
CHAPTER 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 Problems
CHAPTER 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 Problems
CHAPTER 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 Problems
CHAPTER 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) Problems
CHAPTER 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,-∞ 0
6.3 Convergence in Distribution
6.4 Central Limit Theorems and Related Results Problems
CHAPTER 7 Estimation of the Mean and the Autocovariance Function
7.1 Estimation of
7.2 Estimation ofγ(.) and p(.)
7.3* Derivation of the Asymptotic Distributions Problems
CHAPTER 8 Estimation for ARMA Models
8.1 The Yule-Walker Equations and Parameter Estimation for Autoregressive Processes
8.2 Preliminary Estimation for Autoregressive Processes Using the Durbin-Levinson Algorithm
8.3 Preliminary Estimation for Moving Average Processes Using the Innovations Algorithm
8.4 Preliminary Estimation for ARMA(p, q) Processes
8.5 Remarks on Asymptotic Efficiency
8.6 Recursive Calculation of the Likelihood of an Arbitrary Zero-Mean Gaussian Process
8.7 Maximum Likelihood and Least Squares Estimation for ARMA Processes
8.8 Asymptotic Properties of the Maximum Likelihood Estimators
8.9 Confidence Intervals for the Parameters of a Causal Invertible ARMA Process
8.10* Asymptotic Behavior of the Yule-Walker Estimates
8.11 * Asymptotic Normality of Parameter Estimators Problems
CHAPTER 9 Model Building and Forecasting with ARIMA Processes
9.1 ARIMA Models for Non-Stationary Time Series
9.2 Identification Techniques
9.3 Order Selection
9.4 Diagnostic Checking
9.5 Forecasting ARIMA Models
9.6 Seasonal ARIMA Models Problems
CHAPTER 10 Inference for the Spectrum of a Stationary Process
10.1 The Periodogram
10.2 Testing for the Presence of Hidden Periodicities
10.3 Asymptotic Properties of the Periodogram
10.4 Smoothing the Periodogram
10.5 Confidence Intervals for the Spectrum
10.6 Autoregressive, Maximum Entropy, Moving Average and Maximum Likelihood ARMA Spectral Estimators
10.7 The Fast Fourier Transform (FFT) Algorithm
10.8* Derivation of the Asymptotic Behavior of the Maximum Likelihood and Least Squares Estimators of the Coefficients of an ARMA Process Problems
CHAPTER 11 Multivariate Time Series
11.1 Second Order Properties of Multivariate Time Series
11.2 Estimation of the Mean and Covariance Function
11.3 Multivariate ARMA Processes
11.4 Best Linear Predictors of Second Order Random Vectors
11.5 Estimation for Multivariate ARMA Processes
11.6 The Cross Spectrum
11.7 Estimating the Cross Spectrum
11.8* The Spectral Representation of a Multivariate Stationary Time Series Problems
CHAPTER 12 State-Space Models and the Kalman Recursions
12.1 State-Space Models
12.2 The Kalman Recursions
12.3 State-Space Models with Missing Observations
12.4 Controllability and Observability
12.5 Recursive Bayesian State Estimation Problems
CHAPTER 13 Further Topics
13.1 Transfer Function Modelling
13.2 Long Memory Processes
13.3 Linear Processes with Infinite Variance
13.4 Threshold Models Problems
Appendix: Data Sets
Bibliography
Index
