We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the hidden Markov model (HMM). For these models we outline an EM algorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. As an illustration, we provide an example based on the analysis of stock market data referred to different American countries. © 2010 Blackwell Publishing Ltd.
A note on the mixture transition distribution and hidden Markov models / Francesco, Bartolucci; Farcomeni, Alessio. - In: JOURNAL OF TIME SERIES ANALYSIS. - ISSN 0143-9782. - 31:2(2010), pp. 132-138. [10.1111/j.1467-9892.2009.00650.x]
A note on the mixture transition distribution and hidden Markov models
FARCOMENI, Alessio
2010
Abstract
We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the hidden Markov model (HMM). For these models we outline an EM algorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. As an illustration, we provide an example based on the analysis of stock market data referred to different American countries. © 2010 Blackwell Publishing Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.