Course in Time Series Analysis

DANIEL PEÑA, PhD, is Professor of Statistics, Universidad Carlos III de Madrid. GEORGE C. TIAO, PhD, is W. Allen Wallis Professor of Statistics and Econometrics, Graduate School of Business, University of Chicago.RUEY S. TSAY, PhD, is H. G. B. Alexander Professor of Statistics and Econometrics, Graduate School of Business, University of Chicago.

• 1. Introduction 1D. Pena and G. C. Tiao1.1. Examples of time series problems, 11.1.1. Stationary series, 21.1.2. Nonstationary series, 31.1.3. Seasonal series, 51.1.4. Level shifts and outliers in time series, 71.1.5. Variance changes, 71.1.6. Asymmetric time series, 71.1.7. Unidirectional-feedback relation between series, 91.1.8. Comovement and cointegration, 101.2. Overview of the book, 101.3. Further reading, 19PART I BASIC CONCEPTS IN UNIVARIATE TIME SERIES2. Univariate Time Series: Autocorrelation, Linear Prediction, Spectrum, and State-Space Model 25G. T. Wilson2.1. Linear time series models, 252.2. The autocorrelation function, 282.3. Lagged prediction and the partial autocorrelation function, 332.4. Transformations to stationarity, 352.5. Cycles and the periodogram, 372.6. The spectrum, 422.7. Further interpretation of time series acf, pacf, and spectrum, 462.8. State-space models and the Kalman Filter, 483. Univariate Autoregressive Moving-Average Models 53G. C. Tiao3.1. Introduction, 533.1.1. Univariate ARMA models, 543.1.2. Outline of the chapter, 553.2. Some basic properties of univariate ARMA models, 553.2.1. The ø and TT weights, 563.2.2. Stationarity condition and autocovariance structure o f z „ 583.2.3. The autocorrelation function, 593.2.4. The partial autocorrelation function, 603.2.5. The extended autocorrelaton function, 613.3. Model specification strategy, 633.3.1. Tentative specification, 633.3.2. Tentative model specification via SEACF, 673.4. Examples, 684. Model Fitting and Checking, and the Kalman Filter 86G. T. Wilson4.1. Prediction error and the estimation criterion, 864.2. The likelihood of ARMA models, 904.3. Likelihoods calculated using orthogonal errors, 944.4. Properties of estimates and problems in estimation, 984.5. Checking the fitted model, 1014.6. Estimation by fitting to the sample spectrum, 1044.7. Estimation of structural models by the Kalman filter, 1055. Prediction and Model Selection 111D. Pefia5.1. Introduction, 1115.2. Properties of minimum mean-square error prediction, 1125.2.1. Prediction by the conditional expectation, 1125.2.2. Linear predictions, 1135.3. The computation of ARIMA forecasts, 1145.4. Interpreting the forecasts from ARIMA models, 1165.4.1. Nonseasonal models, 1165.4.2. Seasonal models, 1205.5. Prediction confidence intervals, 1235.5.1. Known parameter values, 1235.5.2. Unknown parameter values, 1245.6. Forecast updating, 1255.6.1. Computing updated forecasts, 1255.6.2. Testing model stability, 1255.7. The combination of forecasts, 1295.8. Model selection criteria, 1315.8.1. The FPE and AIC criteria, 1315.8.2. The Schwarz criterion, 1335.9. Conclusions, 1336. Outliers, Influential Observations, and Missing Data 136D. Pena6.1. Introduction, 1366.2. Types of outliers in time series, 1386.2.1. Additive outliers, 1386.2.2. Innovative outliers, 1416.2.3. Level shifts, 1436.2.4. Outliers and intervention analysis, 1466.3. Procedures for outlier identification and estimation, 1476.3.1. Estimation of outlier effects, 1486.3.2. Testing for outliers, 1496.4. Influential observations, 1526.4.1. Influence on time series, 1526.4.2. Influential observations and outliers, 1536.5. Multiple outliers, 1546.5.1. Masking effects, 1546.5.2. Procedures for multiple outlier identification, 1566.6. Missing-value estimation, 1606.6.1. Optimal interpolation and inverse autocorrelation function, 1606.6.2. Estimation of missing values, 1626.7. Forecasting with outliers, 1646.8. Other approaches, 1666.9. Appendix, 1667. Automatic Modeling Methods for Univariate Series 171V. Gomez and A. Maravall7.1. Classical model identification methods, 1717.1.1. Subjectivity of the classical methods, 1727.1.2. The difficulties with mixed ARMA models, 1737.2. Automatic model identification methods, 1737.2.1. Unit root testing, 1747.2.2. Penalty function methods, 1747.2.3. Pattern identification methods, 1757.2.4. Uniqueness of the solution and the purpose of modeling, 1767.3. Tools for automatic model identification, 1777.3.1. Test for the log-level specification, 1777.3.2. Regression techniques for estimating unit roots, 1787.3.3. The Hannan-Rissanen method, 1817.3.4. Liu's filtering method, 1857.4. Automatic modeling methods in the presence of outliers, 1867.4.1. Algorithms for automatic outlier detection and correction, 1867.4.2. Estimation and filtering techniques to speed up the algorithms, 1907.4.3. The need to robustify automatic modeling methods, 1917.4.4. An algorithm for automatic model identification in the presence of outliers, 1917.5. An automatic procedure for the general regression-ARIMA model in the presence of outlierw, special effects, and, possibly, missing observations, 1927.5.1. Missing observations, 1927.5.2. Trading day and Easter effects, 1937.5.3. Intervention and regression effects, 1947.6. Examples, 1947.7. Tabular summary, 1968. Seasonal Adjustment and Signal Extraction Time Series 202V. Gomez and A. Maravall8.1. Introduction, 2028.2. Some remarks on the evolution of seasonal adjustment methods, 2048.2.1. Evolution of the methodologic approach, 2048.2.2. The situation at present, 2078.3. The need for preadjustment, 2098.4. Model specification, 2108.5. Estimation of the components, 2138.5.1. Stationary case, 2158.5.2. Nonstationary series, 2178.6 Historical or final estimator, 2188.6.1. Properties of final estimator, 2188.6.2. Component versus estimator, 2198.6.3. Covariance between estimators, 2218.7. Estimators for recent periods, 2218.8. Revisions in the estimator, 2238.8.1. Structure of the revision, 2238.8.2. Optimality of the revisions, 2248.9. Inference, 2258.9.1. Optical Forecasts of the Components, 2258.9.2. Estimation error, 2258.9.3. Growth rate precision, 2268.9.4. The gain from concurrent adjustment, 2278.9.5. Innovations in the components (pseudoinnovations), 2288.10. An example, 2288.11. Relation with fixed filters, 2358.12. Short-versus long-term trends; measuring economic cycles, 236PART II ADVANCED TOPICS IN UNIVARIATE TIME SERIES9. Heteroscedastic ModelsR. S. Tsay9.1. The ARCH model, 2509.1.1. Some simple properties of ARCH models, 2529.1.2. Weaknesses of ARCH models, 2549.1.3. Building ARCH models, 2549.1.4. An illustrative example, 2559.2. The GARCH Model, 2569.2.1. An illustrative example, 2579.2.2. Remarks, 2599.3. The exponential GARCH model, 2609.3.1. An illustrative example, 2619.4. The CHARMA model, 2629.5. Random coefficient autoregressive (RCA) model, 2639.6. Stochastic volatility model, 2649.7. Long-memory stochastic volatility model, 26510. Nonlinear Time Series Models: Testing and Applications 267R. S. Tsay10.1. Introduction, 26710.2. Nonlinearity tests, 26810.2.1. The test, 26810.2.2. Comparison and application, 27010.3. The Tar model, 27410.3.1. U.S. real GNP, 27510.3.2. Postsample forecasts and discussion, 27910.4. Concluding remarks, 28211. Bayesian Time Series Analysis 286R. S. Tsay11.1. Introduction, 28611.2. A general univariate time series model, 28811.3. Estimation, 28911.3.1. Gibbs sampling, 29111.3.2. Griddy Gibbs, 29211.3.3. An illustrative example, 29211.4. Model discrimination, 29411.4.1. A mixed model with switching, 29511.4.2. Implementation, 29611.5. Examples, 29712 Nonparametric Time Series Analysis: Nonparametric Regression, Locally Weighted Regression, Autoregression, and Quantile Regression 308S. Heiler12.1 Introduction, 30812.2 Nonparametric regression, 30912.3 Kernel estimation in time series, 31412.4 Problems of simple kernel estimation and restricted approaches, 31912.5 Locally weighted regression, 32112.6 Applications of locally weighted regression to time series, 32912.7 Parameter selection, 33012.8 Time series decomposition with locally weighted regression, 33613. Neural Network Models 348K. Hornik and F. Leisch13.1. Introduction, 34813.2. The multilayer perceptron, 34913.3. Autoregressive neural network models, 35413.3.1. Example: Sunspot series, 35513.4. The recurrent perceptron, 35613.4.1. Examples of recurrent neural network models, 35713.4.2. A unifying view, 359PART III MULTIVARIATE TIME SERIES14. Vector ARMA Models 365G. C. Tiao14.1. Introduction, 36514.2. Transfer function or unidirectional models, 36614.3. The vector ARMA model, 36814.3.1. Some simple examples, 36814.3.2. Relationship to transfer function model, 37114.3.3. Cross-covariance and correlation matrices, 37114.3.4. The partial autoregression matrices, 37214.4. Model building strategy for multiple time series, 37314.4.1. Tentative specification, 37314.4.2. Estimation, 37814.4.3. Diagnostic checking, 37914.5. Analyses of three examples, 38014.5.1. The SCC data, 38014.5.2. The gas furnace data, 38314.5.3. The census housing data, 38714.6. Structural analysis of multivariate time series, 39214.6.1. A canonical analysis of multiple time series, 39514.7. Scalar component models in multiple time series, 39614.7.1. Scalar component models, 39814.7.2. Exchangeable models and overparameterization, 40014.7.3. Model specification via canonical correlation analysis, 40214.7.4. An illustrative example, 40314.7.5. Some further remarks, 40415. Cointegration in the VAR Model 4085. Johansen15.1. Introduction, 40815.1.1. Basic definitions, 40915.2. Solving autoregressive equations, 41215.2.1. Some examples, 41215.2.2. An inversion theorem for matrix polynomials, 41415.2.3. Granger's representation, 41715.2.4. Prediction, 41915.3. The statistical model for / ( l ) variables, 42015.3.1. Hypotheses on cointegrating relations, 42115.3.2. Estimation of cointegrating vectors and calculation of test statistics, 42215.3.3. Estimation of â under restrictions, 42615.4. Asymptotic theory, 42615.4.1. Asymptotic results, 42715.4.2. Test for cointegrating rank, 42715.4.3. Asymptotic distribution of â and test for restrictions on â, 42915.5. Various applications of the cointegration model, 43215.5.1. Rational expectations, 43215.5.2. Arbitrage pricing theory, 43315.5.3. Seasonal cointegration, 43316. Identification of Linear Dynamic Multiinput/Multioutput Systems 436M. Deistler16.1. Introduction and problem statement, 43616.2. Representations of linear systems, 43816.2.1. Input/output representations, 43816.2.2. Solutions of linear vector difference equations (VDEs), 44016.2.3. ARMA and state-space representations, 44116.3. The structure of state-space systems, 44316.4. The structure of ARMA systems, 44416.5. The realization of state-space systems, 44516.5.1. General structure, 44516.5.2. Echelon forms, 44716.6. The realization of ARMA systems, 44816.7. Parametrization, 44916.8. Estimation of real-valued parameters, 45216.9. Dynamic specification, 454INDEX 457

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