Abstract
This paper is concerned with a moving average model of order q where the coefficients are allowed to change as functions of time, containing unknown parameters. We derive the exact likelihood function of observations and show under what kinds of functions the maximum likelihood estimators (MLE) have consistency and asymptotic normality for large values of the sample size. Furthermore we consider the asymptotic relationship between the exact MLE and the conditional MLE obtained by letting the starting values be zero.
