Tree structured GARCH models

Francesco Audrino · Peter Bühlmann

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Stock Market Forecasting Methods

Abstract

We propose a new GARCH model with tree-structured multiple thresholds for volatility estimation in nancial 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 dierent 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 exible 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. Keywords: Conditional variance; Financial time series; GARCH model; Maximum likelihood; Threshold model; Tree model. 1 Introduction We propose a new method for estimating volatility in stationary nancial time series; our real data examples are daily log-returns...

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References

1986Generalized autoregressive conditional heteroskedasticity 1990Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized Arch Model 2000Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach 1993Threshold arch models and asymmetries in volatility 1999Nonparametric Autoregression with Multiplicative Volatility and Additive mean 1998Estimating high-frequency foreign exchange rate volatility with nonparametric ARCH models

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2009Splines for Financial Volatility 2008A Bayesian Approach to Detecting Nonlinear Risk Exposures in Hedge Fund Strategies 2010A General Multivariate Threshold GARCH Model With Dynamic Conditional Correlations 2009Semiparametric and Nonparametric ARCH Modeling

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