Linear Models with Correlated Disturbances: 358 (Lecture Notes in Economics and Mathematical Systems, 358) - Softcover

Knottnerus, Paul

Softcover

ISBN 10: 3540539018 ISBN 13: 9783540539018

Publisher: Springer, 1991

Synopsis

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.

About this title

Synopsis

The main aim of this volume is to give a survey of new and old estimation techniques for regression models with correlated disturbances, especially with autoregressive-moving average disturbances. In nearly all chapters the usefulness of the simple geometric interpretation of the classical ordinary Least Squares method is demonstrated. It emerges that both well-known and new results can be derived in a simple geometric manner, e.g., the conditional normal distribution, the Kalman filter equations and the Cramer-Rao inequality. The same geometric interpretation also shows that disturbances which follow an arbitrary correlation process can easily be transformed into a white noise sequence. This is of special interest for Maximum Likelihood estimation. Attention is paid to the appropriate estimation method for the specific situation that observations are missing. Maximum Likelihood estimation of dynamic models is also considered. The final chapter is concerned with several test strategies for detecting the genuine correlation structure among the disturbances.

The geometric approach throughout the book provides a coherent insight in apparently different subjects in the econometric field of time series analysis.

Edition details

• Publisher: Springer
• Publication date: 1991
• Language: English
• ISBN 10: 3540539018
• ISBN 13: 9783540539018
• Binding: Perfect Paperback
• Number of pages: 204