Combining a regression model with a multivariate Markov chain in a forecasting problem

Leader-follower dynamics in real historical time: a Markovian test of non-linear causality between sail and steam (co-)development

“…Markov chain models are increasingly proficiently and interdisciplinary used. To be specific, in Finance (Siu et al 2005;Fung and Siu 2012), Financial Markets (Maskawa 2003;Nicolau 2014;Nicolau and Riedlinger 2015), Biology (Gottschau 1992;Raftery and Tavaré 1994;Berchtold 2001), Environmental Sciences (Turchin 1986;Sahin and Sen 2001), Linguistics (Markov 1913), Medicine (Li et al 2014), Forecasting (Damásio and Nicolau 2013), Management (Ching, Fung, and Ng 2002;Horvath, Autry, and Wilcox 2005;Zhu and Ching 2010), Macroeconomics (Nicolau 2017;Damásio, Louçã, and Nicolau 2018), Economic History (Damásio and Mendonça 2019), among others; see, e.g. (Ching and Ng 2006;Sericola 2013).…”

“…In fact, modeling probabilities ( 6) is impractical to the extent that there are m s states and therefore the total number of states of the process growth exponentially with s. To address this issue (Raftery 1985) proposed the mixture transition distribution model (MTD) 1 . However, the MTD-Probit model (Nicolau 2014;Damásio and Nicolau 2013) stood out because it has the best properties in terms of efficiency, ease of implementation and robustness of results (it can be proved that the probabilities estimated by this model are closer to the true probabilities than the MTD).…”

The changing economic regimes and expected time to recover of the peripheral countries under the euro: A nonparametric approach

“…Therefore k should be no higher than 4 or 5 (say), depending on the sample size, the level of persistence of y and the thresholds x 0 and x 1 . Nevertheless, the literature provides methods to deal with higher k, for example by using the Mixture Transition Distribution [4] or the probit-Mixture Transition Distribution [1,5].…”

GenMarkov: Modeling Generalized Multivariate Markov Chains in R

“…In Damásio (2013); Damásio, Nicolau (2014), a different and innovative concept was proposed: the usage of MMC as regressors in a certain model. Hence, given that the MMC Granger causes a specific dependent variable, and taking advantage of the information about the past state interactions between the MMC categories, it was possible to forecast the current dependent variable more accurately.…”

“…Overall, the published work on MMC models was mostly based on improving the estimation methods and/or making the model more parsimonious. In Damásio (2013); Damásio, Nicolau (2014), a different approach was used, and the work developed focused on the usage of MMC as regressors in a certain model. Notably, it showed that an MMC can improve the forecast of a dependent variable.…”