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A New Model for Multivariate Markov Chains

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  • João Nicolau

Abstract

type="main" xml:id="sjos12087-abs-0001"> We propose a new model for multivariate Markov chains of order one or higher on the basis of the mixture transition distribution (MTD) model. We call it the MTD-Probit. The proposed model presents two attractive features: it is completely free of constraints, thereby facilitating the estimation procedure, and it is more precise at estimating the transition probabilities of a multivariate or higher-order Markov chain than the standard MTD model.

Suggested Citation

  • João Nicolau, 2014. "A New Model for Multivariate Markov Chains," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1124-1135, December.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:1124-1135
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    References listed on IDEAS

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    1. McQueen, Grant & Thorley, Steven, 1991. "Are Stock Returns Predictable? A Test Using Markov Chains," Journal of Finance, American Finance Association, vol. 46(1), pages 239-263, March.
    2. Andre Berchtold, 2001. "Estimation in the Mixture Transition Distribution Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 379-397, July.
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    1. Flavio Ivo Riedlinger & João Nicolau, 2020. "The Profitability in the FTSE 100 Index: A New Markov Chain Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(1), pages 61-81, March.
    2. Euán, Carolina & Sun, Ying, 2020. "Bernoulli vector autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    3. Damásio, Bruno & Nicolau, João, 2024. "Time inhomogeneous multivariate Markov chains: Detecting and testing multiple structural breaks occurring at unknown dates," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Riccardo De Blasis, 2020. "The price leadership share: a new measure of price discovery in financial markets," Annals of Finance, Springer, vol. 16(3), pages 381-405, September.
    5. Nicolau, João, 2017. "A simple nonparametric method to estimate the expected time to cross a threshold," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 146-152.
    6. 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).
    7. Bruno Damásio & João Nicolau, 2020. "Time Inhomogeneous Multivariate Markov Chains: Detecting and Testing Multiple Structural Breaks Occurring at Unknown," Working Papers REM 2020/0136, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    8. Bruno Damásio & Sandro Mendonça, 2018. "Modeling insurgent-incumbent dynamics: Vector autoregressions,multivariate Markov chains, and the nature of technological competition," Working Papers REM 2018/44, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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