Testing for serial correlation against an arma(1, 1) process

Journal of the American Statistical Association

Volumn 91, Issue 435, 1996, Pages 1331-1342

  Andrews, Donald W K ^a   Ploberger, Werner ^b  

^a Cowles Foundation for Research in Economics ^*  (United States)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

Autoregressive moving average model; Consistent test; Lagrange multiplier test; Likelihood ratio test; Nonstandard testing problem; Test of white noise

Indexed keywords

EID: 0030336512     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10477002     Document Type: Article

References (25)

1. Ahlfors, L. V. (1966), Complex Analysis (2nd ed.), New York: McGrawHill.
2. Andrews, D. W. K. (1992), "Generic Uniform Convergence," Econometric Theory, 8, 241-257.
3. Andrews, D. W. K., Liu, X., and Ploberger, W. (1996), ''Tests of Seasonal and Non-Seasonal Serial Correlation," Cowles Foundation Discussion Paper No. 1124, Yale University.
4. Andrews, D. W. K., Liu, X., and Ploberger, W. (1993), ‘Tests for Parameter Instability and Structural Change With Unknown Change Point,” Econometrica, 61, 821-856.
5. Andrews, D. W. K., and Ploberger, W. (1994), “Optimal Tests When a Nuisance Parameter is Present Only Under the Alternative,” Econometrica, 62, 1383-1414.
6. Andrews, D. W. K., and Ploberger, W. (1995), “Admissibility of the Likelihood Ratio Test When a Nuisance Parameter is Present Only Under the Alternative,” The Annals of Statistics, 23, 1609-1629.
7. Ansley, C. F. (1979), “An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process,” Biometrika, 66, 59-65.
8. Bierens, H. J., and Ploberger, W. (1994), “Asymptotic Theory of Integrated Conditional Moment Tests," unpublished working paper, Southern Methodist University, Dept, of Economics.
9. Box, G. E. P., and Pierce, D. A. (1970), “Distribution of Residual Autocorrelation in Autoregressive-Integrated Moving Average Time Scries Models,” Journal of the American Statistical Association, 65, 1509-1526.
10. Davies, R. B. (1977), “Hypothesis Testing When a Nuisance Parameter is Present Only Under the Alternative,” Biometrika, 64, 247-254.
11. Davies, R. B. (1987), “Hypothesis Testing When a Nuisance Parameter is Present Only Under the Alternative,” Biometrika, 74, 33-43.
12. Durbin, J., and Watson, G. S. (1950), ‘Testing for Serial Correlation in Least Squares Regression, I,” Biometrika, 37, 409-428.
13. Hall, P., and Heyde, C. C. (1980), Martingale Limit Theory and Its Applications, New York: Academic Press.
14. Hannan, E. J. (1982), ‘Testing for Autocorrelation and Akaike’s Criterion,” in Essays in Statistical Science, eds. J. Gani and E. J. Hannan, Journal of Applied Probability, Special Volume 19A.
15. Hansen, B. E. (1996), “Inference When a Nuisance Parameter is Not Identified Under the Null Hypothesis,” Econometrica, 64, 413-430.
16. Hermdorf, N. (1984), “A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables," Annals of Probability, 12, 141-153.
17. Pollard, D. (1984), Convergence of Stochastic Processes, New York: Springer-Verlag.
18. Pollard, D. (1990), Empirical Processes: Theory and Applications, CBMS Conference Series in Probability and Statistics, Vol. 2, Hayward, CA: Institute of Mathematical Statistics.
19. Poskitt, D. S., and Tremayne, A. R. (1980), “Testing the Specification of a Fitted Autoregressive Moving Average Model,” Biometrika, 67, 359-363.
20. Pötscher, B. M. (1985), ‘The Behaviour of the Lagrangian Multiplier Test in Testing the Orders of an ARMA Model,” Metrika, 32, 129-150.
21. Pötscher, B. M. (1990), “Estimation of Autoregressive Moving-Average Order Given an Infinite Number of Models and Approximation of Spectral Densities,” Journal of Time Series Analysis, 11, 165-179.
22. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1986), Numerical Recipes: The Art of Scientific Computing, Cambridge, U.K.: Cambridge University Press.
23. Rahman, S., and King, M. (1992), ‘Testing for ARMA(1, 1) Disturbances in the Linear Regression Model,” Working Paper 1/92, Monash University, Dept, of Econometrics.
24. Veres, S. (1987), “Asymptotic Distributions of Likelihood Ratios for Overparameterized ARMA Processes," Journal of Time Series Analysis, 8, 345-357.
25. Wald, A. (1943), ‘Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is Large,” Transactions of the American Mathematical Society, 54, 426-482.