Tree-structured generalized autoregressive conditional heteroscedastic models |
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Authors: | Francesco Audrino & Peter Bühlmann |
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Institution: | Eidgenössiche Technische Hochschule Zürich, Switzerland |
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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. |
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Keywords: | Conditional variance Financial time series Generalized autoregressive conditional heteroscedastic model Maximum likelihood Threshold model Tree model Volatility |
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