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Thread: log likelihood function ARMA

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    log likelihood function ARMA




    To derive the log-likelihood function of an MA(1) we condition on .
    But when deriving the log-likelihood function function for an AR(1) we don't.
    Why not? Is it just because isn't found in the AR(1) equation?

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    Re: log likelihood function ARMA


    That's right. In the AR(1) setting the log-likelihood function can be written completely in terms of the observable time series X_t and the parameters of the model. This is not the case for MA(1). There we need to know the initial shock Epsilon_0 to write the likelihood-terms for subsequent X_t.

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