Some Properties of Conditional Quasi‐likelihood Functions for Time Series Model Fitting

Abstract

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.