Locally Optimal Tests against Periodic Autoregression: Parametric and Nonparametric Approaches

Locally asymptotically optimal tests are derived for the null hypothesis of traditional AR dependence, with unspecified AR coefficients and unspecified innovation densities, against an alternative of periodically correlated AR dependence. Parametric and nonparametric rank-based versions are proposed...

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Bibliographic Details
Published in:Econometric theory 1996-03, Vol.12 (1), p.88-112
Main Authors: Bentarzi, Mohamed, Hallin, Marc
Format: Article
Language:English
Subjects:
Autocorrelation
Autoregressive moving average
Degrees of freedom
Economic models
Lagrange multipliers
Null hypothesis
Time series
Time series analysis
Time series forecasting
Time series models
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Summary:Locally asymptotically optimal tests are derived for the null hypothesis of traditional AR dependence, with unspecified AR coefficients and unspecified innovation densities, against an alternative of periodically correlated AR dependence. Parametric and nonparametric rank-based versions are proposed. Local powers and asymptotic relative efficiencies (with respect, e.g., to the corresponding Gaussian Lagrange multiplier tests proposed in Ghysels and Hall [1992, “Lagrange Multiplier Tests for Periodic Structures,” unpublished manuscript, CRDE, Montreal] and Liitkepohl [1991, Introduction to Multiple Time Series Analysis, Berlin: Springer-Verlag; 1991, pp. 243–264, in W.E. Griffiths, H. Liitkepohl, & M.E. Block (eds.), Readings in Econometric Theory and Practice, Amsterdam: North-Holland] are computed explicitly; a rank-based test of the van der Waerden type is proposed, for which this ARE is uniformly larger than 1. The main technical tool is Le Cam's local asymptotic normality property.
ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466600006459