ALBERT

Note: CONTENTS: 1 Overview. - 1.1 Introduction. - 1.2 Examples and Scope of This Book. - 2 Fundamental Concepts. - 2.1 Stochastic Processes. - 2.2 The Autocovariance and Autocarrelation Functions. - 2.3 The Partial Autocarrelation Function. - 2.4 White Noise Processes. - 2.5 Estimation of the Mean, Autocovariances, and Autocarrelations. - 2.5.1 Sample Mean. - 2.5.2 Sample Autocovariance Function. - 2.5.3 Sample Autocarrelation Function. - 2.5.4 Sample Partial Autocarrelation Function. - 2.6 Moving Average and Autoregressive Representations of Time Series Processes. - 2.7 Linear Difference Equations. - Exercises. - 3 Stationary Time Series Models. - 3.1 Autoregressive Processes. - 3.1.1 The First Order Autoregressive AR(1) Process. - 3.1.2 The Second Order Autoregressive AR(2) Process. - 3.1.3 The General pth Order Autoregressive AR(p)Process. - 3.2 Moving Average Processes. - 3.2.1 The First Order Moving Average MA(1) Process. - 3.2.2 The Second Order Moving Average MA(2) Process. - 3.2.3 The General qth Order Moving Average MA(q) Process. - 3.3 The Dual Relationship between AR(p) and MA(q) Processes. - 3.4 Autoregressive Moving Average ARMA(p,q) Processes. - 3.4.1 The General Mixed ARMA(p,q) Process. - 3.4.2 The ARMA(1, 1) Process. - Exercises. - 4 Nonstationary Time Series Models. - 4.1 Nonstationarity in the Mean. - 4.1.1 Deterministic Trend Models. - 4.1.2 Stochastic Trend Models and Differencing. - 4.2 Autoregressive Integrated Moving Average ARIMA Models. - 4.2.1 The General ARIMA Model. - 4.2.2 The Random Walk Model. - 4.2.3 The ARIMA(0, 1, 1) or IMA(1, 1) Model. - 4.3 Nonstationarity in the Variance and the Autocovariance. - 4.3.1 Variance and Autocovariance of the ARIMA Models. - 4.3.2 Variance Stabilizing Transformations. - Exercises. - 5 Forecasting. - 5.1 lntroduction. - 5.2 Minimum Mean Square Error Forecasts. - 5.2.1 Minimum Mean Square Error Forecasts for ARMA Models. - 5.2.2 Minimum Mean Square Error Forecasts for ARIMA Models. - 5.3 Computation of Forecasts. - 5.4 The ARIMA Forecast as a Weighted Average of Previous Observations. - 5.5 Updating Forecasts. - 5.6 Eventual Forecast Functions. - 5.7 A Numerical Example. - Exercises. - 6 Model ldentification. - 6.1 Steps for Model ldentification. - 6.2 Empirical Examples. - 6.3 Inverse Autocarrelation Function (IACF). - 6.4 Extended Sample Autocarrelation Function and Other ldentification Procedures. - 6.4.1 Extended Sample Autocarrelation Function (ESACF). - 6.4.2 Other ldentification Procedures. - Exercises. - 7 Parameter Estimation, Diagnostic Checking, and Model Selection. - 7.1 The Method of Moments. - 7.2 Maximum Likelihood Method. - 7.2.1 Conditional Maximum Likelihood Estimation. - 7.2.2 Unconditional Maximum Likelihood Estimationand Backcasting Method. - 7.2.3 Exact Likelihood Functions. - 7.3 Nonlinear Estimation. - 7.4 Ordinary Least Squares (OLS) Estimation in Time Series Analysis. - 7.5 Diagnostic Checking. - 7.6 Empirical Examples for Series W1-W7. - 7.7 Model Selection Criteria. - Exercises. - 8 Seasonal Time Series Models. - 8.1 Introduction. - 8.2 Traditional Methods. - 8.2.1 Regression Method. - 8.2.2 Moving Average Method. - 8.3 Seasonal ARIMA Models. - 8.4 Empirical Examples. - Exercises. - 9 Intervention Analysis and Outlier Detection. - 9.1 Intervention Models. - 9.2 Examples of Intervention Analysis. - 9.3 Time Series Outliers. - 9.3.1 Additive and Innovational Outliers. - 9.3.2 Estimation of the Outlier Effect When theTiming of the Outlier ls Known. - 9.3.3 Detection of Outliers Using an Iterative Procedure. - 9.4 Examples of Outlier Analysis. - 9.5 Remarks on Outlier and Intervention Problems. - Exercises. - 10 Fourier Analysis. - 10.1 Introduction. - 10.2 Orthogonal Functions. - 10.3 Fourier Representation of Finite Sequences. - 10.4 Fourier Representation of Periodic Sequences. - 10.5 Fourier Representation of Nonperiodic Sequences - The Discrete-Time Fourier Transform. - 10.6 Fourier Representation of Continuous-Time Functions. - 10.6.1 Fourier Representation of Periodic Functions. - 10.6.2 Fourier Representation of Nonperiodic Functions - The Continuous-Time Fourier Transform. - 10.7 The Fast Fourier Transform. - Exercises. - 11 Spectral Theory of Stationary Processes. - 11.1 The Spectrum. - 11.1.1 The Spectrum and lts Properties. - 11.1.2 The Spectral Representation of Autocovariance Functions - The Spectral Distribution Function. - 11.1.3 Wold's Decomposition of a Stationary Process. - 11.1.4 The Spectral Representation of Stationary Processes. - 11.2 The Spectrum of Same Common Processes. - 11.2.1 The Spectrum and the Autocovariance Generating Function. - 11.2.2 The Spectrum of ARMA Models. - 11.2.3 The Spectrum of the Sum of Two Independent Processes. - 11.2.4 The Spectrum of Seasonal Models. - 11.3 The Spectrum of Linear Filters. - 11.4 Aliasing. - Exercises. - 12 Estimation of the Spectrum. - 12.1 Periodogram Analysis. - 12.1.1 The Periodogram. - 12.1.2 Sampling Properties of the Periodogram. - 12.1.3 Test for Hidden Periodic Components. - 12.2 The Sample Spectrum. - 12.3 The Smoothed Spectrum. - 12.3.1 Smoothing in the Frequency Domain - The Spectral Window. - 12.3.2 Smoothing in the Time Domain - The Lag Window. - 12.3.3 Some Commonly Used Windows. - 12.3.4 Approximate Confidence Intervals for Spectral Ordinates. - 12.4 ARMA Spectral Estimation. - Exercises. - 13 Transfer Function Models. - 13.1 Single-Input Transfer Function Models. - 13.1.1 General Concepts. - 13.1.2 Some Typical Impulse Response Functions. - 13.2 The Cross-Correlation Function and Transfer Function Models. - 13.2.1 The Cross-Correlation Function (CCF). - 13.2.2 The Relationship between the Cross-Correlation Function and the Transfer Function. - 13.3 Construction of Transfer Function Models. - 13.3.1 Sample Cross-Correlation Function. - 13.3.2 Identification of Transfer Function Models. - 13.3.3 Estimation of Transfer Function Models. - 13.3.4 Diagnostic Checking of Transfer Function Models. - 13.3.5 An Empirical Example. - 13.4 Forecasting Using Transfer Function Models. - 13.4.1 Minimum Mean Square Error Forecasts for Stationary Input and Output Series. - 13.4.2 Minimum Mean Square Error Forecasts for Nonstationary Input and Output Series. - 13.4.3 An Example. - 13.5 Bivariate Frequency-Domain Analysis. - 13.5.1 Cross-Covariance Generating Functions and the Cross-Spectrum. - 13.5.2 Interpretation of the Cross-Spectral Functions. - 13.5.3 Examples. - 13.5.4 Estimation of the Cross-Spectrum. - 13.6 The Cross-Spectrum and Transfer Function Models. - 13.6.1 Construction of Transfer Function Models through Cross-Spectrum Analysis. - 13.6.2 Cross-Spectral Functions of Transfer Function Models. - 13.7 Multiple Input Transfer Function Models. - Exercises. - 14 Vector Time Series Models. - 14.1 Covariance and Correlation Matrix Functions. - 14.2 Moving Average and Autoregressive Representations of Vector Processes. - 14.3 The Vector Autoregressive Moving Average Process. - 14.3.1 Vector AR(1) Models. - 14.3.2 Vector AR(p) Models. - 14.3.3 Vector MA(1) Models. - 14.3.4 Vector MA(q) Models. - 14.3.5 Vector ARMA(1, 1) Models. - 14.3.6 Remarks on Vector ARMA Representations. - 14.4 Nonstationary Vector Autoregressive Moving Average Models. - 14.5 Identification of Vector Time Series Models. - 14.5.1 Sample Correlation Matrix Function. - 14.5.2 Partial Autoregression Matrices. - 14.5.3 Partial Lag Correlation Matrix Function. - 14.6 Model Fitting and Forecasting. - 14.7 An Empirical Example. - 14.8 Partial Process and Partial Process Correlation Matrices. - 14.8.1 Covariance Matrix Generating Functions. - 14.8.2 Partial Covariance Matrix Generating Function. - 14.8.3 Partial Process Sample Correlation Matrix Functions. - 14.8.4 An Empirical Example - The U. S. Hog Data. - 14.9 Spectral Properties of Vector Processes. - Exercises. - 15 State Space Models and the Kaiman Filter. - 15.1 Introduction. - 15.2 The Relationship between State Space and ARMA models. - 15.3 State Space Model Fitting and Canonic