Mixtures of Autoregressions with an Improper Component for Panel Data

An EM algorithm for fitting mixtures of autoregressions of low order is constructed and the properties of the estimators are explored on simulated and real datasets. The mixture model incorporates a component with an improper density, which is intended for outliers. The model is proposed as an alternative to the search for the order of a single-component autoregression. The methods can be adapted to other patterns of dependence in panel data. An application to the monthly records of income of the outlets of a retail company is presented.