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Submitted on 13 Jul 2012
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DiscreteTS : two hidden-Markov models for time series
of count data
Julien Alerini, Madalina Olteanu, James Ridgway
To cite this version:
Julien Alerini, Madalina Olteanu, James Ridgway. DiscreteTS : two hidden-Markov models for time
series of count data. 1ères Rencontres R, Jul 2012, Bordeaux, France. �hal-00717493�
J. Alerini
a
,M. Olteanub
and J. Ridgwayb
a
PIREH (Ple Informatiquede Re her he etd'Enseignement en Histoire)
Université Paris1
1 Rue Vi tor Cousin, 75005Paris, Fran e
julien.aleriniuniv-paris1.fr
b
SAMM (Statistique, Analyse etModélisationMultidis iplinaire),EA 4543
Université Paris1
90 Rue de Tolbia ,75013 Paris, Fran e
madalina.olteanuuniv-paris1.fr,James.Ridgwayensae-pariste h.fr
Mots lefs: Integer-valuedtimeseries,hiddenMarkovmodels,autoregressiveregime-swit hing
models.
Time series of ount data are en ountered oftenin Humanities and So ial S ien es. Modeling
this kind of data is a hallenging topi for the statisti ian : autoregressive stru ture,
over-dispersion inzero, existen e of several unobserved regimes ontrolling the pro ess.
One ommon approa h used for modeling integer-valued time series are the hidden Markov
models. However, the available R pa kages su h as HiddenMarkov [1℄or HMM [2℄ are
imple-mented for usual distributions only. Moreover, none of this pa kages performs estimation for
autoregressiveMarkov-swit hing models.
Two new models were re ently introdu ed in[3℄ and [4℄:
1. ZIP-HMM (Hidden Markov models with zero-inated Poisson distributions) were
pro-posed in order to take into a ount the over-dispersion in zero. This model is a usual
hidden Markov model, ex ept that the Poisson distributionof the observed pro ess
on-ditionally tothe hidden state wasrepla ed by a mixture of aPoisson and aDira
distri-bution.
2. INAR(
p
)-HMM (Integer-valued autoregressive models with Markov-swit hing regimes) wereintrodu edasaparalleltotheautoregressivehidden-Markovmodelsexistingalreadyin the ontinuous ase [5℄. The observed pro ess is supposed to behave as an
integer-valued autoregressive INAR(
p
) [6℄, whose parameters are ontrolled by the states of a hiddenMarkov hain.Forbothmodels,theestimationpro edureisa hievedthroughtheEMalgorithm. Thesemodels
were implemented in a R-pa kage alled Dis reteTS. The pa kage provides the possibility of
either simulatingthese models, orof estimating them starting froma given time-series. A toy
example onmedieval histori aldata is alsoprovided.
Referen es
zeros. Pro eedingsof ESANN 2012, 133-138
[4℄Ridgway J. (2011). HiddenMarkov models for time series of ount data. Rapport de stage
[5℄HamiltonJ.D.(1989). Anewapproa htothee onomi analysisofnonstationarytimeseries
and the business y le. E onometri a, 57, 357-384.
[6℄Al-Osh M.A. and Alzaid A.A. (1990). An integer-valued