Linear Models with Correlated Disturbances (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
196
Utgivningsdatum
1991-05-01
Upplaga
Softcover reprint of the original 1st ed. 1991
Förlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Illustrationer
1 Illustrations, black and white; VIII, 196 p. 1 illus.
Dimensioner
244 x 170 x 11 mm
Vikt
345 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISSN
0075-8442
ISBN
9783540539018

Linear Models with Correlated Disturbances

av Paul Knottnerus
Häftad,  Engelska, 1991-05-01
1613
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In each chapter of this volume some specific topics in the econometric analysis of time series data are studied. All topics have in common the statistical inference in linear models with correlated disturbances. The main aim of the study is to give a survey of new and old estimation techniques for regression models with disturbances that follow an autoregressive-moving average process. In the final chapter also several test strategies for discriminating between various types of autocorrelation are discussed. In nearly all chapters it is demonstrated how useful the simple geometric interpretation of the well-known ordinary least squares (OLS) method is. By applying these geometric concepts to linear spaces spanned by scalar stochastic variables, it emerges that well-known as well as new results can be derived in a simple geometric manner, sometimes without the limiting restrictions of the usual derivations, e. g. , the conditional normal distribution, the Kalman filter equations and the Cramer-Rao inequality. The outline of the book is as follows. In Chapter 2 attention is paid to a generalization of the well-known first order autocorrelation transformation of a linear regression model with disturbances that follow a first order Markov scheme. Firstly, the appropriate lower triangular transformation matrix is derived for the case that the disturbances follow a moving average process of order q (MA(q. It turns out that the calculations can be carried out either analytically or in a recursive manner.
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Innehållsförteckning

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.- 2.5 The matrix P in the case of MA(1) disturbances.- 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.- Appendix 2. A Linear vector spaces.- Appendix 2.B The formula for tj if t is small.- III Computational Aspects of data Transformations and Ansleys 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 Ansleys method.- IV GLS Estimation by Kalman Filtering.- 4.1 Introduction.- 4.2 Some results from multivariate analysis.- 4.3 The Kaiman filter equations.- 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.- 5.5 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 Koycks consistent two-step estimator.- 6.5 Efficient estimation of dynamic models.- 6.6 Dynamic models with several geometricdistributed lags.- 6.7 The Cramr-Rao inequality and the Pythagorean theorem.- VII Test Strategies for Discriminating Between Autocorrelation and Misspecification.- 7.1 Introduction.- 7.2 Thursbys test strategy.- 7.3 Comments on Thursbys test strategy.- 7.4 Godfreys test strategy.- 7.5 Comments on Godfreys test strategy.- References.- Author Index.

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