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Asymptotic expansions for time series statistics

Published online by Cambridge University Press:  14 July 2016

Katsuto Tanaka
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Abstract

Asymptotic expansions for the distributions of estimators and test statistics are derived in connection with time series models. The expansions relate to marginal and joint distributions together with the percentiles of marginal distributions. We also consider transforming a statistic so that the transformed statistic has a distribution that coincides with its asymptotic distribution up to a higher order.

Keywords

TEST STATISTICSTIME SERIES MODELMAXIMUM LIKELIHOOD ESTIMATOR
Type
Part 3—Hypothesis Testing and Distribution Theory for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 211 - 227
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Chambers, J. M. (1967) On methods of asymptotic approximation for multivariate distributions. Biometrika 54, 367–383.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
Hayakawa, T. (1977) The likelihood ratio criterion and the asymptotic expansion of its distribution. Ann. Inst. Statist. Math. 29, 359–378.CrossRefGoogle Scholar
Hearn, A. C. (1973) REDUCE-2 User's Manual. UCP-19, University of Utah.Google Scholar
Hill, G. W. and Davis, A. W. (1968) Generalized asymptotic expansions of Cornish-Fisher type. Ann. Math. Statist. 39, 1264–1273.Google Scholar
Phillips, P. C. B. (1977) Approximations to some finite sample distributions associated with a first order stochastic difference equation. Econometrica 45, 463–486.Google Scholar
Sargan, J. D. (1976) Econometric estimators and the Edgeworth approximation. Econometrica 44, 421–448.Google Scholar
Tanaka, K. (1983) Asymptotic expansions associated with the AR(1) model with unknown mean. Econometrica 51, 1221–1231.Google Scholar
Tanaka, K. (1984) An asymptotic expansion associated with the maximum likelihood estimators in ARMA models. J. R. Statist. Soc. B 46, 58–67.Google Scholar