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Tree‐structured generalized autoregressive conditional heteroscedastic models

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  • Francesco Audrino
  • Peter Bühlmann

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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  • Francesco Audrino & Peter Bühlmann, 2001. "Tree‐structured generalized autoregressive conditional heteroscedastic models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 727-744.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:727-744
    DOI: 10.1111/1467-9868.00309
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    Cited by:

    1. Amaya, Johanna & Arellana, Julian & Delgado-Lindeman, Maira, 2020. "Stakeholders perceptions to sustainable urban freight policies in emerging markets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 329-348.
    2. Meister, Alexander & Kreiß, Jens-Peter, 2016. "Statistical inference for nonparametric GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3009-3040.
    3. Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670, June.
    4. Liu, Wei & Garrett, Ian, 2023. "Regime-dependent effects of macroeconomic uncertainty on realized volatility in the U.S. stock market," Economic Modelling, Elsevier, vol. 128(C).
    5. Lee, Paul H. & Yu, Philip L.H., 2010. "Distance-based tree models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1672-1682, June.
    6. Ioannis Papageorgiou & Ioannis Kontoyiannis, 2023. "The Bayesian Context Trees State Space Model for time series modelling and forecasting," Papers 2308.00913, arXiv.org, revised Oct 2023.
    7. Andrew J. Patton & Yasin Simsek, 2023. "Generalized Autoregressive Score Trees and Forests," Papers 2305.18991, arXiv.org.

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