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An Asymptotic Expansion for the Distribution of the Likelihood Radio Criterion for a Gaussian Autoregressive Moving Average Process Under a Local Alternative

Published online by Cambridge University Press:  18 October 2010

Masanobu Taniguchi
Masanobu Taniguchi*
Affiliation:
Hiroshima University
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Abstract

In this paper, we shall derive the asymptotic expansion for the distribution of the likelihood ratio criterion for a Gaussian autoregressive moving average process under a sequence of local alternative hypotheses converging to the null hypothesis with rate of convergence where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).

Information

Type
Research Article
Information
Econometric Theory , Volume 1 , Issue 1 , April 1985 , pp. 73 - 84
Copyright
Copyright © Cambridge University Press 1985 

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References

REFERENCES

1. Hayakawa, T. (1975). The likelihood ratio criterion for a composite hypothesis under a local alternative. Biometrika, 62, 451–460.10.1093/biomet/62.2.451Google Scholar
2. Magnus, J. R., & H, Neudecker. (1979). The commutation matrix: Some properties and applications. Annals of Statistics, 7, 381–394.10.1214/aos/1176344621Google Scholar
3. Peer, H. W. (1971). Likelihood ratio and associated test criteria. Biometrika, 58, 577–587.Google Scholar
4. Phillips, P.C.B. (1977). Approximations to some finite sample distributions associated with a first order stochastic difference equation. Econometrica, 45, 463–486.10.2307/1911222Google Scholar
5. Phillips, P.C.B. (1977). A general theorem in the theory of asymptotic expansions as approximations to the finite sample distributions of econometric estimators. Econometrica, 45, 1517–1534.10.2307/1912315Google Scholar
6. Phillips, P.C.B. (1980). Finite sample theory and the distributions of alternative estimators of the marginal propensity to consume. Review of Economic Studies, XLVII, 183–224.Google Scholar
7. Sargan, J. D. (1975). Gram-Charlier approximations applied to t ratios of /c-class estimators. Econometrica, 43, 327–346.10.2307/1913589Google Scholar
8. Sargan, J. D. (1976). Econometric estimators and the Edgeworth approximation. Econometrica, 44, 421–448.Google Scholar
9. Sargan, J. D. (1980). Some approximations to the distribution of econometric criteria which are asymptotically distributed as chi-squared. Econometrica, 48, 1107–1138.10.2307/1912174Google Scholar
10. Taniguchi, M. (1983). On the second order asymptotic efficiency of estimators of Gaussian Arma processes. Annals of Statistics, 11, 157–169.Google Scholar
11. Whittle, P. (1951). Hypothesis Testing in Time Series Analysis. Uppsala.Google Scholar