On the Futility of Testing the Error Term Assumptions in a Spurious Regression
AbstractA spurious regression model is one in which the dependent and independent variables are non-stationary, but not cointegrated, and the data are not filtered (e.g., by differencing) before the model is estimated. It is well known that in this case the asymptotic behaviour of the least squares parameter estimates, their "t-ratios", the Durbin-Watson statistic and the R-squared, are all non-standard. In particular, the parameter estimates and R-squared converge weakly to functionals of standard Brownian motions; the "t-ratios" diverge in distribution; and the Durbin-Watson statistic converges in probability to zero. In this paper we show that similar results apply to other common tests of a spurious regression model's specification. In particular, standard tests of the Normality and homoskedasticity of the error term are doomed to always reject the null hypotheses, asymptotically. These results further reinforce the need to avoid the estimation of spurious regressions.
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Bibliographic InfoPaper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0203.
Length: 21 pages
Date of creation: 29 May 2002
Date of revision:
Note: ISSN 1485-6441
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Spurious regression; normality; homoskedasticity; asymptotic theory; unit roots;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-06-13 (All new papers)
- NEP-ECM-2002-06-13 (Econometrics)
- NEP-ETS-2002-06-13 (Econometric Time Series)
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