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New introduction to multiple time series analysis

Author: Helmut Lütkepohl
Publisher: Berlin : New York : Springer, 2005.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Deals with analyzing and forecasting multiple time series, considering a range of models and methods. This reference work and graduate-level textbook enables readers to perform their analyses in a competent manner.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lütkepohl, Helmut.
New introduction to multiple time series analysis.
Berlin : New York : Springer, 2005
(DLC) 2005927322
(OCoLC)61028971
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Helmut Lütkepohl
ISBN: 9783540277521 3540277528
OCLC Number: 262681472
Description: 1 online resource (xxi, 764 pages) : illustrations
Contents: 1. Objectives of Analyzing Multiple Time Series --
Some Basics --
Vector Autoregressive Processes --
Outline of the Following Chapters --
Part I. Finite Order Vector Autoregressive Processes --
2. Stable Vector Autoregressive Processes --
Basic Assumptions and Properties of VAR Processes --
Stable VAR(p) Processes --
The Moving Average Representation of a VAR Process --
Stationary Processes --
Computation of Autocovariances and Autocorrelations of Stable VAR Processes --
Forecasting --
The Loss Function --
Point Forecasts --
Interval Forecasts and Forecast Regions --
Structural Analysis with VAR Models --
Granger-Causality, Instantaneous Causality, and Multi-Step Causality --
Impulse Response Analysis --
Forecast Error Variance Decomposition --
Remarks on the Interpretation of VAR Models --
3. Estimation of Vector Autoregressive Processes --
Multivariate Least Squares Estimation --
The Estimator --
Asymptotic Properties of the Least Squares Estimator. Small Sample Properties of the LS Estimator --
Least Squares Estimation with Mean-Adjusted Data and Yule-Walker Estimation --
Estimation when the Process Mean Is Known --
Estimation of the Process Mean --
Estimation with Unknown Process Mean --
The Yule-Walker Estimator --
Maximum Likelihood Estimation --
The Likelihood Function --
The ML Estimators --
Properties of the ML Estimators --
Forecasting with Estimated Processes --
General Assumptions and Results --
The Approximate MSE Matrix --
A Small Sample Investigation --
Testing for Causality --
A Wald Test for Granger-Causality --
Testing for Instantaneous Causality --
Testing for Multi-Step Causality --
The Asymptotic Distributions of Impulse Responses and Forecast Error Variance Decompositions --
The Main Results --
Proof of Proposition 3.6 --
Investigating the Distributions of the Impulse Responses by Simulation Techniques --
Algebraic Problems --
Numerical Problems --
4 . VAR Order Selection and Checking the Model Adequacy. A Sequence of Tests for Determining the VAR Order --
The Impact of the Fitted VAR Order on the Forecast MSE --
The Likelihood Ratio Test Statistic --
A Testing Scheme for VAR Order Determination --
Criteria for VAR Order Selection --
Minimizing the Forecast MSE --
Consistent Order Selection --
Comparison of Order Selection Criteria --
Some Small Sample Simulation Results --
Checking the Whiteness of the Residuals --
The Asymptotic Distributions of the Autocovariances and Autocorrelations of a White Noise Process --
The Asymptotic Distributions of the Residual Autocovariances and Autocorrelations of an Estimated VAR Process --
Portmanteau Tests --
Lagrange Multiplier Tests --
Testing for Nonnormality --
Tests for Nonnormality of a Vector White Noise Process --
Tests for Nonnormality of a VAR Process --
Tests for Structural Change --
Chow Tests --
Forecast Tests for Structural Change --
Algebraic Problems --
Numerical Problems --
5. VAR Processes with Parameter Constraints. Linear Constraints --
The Model and the Constraints --
LS, GLS, and EGLS Estimation --
Maximum Likelihood Estimation --
Constraints for Individual Equations --
Restrictions for the White Noise Covariance Matrix --
Forecasting --
Impulse Response Analysis and Forecast Error Variance Decomposition --
Specification of Subset VAR Models --
Model Checking --
VAR Processes with Nonlinear Parameter Restrictions --
Bayesian Estimation --
Basic Terms and Notation --
Normal Priors for the Parameters of a Gaussian VAR Process --
The Minnesota or Litterman Prior --
Practical Considerations --
Classical versus Bayesian Interpretation of {macr}[alpha] in Forecasting and Structural Analysis --
Algebraic Exercises --
Numerical Problems --
Part II. Cointegrated Processes --
6. Vector Error Correction Models --
Integrated Processes --
VAR Processes with Integrated Variables --
Cointegrated Processes, Common Stochastic Trends, and Vector Error Correction Models --
Deterministic Terms in Cointegrated Processes. Forecasting Integrated and Cointegrated Variables --
Causality Analysis --
Impulse Response Analysis --
7 . Estimation of Vector Error Correction Models --
Estimation of a Simple Special Case VECM --
Estimation of General VECMs --
LS Estimation --
EGLS Estimation of the Cointegration Parameters --
ML Estimation --
Including Deterministic Terms --
Other Estimation Methods for Cointegrated Systems --
Estimating VECMs with Parameter Restrictions --
Linear Restrictions for the Cointegration Matrix --
Linear Restrictions for the Short-Run and Loading Parameters --
Bayesian Estimation of Integrated Systems --
The Model Setup --
The Minnesota or Litterman Prior --
Forecasting Estimated Integrated and Cointegrated Systems --
Testing for Granger-Causality --
The Noncausality Restrictions --
Problems Related to Standard Wald Tests --
A Wald Test Based on a Lag Augmented VAR --
Impulse Response Analysis --
Algebraic Exercises --
Numerical Exercises --
8. Specification of VECMs --
Lag Order Selection. Testing for the Rank of Cointegration --
A VECM without Deterministic Terms --
A Nonzero Mean Term --
A Linear Trend --
A Linear Trend in the Variables and Not in the Cointegration Relations --
Summary of Results and Other Deterministic Terms --
Prior Adjustment for Deterministic Terms --
Choice of Deterministic Terms --
Other Approaches to Testing for the Cointegrating Rank342 --
Subset VECMs --
Model Diagnostics --
Checking for Residual Autocorrelation --
Testing for Nonnormality --
Tests for Structural Change --
Algebraic Exercises --
Numerical Exercises --
Part III. Structural and Conditional Models --
9. Structural VARs and VECMs --
Structural Vector Autoregressions --
The A-Model --
The B-Model --
The AB-Model --
Long-Run Restrictions `a la Blanchard-Quah --
Structural Vector Error Correction Models --
Estimation of Structural Parameters --
Estimating SVAR Models --
Estimating Structural VECMs --
Impulse Response Analysis and Forecast Error Variance Decomposition --
Further Issues. Algebraic Problems --
Numerical Problems --
10. Systems of Dynamic Simultaneous Equations --
Background --
Systems with Unmodelled Variables --
Types of Variables --
Structural Form, Reduced Form, Final Form --
Models with Rational Expectations --
Cointegrated Variables --
Estimation --
Stationary Variables --
Estimation of Models with I(1) Variables --
Remarks on Model Specification and Model Checking --
Forecasting --
Unconditional and Conditional Forecasts --
Forecasting Estimated Dynamic SEMs --
Multiplier Analysis --
Optimal Control --
Concluding Remarks on Dynamic SEMs --
Part IV. Infinite Order Vector Autoregressive Processes --
11. Vector Autoregressive Moving Average Processes --
Finite Order Moving Average Processes --
VARMA Processes --
The Pure MA and Pure VAR Representations of a VARMA Process --
A VAR(1) Representation of a VARMA Process --
The Autocovariances and Autocorrelations of a VARMA(p, q) Process --
Forecasting VARMA Processes. Transforming and Aggregating VARMA Processes --
Linear Transformations of VARMA Processes --
Aggregation of VARMA Processes --
Interpretation of VARMA Models --
Granger-Causality --
Impulse Response Analysis --
12. Estimation of VARMA Models --
The Identification Problem --
Nonuniqueness of VARMA Representations --
Final Equations Form and Echelon Form --
Illustrations --
The Gaussian Likelihood Function --
The Likelihood Function of an MA(1) Process --
The MA(q) Case --
The VARMA(1, 1) Case --
The General VARMA(p, q) Case --
Computation of the ML Estimates --
The Normal Equations --
Optimization Algorithms --
The Information Matrix --
Preliminary Estimation --
An Illustration --
Asymptotic Properties of the ML Estimators --
Theoretical Results --
A Real Data Example --
Forecasting Estimated VARMA Processes --
Estimated Impulse Responses --
13. Specification and Checking the Adequacy of VARMA Models --
Specification of the Final Equations Form --
A Specification Procedure. Specification of Echelon Forms --
A Procedure for Small Systems --
A Full Search Procedure Based on Linear Least Squares Computations --
Hannan-Kavalieris Procedure --
Poskitt's Procedure --
Remarks on Other Specification Strategies for VARMA Models --
Model Checking --
LM Tests --
Residual Autocorrelations and Portmanteau Tests --
Prediction Tests for Structural Change --
Critique of VARMA Model Fitting --
14. Cointegrated VARMA Processes --
The VARMA Framework for I(1) Variables --
Levels VARMA Models --
The Reverse Echelon Form --
The Error Correction Echelon Form --
Estimation --
Estimation of ARMARE Models --
Estimation of EC-ARMARE Models --
Specification of EC-ARMARE Models --
Specification of Kronecker Indices --
Specification of the Cointegrating Rank --
Forecasting Cointegrated VARMA Processes --
Algebraic Exercises --
Numerical Exercises --
15. Fitting Finite Order VAR Models to Infinite Order Processes --
Background. Multivariate Least Squares Estimation --
Forecasting --
Theoretical Results --
Impulse Response Analysis and Forecast Error Variance Decompositions --
Asymptotic Theory --
Cointegrated Infinite Order VARs --
The Model Setup --
Estimation --
Testing for the Cointegrating Rank --
Part V. Time Series Topics --
16. Multivariate ARCH and GARCH Models --
Background --
Univariate GARCH Models --
Definitions --
Forecasting --
Multivariate GARCH Models --
Multivariate ARCH --
MGARCH --
Other Multivariate ARCH and GARCH Models --
Estimation --
Theory --
Checking MGARCH Models --
ARCH-LM and ARCH-Portmanteau Tests --
LM and Portmanteau Tests for Remaining ARCH --
Other Diagnostic Tests --
Interpreting GARCH Models --
Causality in Variance --
Conditional Moment Profiles and Generalized Impulse Responses --
Problems and Extensions. 17. Periodic VAR Processes and Intervention Models --
The VAR(p) Model with Time Varying Coefficients --
General Properties --
ML Estimation --
Periodic Processes --
A VAR Representation with Time Invariant Coefficients --
ML Estimation and Testing for Time Varying Coefficients --
Bibliographical Notes and Extensions --
Intervention Models --
Interventions in the Intercept Model --
A Discrete Change in the Mean --
An Illustrative Example --
Extensions and References --
18. State Space Models --
Background --
State Space Models --
The Model Setup --
More General State Space Models --
The Kalman Filter --
The Kalman Filter Recursions --
Proof of the Kalman Filter Recursions --
Maximum Likelihood Estimation of State Space Models --
The Log-Likelihood Function --
The Identification Problem --
Maximization of the Log-Likelihood Function --
Asymptotic Properties of the ML Estimator. A Real Data Example --
Appendices A. Vectors and Matrices --
Basic Definitions --
Basic Matrix Operations --
The Determinant --
The Inverse, the Adjoint, and Generalized Inverses --
Inverse and Adjoint of a Square Matrix --
Generalized Inverses --
The Rank --
Eigenvalues and -vectors --
Characteristic Values and Vectors --
The Trace --
Some Special Matrices and Vectors --
Idempotent and Nilpotent Matrices --
Orthogonal Matrices and Vectors and Orthogonal Complements --
Definite Matrices and Quadratic Forms --
Decomposition and Diagonalization of Matrices --
The Jordan Canonical Form --
Decomposition of Symmetric Matrices --
The Choleski Decomposition of a Positive Definite Matrix --
Partitioned Matrices --
The Kronecker Product --
The vec and vech Operators and Related Matrices --
The Operators --
Elimination, Duplication, and Commutation Matrices --
Vector and Matrix Differentiation. Optimization of Vector Functions --
Problems --
B. Multivariate Normal and Related Distributions --
Multivariate Normal Distributions --
Related Distributions --
C. Stochastic Convergence and Asymptotic Distributions --
Concepts of Stochastic Convergence --
Order in Probability --
Infinite Sums of Random Variables --
Laws of Large Numbers and Central Limit Theorems --
Standard Asymptotic Properties of Estimators and Test Statistics --
Maximum Likelihood Estimation --
Likelihood Ratio, Lagrange Multiplier, and Wald Tests --
Unit Root Asymptotics --
Univariate Processes --
Multivariate Processes --
D. Evaluating Properties of Estimators and Test Statistics by Simulation and Resampling Techniques --
Simulating a Multiple Time Series with VAR Generation Process --
Evaluating Distributions of Functions of Multiple Time Series by Simulation --
Resampling Methods.
Responsibility: Helmut Lütkepohl.
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