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A New Test for Nonstationarity Against the Stable Alternative

Published online by Cambridge University Press:  11 February 2009

Karim M. Abadir
Karim M. Abadir
Affiliation:
University of Exeter
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Abstract

It was recently shown (Abadir, 1993b) that nonstationarity causes the limiting distributions of the Wald (W) and Lagrange multiplier (LM) statistics to become different from each other. This paper demonstrates that such a divergence between the two distributions can be used as an indicator of the presence of a unit root. A test based on this idea is devised by modifying the normalized autocorrelation coefficient (NAC). It is then shown to be an improvement on NAC in large samples and an improvement on other existing tests in large effective samples. The paper also investigates the effect of nonstationarity on the well-known inequality W ≥ LR ≥ LM.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 1 , February 1995 , pp. 81 - 104
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Abadir, K.M. (1991) The Limiting Distribution of the t Ratio under a Unit Root. Mimeo, American University in Cairo.Google Scholar
Abadir, K.M. (1992) A distribution generating equation for unit-root statistics. Oxford Bulletin of Economics and Statistics 54, 305–323.CrossRefGoogle Scholar
Abadir, K.M. (1993a) OLS bias in a nonstationary autoregression. Econometric Theory 9, 81–93.CrossRefGoogle Scholar
Abadir, K.M. (1993b) On the asymptotic power of unit root tests. Econometric Theory 9, 187–219.CrossRefGoogle Scholar
Abadir, K.M. (1993c) On Variance Reduction Techniques in Dynamic Models. Manuscript.Google Scholar
Abadir, K.M. (1993d) The Joint Density of Two Functional of a Brownian Motion. Manuscript.Google Scholar
Abadir, K.M. (1993e) The limiting distribution of the autocorrelation coefficient under a unit root. Annals of Statistics 21, 1058–1070.CrossRefGoogle Scholar
Berndt, E.R. & Savin, N.E. (1977) Conflict among criteria for testing hypotheses in the multivariate linear regression model. Econometrica 45, 1263–1277.CrossRefGoogle Scholar
Breusch, T.S. (1979) Conflict among criteria for testing hypotheses: Extensions and comments. Econometrica 47, 203–207.CrossRefGoogle Scholar
De Jong, D.N., Nankervis, J.C., Savin, N.E. & Whiteman, C.H. (1992) The power problem of unit root tests in time series with autoregressive errors. Journal of Econometrics 53, 323–343.CrossRefGoogle Scholar
Dickey, D.A. & Fuller, W.A. (1979) Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431.Google Scholar
Dickey, D.A. & Fuller, W.A. (1981) Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 1057–1072.CrossRefGoogle Scholar
Elliott, G., Rothenberg, T.J. & Stock, J.H. (1993) Efficient Tests for an Autoregressive Unit Root. Manuscript.CrossRefGoogle Scholar
Erdélyi, A. (ed.) (1953) Higher Transcendental Functions, vol. 2. New York: McGraw-Hill.Google Scholar
Evans, G.B.A. & Savin, N.E. (1981) Testing for unit roots: 1. Econometrica 49, 753–779.CrossRefGoogle Scholar
Evans, G.B.A. & Savin, N.E. (1982a) Conflict among testing procedures in a linear regression model with lagged dependent variables. In Hildenbrand, W. (ed.), Advances in Econometrics, pp. 263–283. Cambridge: Cambridge University Press.Google Scholar
Evans, G.B.A. & Savin, N.E. (1982b) Conflict among the criteria revisited; the W, LR and LM tests. Econometrica 50, 737–748.CrossRefGoogle Scholar
Evans, G.B.A. & Savin, N.E. (1984) Testing for unit roots: 2. Econometrica 52, 1241–1269.CrossRefGoogle Scholar
Fuller, W.A. (1976) Introduction to Statistical Time Series. New York: John Wiley & Sons.Google Scholar
Gelman, A. & Rubin, D.B. (1992) Inference from iterative simulation using multiple sequences. Statistical Science 7, 457–511 (with discussion).CrossRefGoogle Scholar
Geyer, C.J. (1992) Practical Markov chain Monte Carlo. Statistical Science 7, 473–511 (with discussion).Google Scholar
Nabeya, S. & Tanaka, K. (1990) Limiting power of unit-root tests in time-series regression. Journal of Econometrics 46, 247–271.CrossRefGoogle Scholar
Oberhettinger, F. & Baddi, L. (1973) Tables of Laplace Transforms. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Perron, P. (1991) A continuous time approximation to the stationary first-order autoregressive model. Econometric Theory 7, 236–252.CrossRefGoogle Scholar
Phillips, P.C.B. & Perron, P. (1988) Testing for a unit root in time series regression. Biometrika 75, 335–346.CrossRefGoogle Scholar
Said, S.E. & Dickey, D.A. (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71, 599–607.CrossRefGoogle Scholar
Savin, N.E. (1976) Conflict among testing procedures in a linear regression model with autoregressive disturbances. Econometrica 44, 1303–1315.CrossRefGoogle Scholar
Tsay, R.S. & Tiao, G.C. (1990) Asymptotic properties of multivariate nonstationary process with applications to autoregressions. Annals of Statistics 18, 220–250.CrossRefGoogle Scholar
White, J.S. (1958) The limiting distribution of the serial correlation coefficient in the explosive case. Annals of Mathematical Statistics 29, 1188–1197.CrossRefGoogle Scholar