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Modeling, simulation and inference for multivariate time series of counts using trawl processes

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  • Veraart, Almut E.D.

Abstract

This article presents a new continuous-time modeling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by Lévy noise, called a trawl process, where the serial correlation and the cross-sectional dependence are modeled independently of each other. Such processes can exhibit short or long memory. We derive a stochastic simulation algorithm and a statistical inference method for such processes. The new methodology is then applied to high frequency financial data, where we investigate the relationship between the number of limit order submissions and deletions in a limit order book.

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  • Veraart, Almut E.D., 2019. "Modeling, simulation and inference for multivariate time series of counts using trawl processes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 110-129.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:110-129
    DOI: 10.1016/j.jmva.2018.08.012
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    1. Leonte, Dan & Veraart, Almut E.D., 2024. "Simulation methods and error analysis for trawl processes and ambit fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 518-542.
    2. Bennedsen, Mikkel & Lunde, Asger & Shephard, Neil & Veraart, Almut E.D., 2023. "Inference and forecasting for continuous-time integer-valued trawl processes," Journal of Econometrics, Elsevier, vol. 236(2).
    3. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Chénangnon Frédéric Tovissodé & Sèwanou Hermann Honfo & Jonas Têlé Doumatè & Romain Glèlè Kakaï, 2021. "On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism," Mathematics, MDPI, vol. 9(5), pages 1-17, March.

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