On a mixture autoregressive model

We generalize the Gaussian mixture transition distribution (GMTD) model int roduced by Le and co-workers to the mixture autoregressive (MAR) model for the modelling of non-linear time series. The models consist of a mixture of K stationary or non-stationary AR components. The advantages of the MAR mo del over the GMTD model include a more full range of shape changing predict ive distributions and the ability to handle cycles and conditional heterosc edasticity in the time series. The stationarity conditions and autocorrelat ion function are derived. The estimation is easily done via a simple EM alg orithm and the model selection problem is addressed. The shape changing fea ture of the conditional distributions makes these models capable of modelli ng time series with multimodal conditional distributions and with heterosce dasticity. The models are applied to two real data sets and compared with o ther competing models. The MAR models appear to capture features of the dat a better than other competing models do.