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SOME PROPERTIES OF CONDITIONAL QUASI‐LIKELIHOOD FUNCTIONS FOR TIME SERIES MODEL FITTING
Author(s) -
Huzii Mituaki
Publication year - 1988
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1988.tb00475.x
Subject(s) - mathematics , series (stratigraphy) , likelihood function , infinity , conditional expectation , parametric statistics , parametric model , maximum likelihood , function (biology) , time series , gaussian , conditional probability distribution , gaussian process , statistics , mathematical analysis , paleontology , physics , quantum mechanics , evolutionary biology , biology
. We consider fitting a parametric model to a time series and obtain the maximum likelihood estimates of unknown parameters included in the model by regarding the time series as a Gaussian process satisfying the model. We evaluate the asymptotic value of the conditional quasi‐likelihood function when the number of observations tends to infinity. We show what properties of the time series we can find by examining the behaviour of the conditional quasi‐likelihood function, even when the time series does not necessarily satisfy the model and is not necessarily Gaussian.