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A Note on a Lagrange Multiplier Test for Testing an Autoregressive Unit Root

Published online by Cambridge University Press:  11 February 2009

Pentti Saikkonen
Pentti Saikkonen
Affiliation:
University of Helsinki
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Abstract

It is shown that in a first-order mixed autoregressive moving average model, a Lagrange multiplier test for the autoregressive unit-root hypothesis can be inconsistent against stationary alternatives.

Type
Miscellanea
Information
Econometric Theory , Volume 9 , Issue 3 , June 1993 , pp. 494 - 498
Copyright
Copyright © Cambridge University Press 1993

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References

1.Cox, D.R. & Hinkley, D.V.. Theoretical Statistics. London: Chapman and Hall, 1974.Google Scholar
2.Dickey, D.A. & Fuller, W.A.. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74 (1979): 427–431.Google Scholar
3.Fuller, W.A.Introduction to Statistical Time Series Analysis. New York: Wiley, 1976.Google Scholar
4.Pantula, S.G.Asymptotic distributions of unit-root tests when the process is nearly stationary. Journal of Business & Economic Statistics 9 (1991): 63–71.Google Scholar
5.Phillips, P.C.B.Time series regression with a unit root. Econometrica 55 (1987): 277–301.CrossRefGoogle Scholar
6.Phillips, P.C.B. & Ouliaris, S.. Asymptotic properties of residual based tests for cointegration. Econometrica 58 (1990): 165–193.Google Scholar
7.Phillips, P.C.B. & Perron, P.. Testing for a unit root in time series regression. Biometrika 75 (1988): 335–346.Google Scholar
8.Said, S.E. & Dickey, D.A.. Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71 (1984): 599–607.Google Scholar
9.Said, S.E. & Dickey, D.A.. Hypothesis testing in ARIMA (p,1,q) models. Journal of the American Statistical Association 80 (1985): 369–374.Google Scholar
10.Saikkonen, P. & Luukkonen, R.. Testing for a moving average unit root in autoregressive integrated moving average models. Journal of the American Statistical Association (forthcoming).Google Scholar
11.Solo, V.The order of differencing in ARIMA models. Journal of the American Statistical Association 79 (1984): 916–921.Google Scholar
12.Tanaka, K. & Satchell, S.E.. Asymptotic properties of the maximum likelihood and non-linear least squares estimators for non-invertible moving average models. Econometric Theory 5 (1989): 333–353.Google Scholar