MODELING FLAT STRETCHES, BURSTS, AND OUTLIERS IN TIME-SERIES USING MIXTURE TRANSITION DISTRIBUTION MODELS

The class of mixture transition distribution (MTD) time series models is extended to general non-Gaussian time series. In these models the c onditional distribution of the current observation given the past is a mixture of conditional distributions given each one of the last p obs ervations. They can capture non-Gaussian and nonlinear features such a s flat stretches, bursts of activity, outliers, and changepoints in a single unified model class. They can also represent time series define d on arbitrary state spaces, univariate or multivariate, continuous, d iscrete or mixed, which need not even be Euclidean. They perform well in the usual case of Gaussian time series without obvious nonstandard behaviors. The models are simple. analytically tractable, easy to simu late, and readily estimated. The stationarity and autocorrelation prop erties of the models are derived. A simple EM algorithm is given and s hown to work well for estimation. The models are applied to several re al and simulated datasets with satisfactory results. They appear to ca pture the features of the data better than the best competing autoregr essive integrated moving average (ARIMA) models.