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Unformatted text preview: Chapter 12 Properties of regression models with time series data Overview This chapter begins with a statement of the regression model assumptions for regressions using time series data, paying particular attention to the assumption that the disturbance term in any time period be distributed independently of the regressors in all time periods. There follows a general discussion of autocorrelation: the meaning of the term, the reasons why the disturbance term may be subject to it, and the consequences of it for OLS estimators. The chapter continues by presenting the Durbin–Watson test for AR(1) autocorrelation and showing how the problem may be eliminated. Next it is shown why OLS yields inconsistent estimates when the disturbance term is subject to autocorrelation and the regression model includes a lagged dependent variable as an explanatory variable. Then the chapter shows how the restrictions implicit in the AR(1) specification may be tested using the common factor test, and this leads to a more general discussion of how apparent autocorrelation may be caused by model misspecification. This in turn leads to a general discussion of the issues involved in model selection and, in particular, to the general-to-specific methodology. Learning outcomes After working through the corresponding chapter in the text, studying the corresponding slideshows, and doing the starred exercises in the text and the additional exercises in this guide, you should be able to: state the regression model assumptions for regressions with time series data and explain the implications of the assumption that the disturbance term be distributed independently of the regressors in all time periods • • • • • • • • • • • explain the concept of autocorrelation and the difference between positive and negative autocorrelation describe how the problem of autocorrelation may arise describe the consequences of autocorrelation for OLS estimators, their standard errors, and t and F tests, and how the consequences change if the model includes a lagged dependent variable perform the Durbin–Watson d test for AR(1) autocorrelation and, where appropriate, the Durbin h test explain how the problem of AR(1) autocorrelation may be eliminated describe the restrictions implicit in the AR(1) specification perform the common factor test explain how apparent autocorrelation may arise as a consequence of the omission of an important variable or the mathematical misspecification of the regression model. demonstrate that the static, AR(1), and ADL(1,0) specifications are special cases of the ADL(1,1) model explain the principles of the general-to-specific approach to model selection and the defects of the specific- to-general approach October 2007 2 Additional exercises A12.1 A variable Y t is generated by the autoregressive process t t t u Y Y + + = − 1 2 1 β β (1) where β 2 < 1 and u t satisfies the regression model assumptions....
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This note was uploaded on 05/26/2010 for the course ECON 301 taught by Professor Öcal during the Spring '10 term at Middle East Technical University.
- Spring '10