Tree Structured GARCH Models

Francesco Audrino and Peter Bühlmann

March 2000

Abstract

We propose a new GARCH model with tree-structured multiple thresholds for volatility estimation 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. Fitting of such trees is constructed within the likelihood framework for non-Gaussian observations: it is very different from the well-known CART procedure for regression based on residual sum of squares. Our strategy includes the classical GARCH model and allows in a systematic and flexible way to increase model-complexity. We conclude with simulations and real data analysis that the new method has better predictive potential compared to other approaches.

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