New Introduction To Multiple Time Series Analysis 2th Edition by Helmut Lütkepohl – Ebook PDF Instant Download/Delivery: 3540262393 ,9783540262398
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ISBN 10: 3540262393
ISBN 13: 9783540262398
Author: Helmut Lütkepohl
This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series. The models covered include vector autoregressive, cointegrated,vector autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models. Least squares, maximum likelihood and Bayesian methods are considered for estimating these models. Different procedures for model selection and model specification are treated and a wide range of tests and criteria for model checking are introduced. Causality analysis, impulse response analysis and innovation accounting are presented as tools for structural analysis. The book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on it. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their tasks. It bridges the gap to the difficult technical literature on the topic.
New Introduction To Multiple Time Series Analysis 2th Edition Table of contents:
1.2 Some Basics
1.3 Vector Autoregressive Processes
1.4 Outline of the Following Chapters
2.1.2 The Moving Average Representation of a VAR Process
2.1.3 Stationary Processes
2.1.4 Computation of Autocovariates and Autocorrelations of Stable VAR Processes
2.2 Forecasting
2.2.2 Point Forecasts
2.2.3 Interval Forecasts and Forecast Regions
2.3 Structural Analysis with VAR Models
2.3.2 Impulse Response Analysis
2.3.3 Forecast Error Variance Decomposition
2.3.4 Remarks on the Interpretation of VAR Models
2.4 Exercises
3.2 Multivariate Least Squares Estimation
3.2.2 Asymptotic Properties of the Least Squares Estimator
3.2.3 An Example
3.2.4 Small Sample Properties of the LS Estimator
3.3 Least Squares Estimation with Mean-Adjusted Data and Yule-Walker Estimation
3.3.2 Estimation of the Process Mean
3.3.3 Estimation with Unknown Process Mean
3.3.4 The Yule-Walker Estimator
3.3.5 An Example
3.4 Maximum Likelihood Estimation
3.4.2 The ML Estimators
3.4.3 Properties of the ML Estimators
3.5 Forecasting with Estimated Processes
3.5.2 The Approximate MSE Matrix
3.5.3 An Example
3.5.4 A Small Sample Investigation
3.6 Testing for Causality
3.6.2 An Example
3.6.3 Testing for Instantaneous Causality
3.6.4 Testing for Multi-Step Causality
3.7 The Asymptotic Distributions of Impulse Responses and Forecast Error Variance Decompositions
3.7.2 Proof of Proposition 3.6
3.7.3 An Example
3.7.4 Investigating the Distributions of the Impulse Responses by Simulation Techniques
3.8 Exercises
3.8.2 Numerical Problems
4.2 A Sequence of Tests for Determining the VAR Order
4.2.2 The Likelihood Ratio Test Statistic
4.2.3 A Testing Scheme for VAR Order Determination
4.2.4 An Example
4.3 Criteria for VAR Order Selection
4.3.2 Consistent Order Selection
4.3.3 Comparison of Order Selection Criteria
4.3.4 Some Small Sample Simulation Results
4.4 Checking the Whiteness of the Residuals
4.4.2 The Asymptotic Distributions of the Residual Autocovariances and Autocorrelations of an Estimated VAR Process
4.4.3 Portmanteau Tests
4.4.4 Lagrange Multiplier Tests
4.5 Testing for Normality
4.5.2 Tests for Nonnormality of a VAR Process
4.6 Tests for Structural Change
4.6.2 Forecast Tests for Structural Change
4.7 Exercises
4.7.2 Numerical Problems
5.2 Linear Constraints
5.2.2 LS, GLS, and EGLS Estimation
5.2.3 Maximum Likelihood Estimation
5.2.4 Constraints for Individual Equations
5.2.5 Restrictions for the White Noise Covariance Matrix
5.2.6 Forecasting
5.2.7 Impulse Response Analysis and Forecast Error Variance Decompositions
5.2.8 Specification of Subset VAR Models
5.2.9 Model Checking
5.2.10 An Example
5.3 VAR Processes with Nonlinear Parameter Restrictions
5.4 Bayesian Estimation
5.4.2 Normal Priors for the Parameters of a Gaussian VAR Process
5.4.3 The Minnesota or Litterman Prior
5.4.4 Practical Considerations
5.4.5 An Example
5.4.6 Classical versus Bayesian Interpretation of α in Forecasting and Structural Analysis
5.5 Exercises
5.5.2 Numerical Problems
6.2 VAR Processes with Integrated Variables
6.3 Cointegrated Processes, Common Stochastic Trends, and Vector Error Correction Models
6.4 Deterministic Terms in Cointegrated Processes
6.5 Forecasting Integrated and Cointegrated Variables
6.6 Causality Analysis
6.7 Impulse Response Analysis
6.8 Exercises
7.2 Estimation of General VECMs
7.2.2 EGLS Estimation of the Cointegration Parameters
7.2.3 ML Estimation
7.2.4 Including Deterministic Terms
7.2.5 Other Estimation Methods for Cointegrated Systems
7.2.6 An Example
7.3 Estimating VECMs with Parameter Restrictions
7.3.2 Linear Restrictions for the Short-Run and Loading Parameters
7.3.3 An Example
7.4 Bayesian Estimation of Integrated Systems
7.4.2 The Minnesota or Litterman Prior
7.4.3 An Example
7.5 Forecasting Estimated Integrated and Cointegrated Systems
7.6 Testing for Granger-Causality
7.6.2 Problems Related to Standard Wald Tests
7.6.3 A Wald Test Based on a Lag Augmented VAR
7.6.4 An Example
7.7 Impulse Response Analysis
7.8 Exercises
7.8.2 Numeric Exercises
8.2 Testing for the Rank of Cointegration
8.2.2 A Nonzero Mean Term
8.2.3 A Linear Trend
8.2.4 A Linear Trend in the Variables and Not in the Cointegration Relations
8.2.5 Summary of Results and Other Deterministic Terms
8.2.6 An Example
8.2.7 Prior Adjustment of Deterministic Terms
8.2.8 Choice of Deterministic Terms
8.2.9 Other Approaches to Testing for teh Cointegrating Rank
8.3 Subset VECMs
8.4 Model Diagnostics
8.4.2 Testing for Nonnormality
8.4.3 Tests for Structural Change
8.5 Exercises
8.5.2 Numerical Exercises
9.1.2 The B-Model
9.1.3 The AB-Model
9.1.4 Long-Run Restrictions à la Blanchard-Quah
9.2 Structural Vector Error Correction Models
9.3 Estimation of Structural Parameters
9.3.2 Estimating Structural VECMs
9.4 Impulse Response Analysis and Forecast Error Variance
9.5 Further Issues
9.6 Exercises
9.6.2 Numerical Problems
10.2 Systems with Unmodelled Variables
10.2.2 Structural Form, Reduced Form, Final Form
10.2.3 Models with Rational Expectations
10.2.4 Cointegrated Variables
10.3 Estimation
10.3.2 Estimation of Models with I(1) Variables
10.4 Remarks on Model Specification and Model Checking
10.5 Forecasting
10.5.2 Forecasting Estimated Dynamic SEMs
10.6 Multiplier Analysis
10.7 Optimal Control
10.8 Concluding Remarks on Dynamic SEMs
10.9 Exercises
11.2 Finite Order Moving Average Processes
11.3 VARMA Processes
11.3.2 A VAR(1) Representation of a VARMA Process
11.4 The Autocovariances and Autocorrelations of a VARMA(p, q) Process
11.5 Forecasting VARMA Processes
11.6 Transforming and Aggregating VARMA Processes
11.6.2 Aggregation of VARMA Processes
11.7 Interpretation of VARMA Models
11.7.2 Impulse Reponse Analysis
11.8 Exercises
12.1.2 Final Equations Form and Echelong Form
12.1.3 Illustrations
12.2 The Gaussian Likelihood Function
12.2.2 The MA(q) Case
12.2.3 The VARMA(1,1) Case
12.2.4 The General VARMA(p, q) Case
12.3 Computation of the ML Estimates
12.3.2 Optimization Algorithms
12.3.3 The Information Matrix
12.3.4 Preliminary Estimation
12.3.5 An Illustration
12.4 Asymptotic Properties of the ML Estimators
12.4.2 A Real Data Example
12.5 Forecasting Estimated VARMA Processes
12.6 Estimated Impulse Responses
12.7 Exercises
13.2 Specification of the Final Equations Form
13.2.2 An Example
13.3 Specification of Echelon Forms
13.3.2 A Full Search Procedure Based on Linear Least Squares Computations
13.3.3 Hannan-Kavalieris Procedure
13.3.4 Poskitt’ Procedure
13.4 Remarks on Other Specification Strategies for VARMA Models
13.5 Model Checking
13.5.2 Residual Autocorrelations and Portmanteau Tests
13.5.3 Prediction Tests for Structural Change
13.6 Critique of VARMA Model Fitting
13.7 Exercises
14.2 The VARMA Framework for I(1) Variables
14.2.2 The Reverse Echelon Form
14.2.3 The Error Correction Echelong Form
14.3 Estimation
14.3.2 Estimation of EC-ARMARE Models
14.4 Specification of EC-ARMARE Models
14.4.2 Specification of the Cointegrating Rank
14.5 Forecasting Cointegrated VARMA Processes
14.6 An Example
14.7 Exercises
14.7.2 Numerical Exercises
15.2 Multivariate Least Squares Estimation
15.3 Forecasting
15.3.2 An Example
15.4 Impulse Response Analysis and Forecast Error Variance Decompositions
15.4.2 An Example
15.5 Cointegrated Infinite Order VARs
15.5.2 Estimation
15.5.3 Testing for the Cointegrating Rank
15.6 Exercises
16.2 Univariate GARCH Models
16.2.2 Forecasting
16.3 Multivariate GARCH Models
16.3.2 MGARCH
16.3.3 Other Multivariate ARCH and GARCH Models
16.4 Estimation
16.4.2 An Example
16.5 Checking MGARCH Models
16.5.2 LM and Portmanteau Tests for Remaining ARCH
16.5.3 Other Diagnostic Tests
16.5.4 An Example
16.6 Interpreting GARCH Models
16.6.2 Conditional Moment Profiles and Generalized Impulse Responses
16.7 Problems and Extensions
16.8 Exercises
17.2 The VAR(p) Model with Time Varying Coefficients
17.2.2 ML Estimation
17.3 Periodic Processes
17.3.2 ML Estimation and Testing for Time Varying Coefficients
17.3.3 An Example
17.3.4 Bibliographical Notes and Extensions
17.4 Intervention Models
17.4.2 A Discrete Change in the Mean
17.4.3 An Illustrative Example
17.4.4 Extensions and References
17.5 Exercises
18.2 State Space Models
18.2.2 More General State Space Models
18.3 The Kalman Filter
18.3.2 Proof of the Kalman Filter Recursions
18.4 Maximum Likelihood Estimation of State Space Models
18.4.2 The Identification Problem
18.4.3 Maximization of the Log-Likelihood Function
18.4.4 Asymptotic Properties of the ML Estimator
18.5 A Real Data Example
18.6 Exercises
A.2 Basic Matrix Operations
A.3 The Determinant
A.4 The Inverse, the Adjoint, and Generalized Inverses
A.4.2 Generalized Inverses
A.5 The Rank
A.6 Eigenvalues and -vectors — Characteristic Values and Vectors
A.7 The Trace
A.8 Some Special Matrices and Vectors
A.8.2 Orthogonal Matrices and Vectors and Orthogonal Complements
A.8.3 Definite Matrices and Quadratic Forms
A.9 Decomposition and Diagonalization of Matrices
A.9.2 Decomposition of Symmetric Matrices
A.9.3 The Choleski Decomposition of a Positive Definite Matrix
A.10 Partitioned Matrices
A.11 The Kronecker Product
A.12 The vec and vech Operators and Related Matrices
A.12.2 Elimination, Duplication, and Commutation Matrices
A.13 Vector and Matrix Differentiation
A.14 Optimization of Vector Functions
A.15 Problems
B.2 Related Distributions
C.2 Order in Probability
C.3 Infinite Sums of Random Variables
C.4 Laws of Large Numbers and Central Limit Theorems
C.5 Standard Asymptotic Properties of Estimators and Test Statistics
C.6 Maximum Likelihood Estimation
C.7 Likelihood Ratio, Lagrange Multiplier, and Wald Tests
C.8 Unit Root Asymptotics
C.8.2 Multivariate Processes
D.2 Evaluating Distributions of Functions of Multiple Time Series by Simulation
D.3 Resampling Methods
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