Generalized autoregressive and moving average models: multicollinearity, interpretation and a new modified model

Albarracin, Orlando Yesid Esparza; Alencar, Airlane Pereira; Ho, Linda Lee

doi:10.1080/00949655.2019.1599892

Cited by 9 publications

(8 citation statements)

References 9 publications

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“…The numerical evidence showed that the CMLE are unbiased and consistent. As in Albarracin et al (2019), the GARMA model presented an overestimated moving average parameter while the autoregressive parameter was underestimated, indicating that there is multicollinearity between AR and MA terms. It is thus recommended the inclusion of only AR or MA terms to fit the initial model.…”

Section: Discussionmentioning

confidence: 73%

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

Melo

Alencar

2020

Journal Time Series Analysis

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In this work, we propose a dynamic regression model based on the Conway-Maxwell-Poisson (CMP) distribution with time-varying conditional mean depending on covariates and lagged observations. This new class of Conway-Maxwell-Poisson autoregressive moving average (CMP-ARMA) models is suitable for the analysis of time series of counts. The CMP distribution is a two-parameter generalization of the Poisson distribution that allows the modeling of underdispersed, equidispersed, and overdispersed data. Our main contribution is to combine this dispersion flexibility with the inclusion of lagged terms to model the conditional mean response, inducing an autocorrelation structure, usually relevant in time series. We present the conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis, and forecasting along with their asymptotic properties. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. We conduct a Monte Carlo experiment to evaluate the performance of the estimators in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications.

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Section: Discussionmentioning

confidence: 73%

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

Melo

Alencar

2020

Journal Time Series Analysis

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“…As suggestions for future study, the following is important: (i) to investigate the performance of the method proposed to monitor new observations of the process, compared with the usual 3 rd quartile method, considering a gold standard (known status) for outbreaks and epidemics in the Amazon region; (ii) to carry out numerical simulations using a calibration/tuning process, to improve the performance of the method proposed, investigating the effects associated with estimating the model parameters on the constructed control chart performance in greater detail (JENSEN et al, 2006); (iii) to consider other models for counting processes, such as the state-space models (DURBIN and KOOPMAN, 1997;SHEPHARD and PITT, 1997) and the GARMA model extensions/modifications (CORDEIRO and ANDRADE, 2009;ALBARRACIN et al, 2019); (iv) to evaluate the existence of spatial dependence in the states in the region, and consider this in the modeling process, which is an area that has been underdeveloped in the study of diseases (LYRIO, 2019);and (v)…”

Section: Discussionmentioning

confidence: 99%

O Controle Estatístico de Processos como Ferramenta para Controle e Prevenção de Epidemias de Malária na Região da Amazônia Legal

2022

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A malária ainda é uma doença fatal em muitos países ao redor do mundo. Estabelecer medidas de controle e prevenção dessa doença é uma preocupação mundial desde 1950, quando a Organização Mundial da Saúde lançou um Plano de Erradicação da Malária. No Brasil, a malária foi eliminada em grande parte do território, porém resistindo em uma área conhecida como Amazônia Legal. Posto isto, o escopo principal deste trabalho consiste em desenvolver gráficos de controle estatístico que considerem a estrutura de dependência temporal existente nos dados e sejam adequados para o monitoramento atual e futuro dos casos de malária, com o intuito de detectar possíveis surtos ou epidemias em estados da região da Amazônia Legal. As ferramentas aqui apresentadas poderiam, ainda, colaborar no direcionamento das ações de controle e no combate à propagação da doença. Em particular, pretende-se: (i) construir um modelo estatístico para previsão de ocorrências de casos da doença, o qual considere a existência de uma possível estrutura de dependência temporal entre os dados coletados; (ii) utilizar as técnicas de Controle Estatístico de Processos (CEP), notadamente os gráficos de controle, para monitorar (separadamente para cada forma da doença) os casos de malária dos tipos Plasmodium Vivax, Plasmodium Falciparum e Plasmodium Mista na região amazônica; (iii) estabelecer limiares epidêmicos com base nos gráficos de controle obtidos. Considerando dados de 2013 a 2017, o presente estudo revelou, dentre outros, que os modelos generalizados autorregressivos e de médias móveis com distribuição Binomial Negativa (modelos GARMA Binomial Negativo) se mostraram mais eficientes, ajustando-se melhor, comparativamente aos modelos GARMA Poisson, devido à superdispersão existente nos dados analisados.

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“…In addition, in line with this work, the methodology to model a time series, such as the generalized autoregressive and moving average (GARMA) model can be explored and its effects over CE. Theoretically, GARMA has been discussed by relevant studies ( Albarracin et al, 2019 , Gomes et al, 2018 ), however little effort has been made to apply this model to the real world practice, in particular in the area of inventory management. Furthermore, multivariate time series may be also considered.…”

Section: Discussionmentioning

confidence: 99%

Inventory pooling decisions under demand scenarios in times of COVID-19

Rojas

Bravo

Tan

2021

Computers & Industrial Engineering

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Governments have been challenged to provide timely medical care to face the COVID-19 pandemic. The aim of this research is to propose a novel inventory pooling model to help determine order sizes and safety inventories in local hospital warehouses. The current study attempts to portray the availability of pharmaceutical items in public hospitals facing COVID-19 challenges. Different from previous studies, this research builds upon the consecrated theory of inventory pooling, extending it to pandemic circumstances where the intractability of kurtosis and skewness in inventory models are critical issues for making sure that medicines have high availability at a low cost. These effects on the total cost of inventory are explored and compared to a supply system with no consolidation. A continuous-review model is assumed with allocation rules for centralization and regular transshipment given different skewness and kurtosis structures for the demand, describing them by the copula method. This method models a multivariate demand considering that the marginal distributions of the demand can be specified by the Generalized Additive Model for Location, Scale and Shape, which offers advantages to model demands considering virtually any marginal statistical distribution. Numerical simulations and an illustrative example show that distributions of demands with more negative skewness and high kurtosis favor to a greater extent obtaining lower total costs with regular supply transshipment systems. Our study points out important considerations for supply chain decision makers when having demands with skewness and kurtosis patterns.

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Generalized autoregressive and moving average models: multicollinearity, interpretation and a new modified model

Cited by 9 publications

References 9 publications

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed, Underdispersed, and Overdispersed Count Data

O Controle Estatístico de Processos como Ferramenta para Controle e Prevenção de Epidemias de Malária na Região da Amazônia Legal

Inventory pooling decisions under demand scenarios in times of COVID-19

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