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Structural learning with time‐varying components: tracking the cross‐section of financial time series

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  • Makram Talih
  • Nicolas Hengartner

Abstract

Summary. When modelling multivariate financial data, the problem of structural learning is compounded by the fact that the covariance structure changes with time. Previous work has focused on modelling those changes by using multivariate stochastic volatility models. We present an alternative to these models that focuses instead on the latent graphical structure that is related to the precision matrix. We develop a graphical model for sequences of Gaussian random vectors when changes in the underlying graph occur at random times, and a new block of data is created with the addition or deletion of an edge. We show how a Bayesian hierarchical model incorporates both the uncertainty about that graph and the time variation thereof.

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  • Makram Talih & Nicolas Hengartner, 2005. "Structural learning with time‐varying components: tracking the cross‐section of financial time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 321-341, June.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:3:p:321-341
    DOI: 10.1111/j.1467-9868.2005.00504.x
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    Cited by:

    1. DAVID E. ALLEN & MICHAEL McALEER & ROBERT J. POWELL & ABHAY K. SINGH, 2018. "Non-Parametric Multiple Change Point Analysis Of The Global Financial Crisis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 1-23, June.
    2. Baştürk, N. & Borowska, A. & Grassi, S. & Hoogerheide, L. & van Dijk, H.K., 2019. "Forecast density combinations of dynamic models and data driven portfolio strategies," Journal of Econometrics, Elsevier, vol. 210(1), pages 170-186.
    3. Abdelwahab Allali & Amor Oueslati & Abdelwahed Trabelsi, 2011. "Detection of Information Flow in Major International Financial Markets by Interactivity Network Analysis," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(3), pages 319-344, September.
    4. Ariyarathne, Sakitha & Gangammanavar, Harsha & Sundararajan, Raanju R., 2022. "Change point detection-based simulation of nonstationary sub-hourly wind time series," Applied Energy, Elsevier, vol. 310(C).
    5. Ni Zhan & Yijia Sun & Aman Jakhar & He Liu, 2021. "Graphical Models for Financial Time Series and Portfolio Selection," Papers 2101.09214, arXiv.org.
    6. Grzegorczyk Marco & Husmeier Dirk, 2012. "A Non-Homogeneous Dynamic Bayesian Network with Sequentially Coupled Interaction Parameters for Applications in Systems and Synthetic Biology," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-62, July.
    7. James, Nicholas A. & Matteson, David S., 2015. "ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 62(i07).
    8. Gao, Wei & Zhao, Hongxia, 2013. "Conditional independence graph for nonlinear time series and its application to international financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2460-2469.

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