Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-25T00:36:02.914Z Has data issue: false hasContentIssue false

Testing for a Moving Average Unit Root

Published online by Cambridge University Press:  11 February 2009

Katsuto Tanaka
Affiliation:
Hitotsubashi University, Japan

Abstract

Testing for a unit root in the moving average model is discussed. First, for the stationary MA(1) model, we suggest a score type test which is locally best invariant and unbiased. Performance of the test for finite samples is compared with the most powerful test. The asymptotic behavior of the test is also considered by computing the limiting power under a sequence of local alternatives. We then extend the model to an infinite order MA and suggest a test for this extended case.

Type
Articles
Copyright
Copyright © Cambridge University Press 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Anderson, T.W.The statistical analysis of time series. New York: Wiley, 1971.Google Scholar
2.Anderson, T.W. & Darling, D.A.. Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Annals of Mathematical Statistics 23 (1952): 193212.CrossRefGoogle Scholar
3.Anderson, T.W. & Takemura, A.. Why do noninvertible estimated moving averages occur? Journal of Time Series Analysis 7 (1986): 235254.CrossRefGoogle Scholar
4.Berenblut, I.I. & Webb, G.I.. A new test for autocorrelated errors in the linear regression model. Journal of the Royal Statistical Society, (B) 35 (1973): 3350.Google Scholar
5.Cryer, J.D. & Ledolter, J.. Small-sample properties of the maximum likelihood estimator in the first-order moving average model. Biometrika 68 (1981): 691694.Google Scholar
6.Ferguson, T.S.Mathematical statistics: A decision theoretic approach. New York: Academic Press, 1967.Google Scholar
7.Imhof, J.P.Computing the distribution of quadratic forms in normal variables. Biometrika 48 (1961): 419426.CrossRefGoogle Scholar
8.King, M.L. & Hillier, G.H.. Locally best invariant tests of the error covariance matrix of the linear regression model. Journal of the Royal Statistical Society, (B) 47 (1985): 98102.Google Scholar
9.Phillips, P.C.B.Time series regression with a unit root. Econometrica 55 (1987): 277301.CrossRefGoogle Scholar
10.Sargan, J.D. & Bhargava, A.. Testing residuals from least squares regression for being generated by the Gaussian random walk. Econometrica 51 (1983): 153174.CrossRefGoogle Scholar
11.Sargan, J.D. & Bhargava, A.. Maximum likelihood estimation of regression models with firstorder moving average errors when the root lies on the unit circle. Econometrica 51 (1983): 799820.Google Scholar
12.Tanaka, K.The Fredholm approach to asymptotic inference on nonstationary and noninvertible time series models. Econometric Theory 6 (1990): 411432.Google Scholar
13.Tanaka, K. & Satchell, S.E.. Asymptotic properties of the maximum likelihood and nonlinear least squares estimators for noninvertible moving average models. Econometric Theory 5 (1989): 333353.CrossRefGoogle Scholar
14.White, H. Asymptotic theory for econometricians. New York: Academic Press, 1984.Google Scholar