Mei-Yu LEE

The Effect of Nonzero Autocorrelation Coefficients on the Distributions of Durbin-Watson Test Estimator: Three Autoregressive Models

This paper investigates the effect of the nonzero autocorrelation coefficients on the sampling distributions of the Durbin-Watson test estimator in three time-series models that have different variance-covariance matrix assumption, separately. We show that the expected values and variances of the Durbin-Watson test estimator are slightly different, but the skewed and kurtosis coefficients are considerably different among three models. The shapes of four coefficients are similar between the Durbin-Watson model and our benchmark model, but are not the same with the autoregressive model cut by one-lagged period. Second, the large sample case shows that the three models have the same expected values, however, the autoregressive model cut by one-lagged period explores different shapes of variance, skewed and kurtosis coefficients from the other two models. This implies that the large samples lead to the same expected values, 2(1 – ρ0), whatever the variance-covariance matrix of the errors is assumed. Finally, comparing with the two sample cases, the shape of each coefficient is almost the same, moreover, the autocorrelation coefficients are negatively related with expected values, are inverted-U related with variances, are cubic related with skewed coefficients, and are U related with kurtosis coefficients.
JEL Classification C32, C15, C52
Full Article
  1. Durbin, J. and Watson , G.S., 1950. Testing for Serial Correlation in Least Squares Regression. I. Biometrika, 37, pp. 409-428.
  2. Durbin, J. and Watson , G.S., 1951. Testing for Serial Correlation in Least Squares Regression. II. Biometrika, 38, pp. 159-177.
  3. Imhof, J.P., 1961. Durbin-Watson Test for Serial Correlation with Extreme Sample Sizes or Many Regressors. Biometrika, 48, pp. 419-426.
  4. Lee, M.Y., 2014a. Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with First-order Autoregressive Procedures, Journal of Statistical and Econometric Methods, 3, pp. 1-22.
  5. Lee, M.Y., 2014b. On Durbin-Watson Test Statistic Based on Z Test in Large Samples, working paper.
  6. Pan, J.J., 1968. Distributions of the noncircular serial correlation coefficients. American Mathematical Society and Institute of Mathematical Statistics Selected Translations in Prob- ability and Statistics, 7, pp. 281-291.
  7. Savin, N.E. and White, K.J., 1978. Estimation and Testing for Functional Form and Autocorrelation: A Simultaneous Approach. Journal of Econometrics, 8, pp. 1-12.

Article Rights and License
© 2014 The Author. Published by Sprint Investify. ISSN 2359-7712. This article is licensed under a Creative Commons Attribution 4.0 International License. Creative Commons License
Corresponding Author
Mei-Yu Lee, Yuanpei University, Department of Applied Finance, Taiwan
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Mei-Yu LEE
Yuanpei University, Taiwan