Count Time Series: A Methodological Review

Davis, Richard A.; Fokianos, Konstantinos; Holan, Scott H.; Joe, Harry; Livsey, James; Lund, Robert; Pipiras, Vladas; Равишанкер, Налини

doi:10.1080/01621459.2021.1904957

Cited by 80 publications

(59 citation statements)

References 112 publications

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“…The incidence prediction for day t and region s is produced by considering all s and all days up to day t − 1 and the model is far more complicated than a simple Autoregressive (AR) model of order p. For instance, an AR(1) would consider the prediction using only counts observed at day t − 1. The recent review on models for count series in [6] locates this model among the multivariate observation-driven models (formula (23) in [6]) but with a random effect later specified in Equations ( 3)- (6). As pointed in [6], the proposed model does not imply that the marginal distribution of Y ts is Poisson as it can be far from Poisson.…”

Section: Modelmentioning

confidence: 99%

“…The recent review on models for count series in [6] locates this model among the multivariate observation-driven models (formula (23) in [6]) but with a random effect later specified in Equations ( 3)- (6). As pointed in [6], the proposed model does not imply that the marginal distribution of Y ts is Poisson as it can be far from Poisson. However, the Poisson conditional assumption allows easy derivation of a conditional likelihood (3).…”

Section: Modelmentioning

confidence: 99%

“…Unfortunately, this paper needs some translation to a statistical audience. Still, basically, an RNN acts similarly to a Hidden Markov Model (HMM) [6] or more specifically to a Dynamic Linear Model (DLM) [13] for observed sequences Y 1 , . .…”

Section: Long Short Term Memory (Lstm)mentioning

confidence: 99%

“…Looking at COVID-19 in this way is what we try to do in reading a text: a new word sometimes can be understood reading forward rather than just looking backwards. This way of modelling the counts recalls that of an ARMA process [6] where the AR part and the Moving Average (MA) mimic the bidirectional network Auto Correlation Function (ACF). However, it is worth noting that the proposed model differs from the ARMA as it may account for the non-monotone behaviour of the ACF.…”

Section: Introductionmentioning

confidence: 99%

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A Bayesian-Deep Learning Model for Estimating COVID-19 Evolution in Spain

Cabras

2021

Mathematics

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This work proposes a semi-parametric approach to estimate the evolution of COVID-19 (SARS-CoV-2) in Spain. Considering the sequences of 14-day cumulative incidence of all Spanish regions, it combines modern Deep Learning (DL) techniques for analyzing sequences with the usual Bayesian Poisson-Gamma model for counts. The DL model provides a suitable description of the observed time series of counts, but it cannot give a reliable uncertainty quantification. The role of expert elicitation of the expected number of counts and its reliability is DL predictions’ role in the proposed modelling approach. Finally, the posterior predictive distribution of counts is obtained in a standard Bayesian analysis using the well known Poisson-Gamma model. The model allows to predict the future evolution of the sequences on all regions or estimates the consequences of eventual scenarios.

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Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Long Short Term Memory (Lstm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Bayesian-Deep Learning Model for Estimating COVID-19 Evolution in Spain

Cabras

2021

Mathematics

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“…The count time series data have multiple applications, many of which have been covered in the literature; see [4] for a comprehensive review. Sometimes, in finance, climate, public health, and crime data analysis, time series counts come as bivariate vectors that observe not only serial dependence within each time series, but also interdependence or cross-dependence between the two series.…”

Section: Introductionmentioning

confidence: 99%

A Class of Copula-Based Bivariate Poisson Time Series Models with Applications

2021

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A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models.

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Bayesian Sequential Learning and Decision Making in Bike‐Sharing Systems

Aktekin,

Kim,

Novoa

et al. 2024

Appl Stoch Models Bus & Ind

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In this article, we introduce modeling strategies for sequentially learning various types of demand uncertainty in bike‐share networks and propose methods for optimal station inventory management. Our approach is motivated by a real bike‐share network in Seoul, South Korea, with 40,000 bikes over a network of 2500 stations covering 25 municipal districts. In doing so, we consider novel Bayesian state space models that are suitable for fast and efficient learning of dynamically evolving system parameters for both intra‐day and inter‐week planning horizons. Our proposed approach provides an overall solution for operation managers where sequential parameter updating, demand prediction, and inventory decision making are addressed simultaneously and is straightforward to implement for the end‐user. We illustrate how our approach can be applied to a large metropolitan area like Seoul and discuss practical implementation insights.

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Count Time Series: A Methodological Review

Cited by 80 publications

References 112 publications

A Bayesian-Deep Learning Model for Estimating COVID-19 Evolution in Spain

A Bayesian-Deep Learning Model for Estimating COVID-19 Evolution in Spain

A Class of Copula-Based Bivariate Poisson Time Series Models with Applications

Bayesian Sequential Learning and Decision Making in Bike‐Sharing Systems

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