Linear Models with Correlated Disturbances

Linear Models with Correlated Disturbances

by Paul Knottnerus

Paperback(Softcover reprint of the original 1st ed. 1991)

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Product Details

ISBN-13: 9783540539018
Publisher: Springer Berlin Heidelberg
Publication date: 06/03/1991
Series: Lecture Notes in Economics and Mathematical Systems , #358
Edition description: Softcover reprint of the original 1st ed. 1991
Pages: 196
Product dimensions: 6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

I Introduction.- II Transformation Matrices and Maximum Likelihood Estimation of Regression Models with Correlated Disturbances.- 2.1 Introduction.- 2.2 The algebraic problem.- 2.3 A dual problem.- 2.4 Recursive methods for calculating the transformation matrix P.- 2.4.1 A recursive algorithm for calculating P.- 2.4.2 The recursive Levinson-Durbin algorithm.- 2.4.3 A supplementary Levinson-Durbin algorithm.- 2.4.4 Inversion of an arbitrary nonsingular matrix.- 2.5 The matrix P in the case of MA(1) disturbances.- 2.5.1 The matrix P.- 2.5.2 A new derivation of the inverse of the autocovariance matrix of an MA(1) process.- 2.6 The matrix P in the case of MA(q) disturbances.- 2.7 The matrix P in the case of ARMA(p,q) disturbances.- 2.7.1 A derivation of the formula for the autocovariance matrix of an ARMA(p,q) process.- 2.7.2 The matrix P in the case of ARMA(p,q) disturbances.- Appendix 2. A Linear vector spaces.- Appendix 2.B The formula for ßtj if t is small.- III Computational Aspects of data Transformations and Ansley’s Algorithm.- 3.1 Introduction.- 3.2 Recursive computations for models with MA(q) disturbances.- 3.3 Recursive computations for models with ARMA(p,q) disturbances.- 3.4 Ansley’s method.- IV GLS Estimation by Kalman Filtering.- 4.1 Introduction.- 4.2 Some results from multivariate analysis.- 4.2.1 Likelihood functions.- 4.2.2 Conditional normal distributions and minimum variance estimators.- 4.3 The Kaiman filter equations.- 4.3.1 The state space model.- 4.3.2 A general geometric derivation of the Kaiman filter equations.- 4.3.3 Comparison with other derivations.- 4.4 The likelihood function.- 4.5 Estimation of linear models with ARMA(p,q) disturbances by means of Kaiman filtering.- 4.6 The exact likelihood function for models with ARMA(p,q) disturbances.- 4.7 Predictions and prediction intervals by using Kaiman filtering.- V Estimation of Regression Models with Missing Observations and Serially Correlated Disturbances.- 5.1 Introduction.- 5.2 The model.- 5.3 Derivation of the transformation matrix.- 5.4 Estimation and test procedures.- 5.4.1 Estimation.- 5.4.2 Tests for autocorrelation if observations are missing.- The likelihood ratio test.- The modified Lagrange multiplier (MLM) test.- An infinite number of missing observations.- The power of the MLM test.- An adjusted Lagrange multiplier test.- 5.5 Kaiman filtering with missing observations.- Appendix 5.A Stationarity conditions for an AR(2) process.- VI Distributed lag Models and Correlated Disturbances.- 6.1 Introduction.- 6.2 The geometric distributed lag model.- 6.3 Estimation methods.- 6.4 A simple formula for Koyck’s consistent two-step estimator.- 6.5 Efficient estimation of dynamic models.- 6.5.1 Introduction.- 6.5.2 An efficient 3-step Gauss-Newton estimation method.- 6.5.3 A Gauss-Newton-Prais-Winsten estimation method with small sample adjustments.- 6.6 Dynamic models with several geometric distributed lags.- 6.7 The Cramér-Rao inequality and the Pythagorean theorem.- VII Test Strategies for Discriminating Between Autocorrelation and Misspecification.- 7.1 Introduction.- 7.2 Thursby’s test strategy.- 7.3 Comments on Thursby’s test strategy.- 7.3.1 Introduction.- 7.3.2 The simple AR(2) disturbances model.- 7.3.3 The general disturbances model.- 7.4 Godfrey’s test strategy.- 7.5 Comments on Godfrey’s test strategy.- References.- Author Index.

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