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Asymptotic Distributions Of Likelihood Ratios For Overparametrized Arma Processes

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  • Sándor Veres

Abstract

. This paper is devoted to an extension of a classical problem of statistics to the asymptotic distribution of likelihood ratios. Two main types of likelihood ratios are considered for Gaussian ARMA processes. It is assumed in both cases that the asymptotic Fisher information matrix of estimation is singular in the higher order models. It is proved that the asymptotic distributions of the log likelihood ratios are invariant with respect to the parameters generating the process. A simulation shows that the sample distribution of the log likelihood ratio approaches the asymptotic one. Finally, the likelihood ratio test is proposed for model order reduction.

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  • Sándor Veres, 1987. "Asymptotic Distributions Of Likelihood Ratios For Overparametrized Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 345-357, May.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:3:p:345-357
    DOI: 10.1111/j.1467-9892.1987.tb00446.x
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