Analysis of Economic Time Series

PrefaceChapter I A History of the Idea of Unobserved Components in the Analysis of Economic Time Series 1. Introduction 2. Background 3. Origins 4. Nineteenth Century Contributors 5. Recent Developments 6. Application to Seasonal Adjustment and "Current Analysis" 7. Application to the Historical Analysis of Business CyclesChapter II Introduction to the Theory of Stationary Time Series 1. Introduction 2. What Is a Stationary Time Series? Ergodicity 3. The Wold Decomposition TheoremChapter III The Spectral Representation and Its Estimation 1. Introduction 2. Covariance Generating Functions 3. The Spectral Representation of a Stationary Time Series 4. The Cross-Spectral Distribution Function of Two Jointly Stationary Time Series and Filtering 5. Estimation of the Autocovariance Function and the Spectral Density FunctionChapter IV Formulation and Analysis of Unobserved-Components Models 1. Introduction 2. Unobserved-Components Models and Their Canonical Forms 3. Digression on a General Method for the Determination of the Autocovariances of a Mixed Moving-Average Autoregressive ProcessChapter V Elements of the Theory of Prediction and Extraction 1. Introduction 2. Prediction 3. Examples of the Application of Minimum-Mean-Square-Error Forecasts 4. Signal Extraction 5. Examples of Minimum-Mean-Square-Error Signal ExtractionChapter VI Formulation of Unobserved-Components Models and Canonical Forms 1. Introduction 2. Determining the Form of a Univariate Time-Series ARMA Model 3. Determining the Form of a Univariate Time-Series Unobserved-Components Model 4. The Analysis of a Time Series by More Than Its Own PastChapter VII Estimation of Unobserved-Components and Canonical Models 1. Introduction 2. ARMA Model Estimation in the Time Domain 3. UC Model Estimation in the Time Domain 4. ARMA Model Estimation in the Frequency Domain 5. Unobserved-Components Model Estimation in the Frequency Domain 6. Hypothesis Testing 7. Estimation of Multiple Time-Series ModelsChapter VIII Appraisal of Seasonal Adjustment Techniques 1. Criteria for "Optimal" Seasonal Adjustment 2. Choice of Models 3. Some Results 4. Seasonal Adjustment and the Estimation of Structural Models 5. ConclusionChapter IX On the Comparative Structure of Serial Dependence in Some U.S. Price Series 1. Introduction 2. Brief Characterization of Selected Nonindustrial Price Series of the Bureau of Labor Statistics 3. Buyer's Prices and Seller's Prices: The National Bureau of Economic Research Series and the Stigler-Kindahl Study 4. ConclusionsChapter X Formulation and Estimation of Mixed Moving-Average Autoregressive Models for Single Time Series: Examples 1. Introduction 2. The Formulation Procedure of Box and Jenkins 3. An Alternative Method for the Formulation of an A RIMA Model 4. The Detailed Examples 5. Comparison Between Estimation Methods in the Frequency and Time DomainsChapter XI Formulation and Estimation of Multivariate Mixed Moving-Average Autoregressive Time-Series Models 1. Introduction 2. A Single-Equation Approach 3. A Simultaneous-Equations Approach 4. Estimation of Multiple Time-Series Models for Interrelated Agricultural Prices 5. Testing and Checking the Multiple Time-Series Models for Interrelated Agricultural PricesChapter XII Formulation and Estimation of Unobserved-Components Models: Examples 1. Introduction 2. Formulation of the Models: Trend Reduction 3. Estimation of the Models in Time and Frequency Domains 4. Predictive Properties of Unobserved-Components ModelsChapter XIII Application to the Formulation of Distributed-Lag Models 1. Introduction 2. Prediction and Expectation-Formation Models 3. Signal Extraction 4. Distributed Lags in Dynamic Models 5. EstimationChapter XIV A Time-Series Model of the U.S. Cattle Industry 1. Introduction 2. The Cattle Industry 3. Cattleman Behavior: A Simple Example 4. Cattleman Behavior: A Quarterly Model 5. Tests of the Model with Quasi-Rational ExpectationsAppendix A The Work of Buys BallotAppendix B Some Requisite Theory of Functions of a Complex Variable 1. Complex Numbers 2. Simple Functions of a Complex Variable 3. Limits, Continuity, Derivatives, Singularities, and Rational Functions 4. Complex Integration: Cauchy's Theorem 5. Series Expansions; Taylor's Series; Laurent's Series 6. The Residue Theorem and Its ApplicationsAppendix C Fourier Series and Analysis 1. Introduction 2. Periodic Functions and Trigonometric Series of a Periodic Function 3. Orthogonal System of Functions 4. Questions of Convergence and Goodness of Approximation 5. Fourier Transforms and "Windows"Appendix D Whittle's TheoremAppendix E Inversion of Tridiagonal Matrices and a Method for Inverting Toeplitz MatricesAppendix F Spectral Densities, Actual and Theoretical, Eight SeriesAppendix G Derivation of a Distributed-Lag Relation Between Sales and Production: A Simple ExampleReferencesAuthor IndexSubject Index