Nerlove / Grether / Carvalho Analysis of Economic Time Series

A Synthesis
1. Auflage 2014
ISBN: 978-1-4832-1888-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 488 Seiten, Web PDF

Analysis of Economic Time Series: A Synthesis integrates several topics in economic time-series analysis, including the formulation and estimation of distributed-lag models of dynamic economic behavior; the application of spectral analysis in the study of the behavior of economic time series; and unobserved-components models for economic time series and the closely related problem of seasonal adjustment. Comprised of 14 chapters, this volume begins with a historical background on the use of unobserved components in the analysis of economic time series, followed by an Introduction to the theory of stationary time series. Subsequent chapters focus on the spectral representation and its estimation; formulation of distributed-lag models; elements of the theory of prediction and extraction; and formulation of unobserved-components models and canonical forms. Seasonal adjustment techniques and multivariate mixed moving-average autoregressive time-series models are also considered. Finally, a time-series model of the U.S. cattle industry is presented. This monograph will be of value to mathematicians, economists, and those interested in economic theory, econometrics, and mathematical economics.

Autoren/Hrsg.

Nerlove, Marc

Grether, David M.

Carvalho, José L.

Shell, Karl

Inhaltsverzeichnis

1;Front Cover;1
2;Analysis of Economic Time Series: A Synthesis;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;14
7;Chapter I.
A History of the Idea of Unobserved Components in the Analysis of Economic Time Series;20
7.1;1. Introduction;20
7.2;2. Background;21
7.3;3. Origins;21
7.4;4. Nineteenth Century Contributors;25
7.5;5. Recent Developments;30
7.6;6. Application to Seasonal Adjustment and "Current Analysis";35
7.7;7. Application to the Historical Analysis of Business
Cycles;37
8;Chapter II.
Introduction to the Theory of Stationary Time Series;41
8.1;1. Introduction;41
8.2;2. What Is a Stationary Time Series? Ergodicity;42
8.3;3. The Wold Decomposition Theorem;49
9;Chapter III.
The Spectral Representation and Its Estimation;56
9.1;1. Introduction;56
9.2;2. Covariance Generating Functions;56
9.3;3. The Spectral Representation of a Stationary Time
Series;62
9.4;4. The Cross-Spectral Distribution Function of Two
Jointly Stationary Time Series and Filtering;72
9.5;5. Estimation of the Autocovariance Function
and the Spectral Density Function;76
10;Chapter IV.
Formulation and Analysis of Unobserved-Components Models;88
10.1;1. Introduction;88
10.2;2. Unobserved-Components Models and Their Canonical Forms;89
10.3;3. Digression on a General Method for the Determination of the Autocovariances of a Mixed Moving-Average Autoregressive Process;97
11;Chapter V.
Elements of the Theory of Prediction and Extraction;105
11.1;1. Introduction;105
11.2;2. Prediction;105
11.3;3. Examples of the Application of
Minimum-Mean-Square-Error Forecasts;108
11.4;4. Signal Extraction;116
11.5;5. Examples of Minimum-Mean-Square-Error Signal Extraction;117
12;Chapter VI.
Formulation of Unobserved-Components Models and Canonical Forms;122
12.1;1. Introduction;122
12.2;2. Determining the Form of a Univariate Time-Series
ARMA Model;123
12.3;3. Determining the Form of a Univariate Time-Series
Unobserved-Components Model;128
12.4;4. The Analysis of a Time Series by More Than Its Own
Past;134
13;Chapter VII.
Estimation of Unobserved-Components and Canonical Models;139
13.1;1. Introduction;139
13.2;2. ARMA Model Estimation in the Time Domain;140
13.3;3. UC Model Estimation in the Time Domain;144
13.4;4. ARMA Model Estimation in the Frequency Domain;151
13.5;5. Unobserved-Components Model Estimation
in the Frequency Domain;156
13.6;6. Hypothesis Testing;158
13.7;7. Estimation of Multiple Time-Series Models;158
14;Chapter VIII.
Appraisal of Seasonal Adjustment Techniques;166
14.1;1. Criteria for "Optimal" Seasonal Adjustment;166
14.2;2. Choice of Models;173
14.3;3. Some Results;175
14.4;4. Seasonal Adjustment and the Estimation of Structural
Models;181
14.5;5. Conclusion;189
15;Chapter IX.
On the Comparative Structure of Serial Dependence in Some U.S. Price Series;191
15.1;1. Introduction;191
15.2;2. Brief Characterization of Selected Nonindustrial Price
Series of the Bureau of Labor Statistics;194
15.3;3. Buyer's Prices and Seller's Prices: The National Bureau of Economic Research Series and the Stigler-Kindahl Study;200
15.4;4. Conclusions;219
16;Chapter X.
Formulation and Estimation of Mixed Moving-Average Autoregressive Models for Single Time Series: Examples;220
16.1;1. Introduction;220
16.2;2. The Formulation Procedure of Box and Jenkins;221
16.3;3. An Alternative Method for the Formulation of an ARIMA Model;224
16.4;4. The Detailed Examples;227
16.5;5. Comparison between Estimation Methods in the Frequency and Time Domains;238
17;Chapter XI.
Formulation and Estimation of Multivariate Mixed Moving-Average Autoregressive Time-Series Models;248
17.1;1. Introduction;248
17.2;2. A Single-Equation Approach;249
17.3;3. A Simultaneous-Equations Approach;257
17.4;4. Estimation of Multiple Time-Series Models for Interrelated Agricultural Prices;261
17.5;5. Testing and Checking the Multiple Time-Series Models for Interrelated Agricultural Prices;276
18;Chapter XII.
Formulation and Estimation of Unobserved-Components Models: Examples;280
18.1;1. Introduction;280
18.2;2. Formulation of the Models: Trend Reduction;281
18.3;3. Estimation of the Models in Time and Frequency Domains;289
18.4;4. Predictive Properties of Unobserved-Components Models;303
19;Chapter XIII.
Application to the Formulation of Distributed-Lag Models;310
19.1;1. Introduction;310
19.2;2. Prediction and Expectation-Formation Models;313
19.3;3. Signal Extraction;327
19.4;4. Distributed Lags in Dynamic Models;330
19.5;5. Estimation;339
20;Chapter XIV.
A Time-Series Model of the U.S. Cattle Industry;346
20.1;1. Introduction;346
20.2;2. The Cattle Industry;347
20.3;3. Cattleman Behavior: A Simple Example;348
20.4;4. Cattleman Behavior: A Quarterly Model;356
20.5;5. Tests of the Model with Quasi-Rational Expectations;367
21;Appendix A:
The Work of Buys Ballot;373
22;Appendix B: Some Requisite Theory of Functions of a Complex Variable;380
22.1;1. Complex Numbers;380
22.2;2. Simple Functions of a Complex Variable;383
22.3;3. Limits, Continuity, Derivatives, Singularities, and Rational Functions;386
22.4;4. Complex Integration: Cauchy's Theorem;388
22.5;5. Series Expansions; Taylor's Series; Laurent's Series;392
22.6;6. The Residue Theorem and Its Applications;395
23;Appendix C:
Fourier Series and Analysis;399
23.1;1. Introduction;399
23.2;2. Periodic Functions and Trigonometric Series of a Periodic Function;400
23.3;3. Orthogonal System of Functions;407
23.4;4. Questions of Convergence and Goodness of Approximation;412
23.5;5. Fourier Transforms and "Windows";423
24;Appendix D: Whittle's Theorem;432
25;Appendix E:
Inversion of Tridiagonal Matrices and a Method for Inverting Toeplitz Matrices;435
26;Appendix F:
Spectral Densities, Actual and Theoretical, Eight Series;441
27;Appendix G:
Derivation of a Distributed-Lag Relation between Sales and Production: A Simple Example;450
28;References;456
29;Author Index;468
30;Subject Index;472