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Estimation in the Mixture Transition Distribution Model

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  • Andre Berchtold

Abstract

This paper introduces a new iterative algorithm for the estimation of the mixture transition distribution (MTD) model, which does not require the use of any specific external optimization procedure and can therefore be programmed in any computing language. Comparisons with previously published results show that this new algorithm performs at least as well as or better than other methods. The choice of initial values is also discussed. The MTD model was designed for the modeling of high‐order Markov chains and has already proved to be a useful tool for the analysis of different types of time series such as wind speeds and social relationships. In this paper, we also propose to use it for the modeling of one‐dimensional spatial data. An application using a DNA sequence shows that this approach can lead to better results than the classical Potts model.

Suggested Citation

  • Andre Berchtold, 2001. "Estimation in the Mixture Transition Distribution Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 379-397, July.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:4:p:379-397
    DOI: 10.1111/1467-9892.00231
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. A. Prinzie & D. Van Den Poel, 2003. "Investigating Purchasing Patterns for Financial Services using Markov, MTD and MTDg Models," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 03/213, Ghent University, Faculty of Economics and Business Administration.
    4. 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).
    5. Ioannis Kontoyiannis & Lambros Mertzanis & Athina Panotopoulou & Ioannis Papageorgiou & Maria Skoularidou, 2022. "Bayesian context trees: Modelling and exact inference for discrete time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1287-1323, September.
    6. Prinzie, Anita & Van den Poel, Dirk, 2006. "Investigating purchasing-sequence patterns for financial services using Markov, MTD and MTDg models," European Journal of Operational Research, Elsevier, vol. 170(3), pages 710-734, May.
    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. Berchtold, Andre, 2003. "Mixture transition distribution (MTD) modeling of heteroscedastic time series," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 399-411, January.
    9. J. Burez & D. Van Den Poel, 2005. "CRM at a Pay-TV Company: Using Analytical Models to Reduce Customer Attrition by Targeted Marketing for Subscription Services," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 05/348, Ghent University, Faculty of Economics and Business Administration.
    10. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model," Papers 1604.07556, arXiv.org.

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