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An Approximation to the Null Distribution of the Durbin-Watson Statistic in Models Containing Lagged Dependent Variables

Published online by Cambridge University Press:  18 October 2010

Brett Inder
Affiliation:
Monash University, Australia

Abstract

We consider testing for autoregressive disturbances in the linear regression model with a lagged dependent variable. An approximation to the null distribution of the Durbin—Watson statistic is developed using small-disturbance asymptotics, and is used to obtain test critical values. We also obtain nonsimilar critical values for the Durbin—Watson and Durbin's h and t tests. Monte Carlo results are reported comparing the performances of the tests under the null and alternative hypotheses. The Durbin–Watson test is found to be more powerful and to perform more consistently than either of Durbin's tests under Ho.

Type
Articles
Copyright
Copyright © Cambridge University Press 1986

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References

REFERENCES

1.Dufour, J. M. Recursive stability analysis of linear regression relationships: An exploratory methodology. Journal of Econometrics 19 (1982): 3176.Google Scholar
2.Durbin, J. Testing for serial correlation in least squares regression when some of the regressors are lagged dependent variables. Econometrica 38 (1970): 410421.Google Scholar
3.Durbin, J. and Watson, G. S.. Testing for serial correlation in least squares regression I. Biometrika 37 (1950): 409428.Google ScholarPubMed
4.Durbin, J. and Watson, G. S.. Testing for serial correlation in least squares regression II. Biometrika 38 (1951): 159178.Google Scholar
5.Harvey, A. C. The Econometric Analysis of Time Series. Philip Allan, Oxford, 1981.Google Scholar
6.Imhof, P. J. Computing the distribution of quadratic forms in normal variables. Biometrika 48 (1961): 419426.Google Scholar
7.Inder, B. A. Finite-sample power of tests for autocorrelation in models containing lagged dependent variables. Economics Letters 14 (1984a): 179185.Google Scholar
8.Inder, B. A. Finite-sample power of tests for autocorrelation in models containing lagged dependent variables: A Correction, Department of Econometrics and Operations Research, Monash University, Working Paper No. 3/84, (1984b).CrossRefGoogle Scholar
9.Inder, B. A. An approximation to the null distribution of the Durbin-Watson statistic in models containing lagged dependent variables, Department of Econometrics and Operations Research, Monash University Working Paper No. 4/86, (1986).CrossRefGoogle Scholar
10.Kenkel, J. L. Some small sample properties of Durbin's tests for serial correlation in regression models containing lagged dependent variables. Econometrica 42 (1974): 763769.CrossRefGoogle Scholar
11.Kenkel, J. L. Small sample tests for serial correlation in models containing lagged dependent variables. Review of Economics and Statistics 57 (1975): 383386.Google Scholar
12.L, King M.. The Durbin-Watson test for serial correlation: Bounds for regressions with trend and/or seasonal dummy variables. Econometrica 49 (1981): 15711581.Google Scholar
13.L., King M. Testing for autocorrelation in linear regression models: A Survey, forthcoming in King, M. L. and Giles, D.E.A. (eds) Specification Analysis in the Linear Model (in Honour of Donald Cochrane), (1986).Google Scholar
14.Kiviet, J. F. On the rigour of some misspecification tests for modeling dynamic relationships, Report AE 11/81 (Revised Edition), Faculty of Actuarial Science and Econometrics, University of Amsterdam, (1983).Google Scholar
15.Koerts, J. and Abrahamse, A.P.J.. On the Theory and Application of the General Linear Model. Rotterdam University Press: Rotterdam, (1969).Google Scholar
16.Maddala, G. S. and Rao, A. S.. Tests for serial correlation in regression models with lagged dependent variables and serially correlated errors. Econometrica 41 (1973): 761774.Google Scholar
17.McNown, R. F. and Hunter, K. R.. A test for autocorrelation in models with lagged dependent variables. Review of Economics and Statistics 62 (1980): 313317.CrossRefGoogle Scholar
18.Nankervis, J. C. and Savin, N. E.. Student's t approximation in a stationary first-order autoregressive model, mimeo, Trinity College, Cambridge, (1984).Google Scholar
19.Park, S. On the small-sample power of Durbin's h test. Journal of the American Statistical Association 70 (1975): 6063.Google Scholar
20.Phillips, P.C.B. Finite sample theory and the distributions of alternative estimators of the marginal propensity to consume. Review of Economic Studies 47 (1980): 183224.CrossRefGoogle Scholar
21.Spencer, B. G. The small sample bias of Durbin's tests for serial correlation when one of the regressors is the lagged dependent variable and the null hypothesis is true. Journal of Econometrics 3 (1975): 249254.CrossRefGoogle Scholar
22.Tse, Y. K.Edgeworth approximations in first-order stochastic difference equations with exogenous variables. Journal of Econometrics 20 (1982): 175195.Google Scholar