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Remarks Concerning Graphical Models for Time Series and Point Processes

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  • Brillinger, David R.

Abstract

A statistical network is a collection of nodes representing random variables and a set of edges that connect the nodes. A probabilistic model for such is called a graphical modeL These models, graphs and networks are particularly useful for examining statistical dependencies based on conditioning as often occurs in economics and statistics. In this paper the nodal random variables will be time series or point processes. The cases of undirected and directed graphs are focussed on.

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  • Brillinger, David R., 1996. "Remarks Concerning Graphical Models for Time Series and Point Processes," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 16(1), November.
    • Handle: RePEc:sbe:breart:v:16:y:1996:i:1:a:2878
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    1. HENDRY, David F. & RICHARD, Jean-François, 1983. "The econometric analysis of economic time series," LIDAM Reprints CORE 531, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Robinson, P. M., 1986. "On the errors-in-variables problem for time series," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 240-250, August.
    3. Brillinger, David R & Hatanaka, Michio, 1969. "An Harmonic Analysis of Nonstationary Multivariate Economic Processes," Econometrica, Econometric Society, vol. 37(1), pages 131-141, January.
    4. Geweke, John, 1984. "Inference and causality in economic time series models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 19, pages 1101-1144, Elsevier.
    5. D. A. Freedman, 1987. "As Others See Us: A Case Study in Path Analysis," Journal of Educational and Behavioral Statistics, , vol. 12(2), pages 101-128, June.
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    1. Xu, Huyang & Fard, Nasser & Fang, Yuanchen, 2020. "Time series chain graph for modeling reliability covariates in degradation process," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. 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.
    3. Gorban, Alexander N. & Smirnova, Elena V. & Tyukina, Tatiana A., 2010. "Correlations, risk and crisis: From physiology to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3193-3217.
    4. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Sparse Graphical Vector Autoregression: A Bayesian Approach," Annals of Economics and Statistics, GENES, issue 123-124, pages 333-361.
    5. Fried, Roland & Didelez, Vanessa, 2005. "Latent variable analysis and partial correlation graphs for multivariate time series," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 287-296, July.
    6. Ralf Brüggemann & Christian Kascha, 2017. "Directed Graphs and Variable Selection in Large Vector Autoregressive Models," Working Paper Series of the Department of Economics, University of Konstanz 2017-06, Department of Economics, University of Konstanz.
    7. Marianna Bolla & Dongze Ye & Haoyu Wang & Renyuan Ma & Valentin Frappier & William Thompson & Catherine Donner & Máté Baranyi & Fatma Abdelkhalek, 2023. "Causal Vector Autoregression Enhanced with Covariance and Order Selection," Econometrics, MDPI, vol. 11(1), pages 1-30, February.
    8. Dominik Bertsche & Ralf Brüggemann & Christian Kascha, 2023. "Directed graphs and variable selection in large vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 223-246, March.
    9. Dallakyan, Aramayis & Kim, Rakheon & Pourahmadi, Mohsen, 2022. "Time series graphical lasso and sparse VAR estimation," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    10. Daniel Cederberg, 2025. "First-Order Methods for Nonnegative Trigonometric Matrix Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 204(2), pages 1-28, February.
    11. Eckardt, Matthias & González, Jonatan A. & Mateu, Jorge, 2021. "Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    12. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Bayesian Graphical Models for STructural Vector Autoregressive Processes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 357-386, March.
    13. Yuen, T.P. & Wong, H. & Yiu, K.F.C., 2018. "On constrained estimation of graphical time series models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 27-52.
    14. 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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