In this post, we briefly review the paper Autoregressive Tree Models for Time-Series Analysis by Meek, Chickering and Herman. This paper identifies models for continuous time series data which they call ART model. These models are built this way : First, the time series data is transformed into a set of cases suitable for a regression analysis. The predictor and target variables are the past and the current value. This transformed data set is used to learn a decision tree for the target variable. The decision tree has linear regressions at its leaves and thus producing a piecewise-linear auto regression model.  A Bayesian technique is used to learn the structure and parameter of the decision tree.
The Time Series data can be viewed as a p-order Markov chain where p is the number of previous observations taken into consideration. From our previous posts on Markov chain, we know that the current event is independent of the previous observations. However, the dependence of the current event on the preceding regressor variables does not change with time. The models are therefore linear predictors and are simple and windowing based so they are easy to interpret. The structure and parameters of the decision tree is learned using the Bayes rule which places probability distributions on the structure and the parameter and choosing the structure s that has the highest probability given the data d and make predictions based on that structure. The models described in this paper yield accurate forecasts.