Tree-structured generalized autoregressive conditional heteroscedastic models

We propose a new generalized autoregressive conditional heteroscedastic (GA RCH) model with tree-structured multiple thresholds for the estimation of v olatility in financial time series. The approach relies on the idea of a bi nary tree where every terminal node parameterizes a (local) GARCH model for a partition cell of the predictor space. The fitting of such trees is cons tructed within the likelihood framework for non-Gaussian observations: it i s very different from the well-known regression tree procedure which is bas ed on residual sums of squares. Our strategy includes the classical GARCH m odel as a special case and allows us to increase model complexity in a syst ematic and flexible way. We derive a consistency result and conclude from s imulation and real data analysis that the new method has better predictive potential than other approaches.