A Novel Estimation Approach for Mixture Transition Distribution Model in High-Order Markov Chains

Chen, Ding‐Geng; Lio, Yuhlong

doi:10.1080/03610910802715009

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…Other relevant contributions are related to the optimization algorithm, as in Lèbre, Bourguignon (2008) and Chen, Lio (2009), and to empirical applications (Ching et al, 2003;Ching, Ng, 2006;Damásio et al, 2018;Damásio, Mendonça, 2019;Damásio, Mendonça, 2020). Also, Damásio, Nicolau (2020) proposed a new methodology for detecting and testing the presence multiple structural breaks in a Markov chain occurring at unknown dates.…”

Section: Multivariate Markov Chainsmentioning

confidence: 99%

GenMarkov: Modeling Generalized Multivariate Markov Chains in R

Vasconcelos¹,

Damásio²

2022

Preprint

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This article proposes a new generalization of the Multivariate Markov Chains (MMC) model. The future values of a Markov chain commonly depend on only the past values of the chain in an autoregressive fashion. The generalization proposed in this work also considers exogenous variables that can be deterministic or stochastic. Furthermore, the effects of the MMC's past values and the effects of pre-determined or exogenous covariates are considered in our model by considering a non-homogeneous Markov chain. The Monte Carlo simulation study findings showed that our model consistently detected a non-homogeneous Markov chain. Besides, an empirical illustration demonstrated the relevance of this new model by estimating probability transition matrices over the space state of the exogenous variable. An additional and practical contribution of this work is the development of a novel R package with this generalization. Keywords Multivariate Markov chains and Mixture transition distribution Model and High order Markov chains and Multivariate Markov chains with exogenous variables and R

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Section: Multivariate Markov Chainsmentioning

confidence: 99%

GenMarkov: Modeling Generalized Multivariate Markov Chains in R

Vasconcelos¹,

Damásio²

2022

Preprint

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“…2 and 3, Lèbre and Bourguignon in [25] introduce a hidden process for the coefficients of the MTDg and propose an Expectation-Maximization approach for the parameters estimation. Chen et al in [26] note that all the previous constraints can be rewritten in a boxconstrained form, which is easier to handle.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Linear Models for the Impact of Order Flow on Prices II. The Mixture Transition Distribution Model

et al. 2016

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Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be obtained when one incorporates the impact of past returns on the future order flow. However, impact models presented in Part I consider the order flow as an exogenous process, only characterized by its two-point correlations. This assumption seriously limits the forecasting ability of the model. Here we attempt to model directly the stream of discrete events with a so-called Mixture Transition Distribution (MTD) framework, introduced originally by Raftery (1985). We distinguish between price-changing and non price-changing events and combine them with the order sign in order to reduce the order flow dynamics to the dynamics of a four-state discrete random variable. The MTD represents a parsimonious approximation of a full high-order Markov chain. The new approach captures with adequate realism the conditional correlation functions between signed events for both small and large tick stocks and signature plots. From a methodological viewpoint, we discuss a novel and flexible way to calibrate a large class of MTD models with a very large number of parameters. In spite of this large number of parameters, an out-of-sample analysis confirms that the model does not overfit the data.

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“…They used the expectation–maximization algorithm to estimate the parameters of the MTD model, with good results, although Chen and Lio mentioned that the complexity from the counts of the pattern of sequences is still unsolved in the search for a global maximizer. Chen & Lio () proposed transforming the non‐linear constraints of the parameters in the MTD into box‐constraints in that each parameter is given a lower and/or upper bound. This technique allows the MLE to be obtained via a hybrid algorithm from the evolutionary algorithms and/or quasi‐Newton algorithms and has the advantage of focusing on a search for a global maximizer.…”

Section: A Brief Literature Reviewmentioning

confidence: 99%

“…One of the main challenges in applying the MTD model is linked to the estimation and the way the non‐linear constraints are dealt with in the numerical optimization, although some progress has been made as we described in the previous section (e.g. Berchtold, , Lèbre and Bourguignon, and Chen and Lio, ). However, the constraints associated with the MTD model still pose difficulties.…”

Section: The Mixture Transition Distribution‐probit Modelmentioning

confidence: 99%

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A New Model for Multivariate Markov Chains

Nicolau

2014

Scandinavian J Statistics

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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.

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A Novel Estimation Approach for Mixture Transition Distribution Model in High-Order Markov Chains

Cited by 7 publications

References 13 publications

GenMarkov: Modeling Generalized Multivariate Markov Chains in R

GenMarkov: Modeling Generalized Multivariate Markov Chains in R

Linear Models for the Impact of Order Flow on Prices II. The Mixture Transition Distribution Model

A New Model for Multivariate Markov Chains

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