Tree‐structured generalized autoregressive conditional heteroscedastic models

Francesco Audrino and Peter Bühlmann

Journal of the Royal Statistical Society Series B, 2001, vol. 63, issue 4, 727-744

Abstract: We propose a new generalized autoregressive conditional heteroscedastic (GARCH) model with tree‐structured multiple thresholds for the estimation of volatility in financial time series. The approach relies on the idea of a binary tree where every terminal node parameterizes a (local) GARCH model for a partition cell of the predictor space. The fitting of such trees is constructed within the likelihood framework for non‐Gaussian observations: it is very different from the well‐known regression tree procedure which is based on residual sums of squares. Our strategy includes the classical GARCH model as a special case and allows us to increase model complexity in a systematic and flexible way. We derive a consistency result and conclude from simulation and real data analysis that the new method has better predictive potential than other approaches.

Date: 2001
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