• Aucun résultat trouvé

DiscreteTS : two hidden-Markov models for time series of count data

N/A
N/A
Protected

Academic year: 2021

Partager "DiscreteTS : two hidden-Markov models for time series of count data"

Copied!
3
0
0

Texte intégral

(1)

HAL Id: hal-00717493

https://hal.archives-ouvertes.fr/hal-00717493

Submitted on 13 Jul 2012

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

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�

(2)

J. Alerini

a

,M. Olteanu

b

and J. Ridgway

b

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-Markovmodelsexistingalready

in 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

(3)

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

p

th-order autoregressive stru ture (INAR(

p

)) pro ess. Journal of Applied Probability, vol.27(2), 314-324

Références

Documents relatifs

Each subject i is described by three random variables: one unobserved categorical variable z i (defining the membership of the class of homogeneous physical activity behaviors

In a greater detail, the siRNA molecule is constrained to assume a curved and wrapped arrangement around DM, being anchored by morpholinium oxygens (Figure 4, and

Markov chain but non-homogeneous AR models can reproduce the characteristics of these variations. For example, Figure 6 shows that the fitted model can reproduce both the

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

We have proposed to use hidden Markov models to clas- sify images modeled by strings of interest points ordered with respect to saliency.. Experimental results have shown that

1) Closed Formulas for Renyi Entropies of HMMs: To avoid random matrix products or recurrences with no explicit solution, we change the approach and observe that, in case of integer

trying to problem in very well defined.. CHAPTER II: REPLICATION PAGE 21 logic; when the ill-defined nature of city design problems was added to the apparently

Applied to RNA-Seq data from 524 kidney tumor samples, PLASMA achieves a greater power at 50 samples than conventional QTL-based fine-mapping at 500 samples: with over 17% of