Time Series Regression for Zero-Inflated and Overdispersed Count Data: A Functional Response Model Approach

Ghahramani, M.; White, S. S.

doi:10.1007/s42519-020-00094-8

Cited by 4 publications

(8 citation statements)

References 16 publications

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“…Note we chose the linear trend regression to be of the form

x_{t}^{T} = [\begin{matrix} 1 & t false/ 1000 \end{matrix}]

, since this form has been used before in the literature (see Ghahramani & White, 2020; Yang et al, 2013). The EM‐based results for the chosen model are shown in Table 7.…”

Section: Analyzing the Syphilis Datamentioning

confidence: 99%

“…We compared our model's performance with the distribution‐free functional response (FRM) model of Ghahramani and White (2020), a zero‐inflated Poisson (ZIP), and a zero‐inflated NB (ZINB). The comparison is shown in Table 8.…”

Section: Analyzing the Syphilis Datamentioning

confidence: 99%

“…Other than AR models, generalized AR conditional heteroskedastic models suited for zero‐inflated integer‐valued time series have also been used by Zhu (2012) and Xu, Chen, Chen, Lin, et al (2020). Very recently, a distribution‐free approach for estimation of regression parameters was studied by Ghahramani and White (2020). Other techniques, like integer autoregressive (INAR) class of models, for modeling such zero‐inflated count time series data modeled have also been discussed by Zhu (2012), Jazi, Jones, and Lai (2012), and Qi, Li, and Zhu (2019).…”

Section: Introductionmentioning

confidence: 99%

“…A superior predictive performance of our proposed model when compared with various other available techniques for modeling dengue, establishes the need for using a zero‐inflated NB‐ARMA regression model. We also fit our proposed model to the popular syphilis data (see Ghahramani & White, 2020), and compare our model's performance with other methods available in the statistical literature.…”

Section: Introductionmentioning

confidence: 99%

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Autoregressive and moving average models for zero‐inflated count time series

Sathish

Mukhopadhyay

Tiwari

2021

Statistica Neerlandica

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Zero inflation is a common nuisance while monitoring disease progression over time. This article proposes a new observation-driven model for zero-inflated and over-dispersed count time series. The counts given from the past history of the process and available information on covariates are assumed to be distributed as a mixture of a Poisson distribution and a distribution degenerated at zero, with a time-dependent mixing probability, 𝜋 t . Since, count data usually suffers from overdispersion, a Gamma distribution is used to model the excess variation, resulting in a zero-inflated negative binomial regression model with mean parameter 𝜆 t . Linear predictors with autoregressive and moving average (ARMA) type terms, covariates, seasonality and trend are fitted to 𝜆 t and 𝜋 t through canonical link generalized linear models. Estimation is done using maximum likelihood aided by iterative algorithms, such as Newton-Raphson (NR) and Expectation and Maximization. Theoretical results on the consistency and asymptotic normality of the estimators are given. The proposed model is illustrated using in-depth simulation studies and two disease datasets.

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“…Note we chose the linear trend regression to be of the form

x_{t}^{T} = [\begin{matrix} 1 & t false/ 1000 \end{matrix}]

, since this form has been used before in the literature (see Ghahramani & White, 2020; Yang et al, 2013). The EM‐based results for the chosen model are shown in Table 7.…”

Section: Analyzing the Syphilis Datamentioning

confidence: 99%

Section: Analyzing the Syphilis Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Autoregressive and moving average models for zero‐inflated count time series

Sathish

Mukhopadhyay

Tiwari

2021

Statistica Neerlandica

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“…The literature on counting time series considering excess zeros is still sparse (YANG; ZAMBA; CAVA-NAUGH, 2013) but is a topic of recent interest in statistics (ALQAWBA; DIAWARA; CHAGANTY, 2019). Yang, Zamba and Cavanaugh (2013), Alqawba, Diawara and Chaganty (2019), Ghahramani and White (2020), Tawiah, Iddrisu and Asosega (2021) are examples of studies that have modelled count time series with many zeros.…”

Section: Introductionmentioning

confidence: 99%

Count time series with excess zeros: A Bayesian perspective using zero-adjusted distributions

Pala

Carvalho

Sáfadi

2022

Semina: Ciênc. Ex. Tech.

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Models for count data which are temporally correlated have been studied using many conditional distributions, such as the Poisson distribution, and the insertion of different dependence structures. Nonetheless, excess of zeros and over dispersion may be observed during the counting process and need to be considered when modelling and choosing a conditional distribution. In this paper, we propose models for counting time series using zero-adjusted distributions by inserting a dependence structure following the ARMA(p, q) process on a Bayesian framework. We perform a simulation study using the proposed Bayesian analysis and analyse the monthly time series of the number of deaths due to dengue haemorrhagic fever (ICD-A91) in Brazil.

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