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Preface | |
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About ECAS | |
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Contributors | |
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Introduction | |
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Examples of time series problems | |
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Stationary series | |
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Nonstationary series | |
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Seasonal series | |
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Level shifts and outliers in time series | |
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Variance changes | |
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Asymmetric time series | |
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Unidirectional-feedback relation between series | |
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Comovement and cointegration | |
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Overview of the book | |
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Further reading | |
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Basic Concepts in Univariate Time Series | |
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Univariate Time Series: Autocorrelation, Linear Prediction, Spectrum, and State-Space Model | |
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Linear time series models | |
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The autocorrelation function | |
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Lagged prediction and the partial autocorrelation function | |
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Transformations to stationarity | |
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Cycles and the periodogram | |
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The spectrum | |
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Further interpretation of time series acf, pacf, and spectrum | |
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State-space models and the Kalman Filter | |
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Univariate Autoregressive Moving-Average Models | |
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Introduction | |
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Univariate ARMA models | |
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Outline of the chapter | |
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Some basic properties of univariate ARMA models | |
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The [phi] and [pi] weights | |
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Stationarity condition and autocovariance structure of z[subscript t] | |
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The autocorrelation function | |
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The partial autocorrelation function | |
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The extended autocorrelation function | |
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Model specification strategy | |
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Tentative specification | |
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Tentative model specification via SEACF | |
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Examples | |
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Model Fitting and Checking, and the Kalman Filter | |
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Prediction error and the estimation criterion | |
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The likelihood of ARMA models | |
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Likelihoods calculated using orthogonal errors | |
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Properties of estimates and problems in estimation | |
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Checking the fitted model | |
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Estimation by fitting to the sample spectrum | |
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Estimation of structural models by the Kalman filter | |
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Prediction and Model Selection | |
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Introduction | |
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Properties of minimum mean-square error prediction | |
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Prediction by the conditional expectation | |
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Linear predictions | |
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The computation of ARIMA forecasts | |
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Interpreting the forecasts from ARIMA models | |
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Nonseasonal models | |
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Seasonal models | |
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Prediction confidence intervals | |
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Known parameter values | |
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Unknown parameter values | |
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Forecast updating | |
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Computing updated forecasts | |
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Testing model stability | |
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The combination of forecasts | |
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Model selection criteria | |
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The FPE and AIC criteria | |
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The Schwarz criterion | |
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Conclusions | |
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Outliers, Influential Observations, and Missing Data | |
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Introduction | |
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Types of outliers in time series | |
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Additive outliers | |
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Innovative outliers | |
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Level shifts | |
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Outliers and intervention analysis | |
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Procedures for outlier identification and estimation | |
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Estimation of outlier effects | |
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Testing for outliers | |
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Influential observations | |
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Influence on time series | |
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Influential observations and outliers | |
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Multiple outliers | |
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Masking effects | |
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Procedures for multiple outlier identification | |
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Missing-value estimation | |
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Optimal interpolation and inverse autocorrelation function | |
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Estimation of missing values | |
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Forecasting with outliers | |
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Other approaches | |
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Appendix | |
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Automatic Modeling Methods for Univariate Series | |
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Classical model identification methods | |
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Subjectivity of the classical methods | |
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The difficulties with mixed ARMA models | |
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Automatic model identification methods | |
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Unit root testing | |
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Penalty function methods | |
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Pattern identification methods | |
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Uniqueness of the solution and the purpose of modeling | |
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Tools for automatic model identification | |
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Test for the log-level specification | |
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Regression techniques for estimating unit roots | |
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The Hannan--Rissanen method | |
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Liu's filtering method | |
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Automatic modeling methods in the presence of outliers | |
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Algorithms for automatic outlier detection and correction | |
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Estimation and filtering techniques to speed up the algorithms | |
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The need to robustify automatic modeling methods | |
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An algorithm for automatic model identification in the presence of outliers | |
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An automatic procedure for the general regression--ARIMA model in the presence of outlierw, special effects, and, possibly, missing observations | |
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Missing observations | |
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Trading day and Easter effects | |
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Intervention and regression effects | |
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Examples | |
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Tabular summary | |
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Seasonal Adjustment and Signal Extraction Time Series | |
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Introduction | |
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Some remarks on the evolution of seasonal adjustment methods | |
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Evolution of the methodologic approach | |
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The situation at present | |
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The need for preadjustment | |
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Model specification | |
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Estimation of the components | |
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Stationary case | |
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Nonstationary series | |
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Historical or final estimator | |
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Properties of final estimator | |
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Component versus estimator | |
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Covariance between estimators | |
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Estimators for recent periods | |
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Revisions in the estimator | |
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Structure of the revision | |
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Optimality of the revisions | |
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Inference | |
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Optical Forecasts of the Components | |
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Estimation error | |
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Growth rate precision | |
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The gain from concurrent adjustment | |
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Innovations in the components (pseudoinnovations) | |
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An example | |
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Relation with fixed filters | |
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Short-versus long-term trends; measuring economic cycles | |
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Advanced Topics in Univariate Time Series | |
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Heteroscedastic Models | |
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The ARCH model | |
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Some simple properties of ARCH models | |
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Weaknesses of ARCH models | |
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Building ARCH models | |
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An illustrative example | |
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The GARCH Model | |
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An illustrative example | |
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Remarks | |
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The exponential GARCH model | |
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An illustrative example | |
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The CHARMA model | |
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Random coefficient autoregressive (RCA) model | |
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Stochastic volatility model | |
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Long-memory stochastic volatility model | |
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Nonlinear Time Series Models: Testing and Applications | |
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Introduction | |
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Nonlinearity tests | |
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The test | |
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Comparison and application | |
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The Tar model | |
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U.S. real GNP | |
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Postsample forecasts and discussion | |
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Concluding remarks | |
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Bayesian Time Series Analysis | |
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Introduction | |
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A general univariate time series model | |
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Estimation | |
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Gibbs sampling | |
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Griddy Gibbs | |
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An illustrative example | |
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Model discrimination | |
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A mixed model with switching | |
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Implementation | |
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Examples | |
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Nonparametric Time Series Analysis: Nonparametric Regression, Locally Weighted Regression, Autoregression, and Quantile Regression | |
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Introduction | |
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Nonparametric regression | |
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Kernel estimation in time series | |
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Problems of simple kernel estimation and restricted approaches | |
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Locally weighted regression | |
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Applications of locally weighted regression to time series | |
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Parameter selection | |
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Time series decomposition with locally weighted regression | |
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Neural Network Models | |
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Introduction | |
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The multilayer perceptron | |
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Autoregressive neural network models | |
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Example: Sunspot series | |
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The recurrent perceptron | |
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Examples of recurrent neural network models | |
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A unifying view | |
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Multivariate Time Series | |
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Vector ARMA Models | |
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Introduction | |
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Transfer function or unidirectional models | |
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The vector ARMA model | |
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Some simple examples | |
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Relationship to transfer function model | |
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Cross-covariance and correlation matrices | |
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The partial autoregression matrices | |
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Model building strategy for multiple time series | |
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Tentative specification | |
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Estimation | |
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Diagnostic checking | |
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Analyses of three examples | |
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The SCC data | |
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The gas furnace data | |
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The census housing data | |
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Structural analysis of multivariate time series | |
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A canonical analysis of multiple time series | |
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Scalar component models in multiple time series | |
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Scalar component models | |
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Exchangeable models and overparameterization | |
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Model specification via canonical correlation analysis | |
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An illustrative example | |
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Some further remarks | |
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Cointegration in the VAR Model | |
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Introduction | |
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Basic definitions | |
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Solving autoregressive equations | |
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Some examples | |
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An inversion theorem for matrix polynomials | |
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Granger's representation | |
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Prediction | |
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The statistical model for I(1) variables | |
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Hypotheses on cointegrating relations | |
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Estimation of cointegrating vectors and calculation of test statistics | |
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Estimation of [beta] under restrictions | |
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Asymptotic theory | |
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Asymptotic results | |
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Test for cointegrating rank | |
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Asymptotic distribution of [beta] and test for restrictions on [beta] | |
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Various applications of the cointegration model | |
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Rational expectations | |
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Arbitrage pricing theory | |
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Seasonal cointegration | |
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Identification of Linear Dynamic Multiinput/Multioutput Systems | |
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Introduction and problem statement | |
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Representations of linear systems | |
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Input/output representations | |
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Solutions of linear vector difference equations (VDEs) | |
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ARMA and state-space representations | |
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The structure of state-space systems | |
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The structure of ARMA systems | |
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The realization of state-space systems | |
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General structure | |
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Echelon forms | |
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The realization of ARMA systems | |
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Parametrization | |
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Estimation of real-valued parameters | |
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Dynamic specification | |
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Index | |