This paper discusses the problem of estimating multiple change points in the trend function of a time series regression model where the residual process is a circular ARMA model, and the trend function satisfies a sort of Grenander's conditions. First, the asymptotic representation of the likelihood ratio between contiguous hypothesis is given. Then the limiting distributions of the maximum likelihood estimator (MLE) and the Bayes estimator (BE) for the regression coefficients and change points are derived. It is seen that the BE is asymptotically efficient, and that the MLE is not so generally.