Integer-valued autoregressive processes with periodic structure

Monteiro, Magda; Scotto, Manuel G.; Pereira, Isabel

doi:10.1016/j.jspi.2009.12.015

Cited by 45 publications

(27 citation statements)

References 32 publications

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“…Still, X t 1 and W t , and X t 2 and W t are assumed to be independent. This INAR(1) model is a particular case of the model reported in [6]. As far as we know, the INAR(2) model introduced here is new.…”

Section: Model Definitionmentioning

confidence: 99%

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A statistical model for hospital admissions caused by seasonal diseases

Moriña

Puig

Ríos

et al. 2011

Statistics in Medicine

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We present a model based on two-order integer-valued autoregressive time series to analyze the number of hospital emergency service arrivals caused by diseases that present seasonal behavior. We also introduce a method to describe this seasonality, on the basis of Poisson innovations with monthly means. We show parameter estimation by maximum likelihood and model validation and show several methods for forecasting, on the basis of long-time means and short-time and long-time prediction regions. We analyze an application to model the number of hospital admissions per week caused by influenza.

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Section: Model Definitionmentioning

confidence: 99%

“…Expression (7) is generalized to higher-order models in the same paper [9]. The maximization of the likelihood function (6) has been carried out with a program developed in R that is available from the authors upon request. This program uses the nonlinear minimization procedure called nlm.…”

Section: Parameter Estimation and Model Validationmentioning

confidence: 99%

A statistical model for hospital admissions caused by seasonal diseases

Moriña

Puig

Ríos

et al. 2011

Statistics in Medicine

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“…The PAR(1) process, { X s , n }, which represents the periodic stochastic slopes, is cyclostationary when

false| \prod_{k = 1}^{S} ϕ_{k} false| < 1

, (Gardner, Napolitano, & Paura, ; Monteiro, Pereira, & Scotto, ; Obeysekera & Salas, ) In this case, E( X s , n ) = μ s and

Var false(X_{s, n} false) = σ_{s}^{2} = ({}, σ_{ε, s}^{2} + true \sum_{i = 1}^{S - 1} ((), true \prod_{j = 1}^{i} ϕ_{s - j}^{2} σ_{ε, s - i}^{2})) {((), 1 - true \prod_{k = 1}^{S} ϕ_{k}^{2})}^{- 1},

with the convention ϕ − i = ϕ S − i and

σ_{ε, - i}^{2} = σ_{ε, S - i}^{2}

, for i = 0,1,…, S − 1.…”

Section: The Periodic Mixed Linear State‐space Modelmentioning

confidence: 99%

A periodic mixed linear state‐space model to monthly long‐term temperature data

Costa

Monteiro

2018

Environmetrics

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In recent decades, the world has been confronted with the consequences of global warming; however, this phenomenon is not reflected equally in every part of the globe. Thus, the warming phenomenon must be monitored in a more regional or local scale. This paper analyzes monthly long‐term time series of air temperatures in three Portuguese cities: Lisbon, Oporto, and Coimbra. We propose a periodic state‐space framework, associated with a suitable version of the Kalman filter; which allows for the estimation of monthly warming rates taking into account the seasonal behavior and serial correlation. Results about the monthly mean of the daily midrange temperature time series show that there are different monthly warming rates. The greatest annual mean rise was found in Oporto with 2.17°C, whereas in Lisbon and Coimbra, it was respectively 0.62°C and 0.55°C per century.

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“…Monteiro et al (2010) considered an INAR(1) model based on the binomial thinning operator with periodically varying parameter of the form X t = a t • X t−1 + Z t , with a t =˛( j) 1 ∈ [0; 1) for t = j + kT, (j = 1, . .…”

Section: Statistical Modelling Xxxx; Xx(x): 1-29mentioning

confidence: 99%

Thinning-based models in the analysis of integer-valued time series: a review

Scotto

Weiß

Gouveia

2015

Statistical Modelling

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123

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This article aims at providing a comprehensive survey of recent developments in the field of integer-valued time series modelling, paying particular attention to models obtained as discrete counterparts of conventional autoregressive moving average and bilinear models, and based on the concept of thinning. Such models have proven to be useful in the analysis of many real-world applications ranging from economy and finance to medicine. We review the literature of the most relevant thinning operators proposed in the analysis of univariate and multivariate integer-valued time series with either finite or infinite support. Finally, we also outline and discuss possible directions of future research.

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Integer-valued autoregressive processes with periodic structure

Cited by 45 publications

References 32 publications

A statistical model for hospital admissions caused by seasonal diseases

A statistical model for hospital admissions caused by seasonal diseases

A periodic mixed linear state‐space model to monthly long‐term temperature data

Thinning-based models in the analysis of integer-valued time series: a review

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