On some properties of Autoregressive Conditional Poisson (ACP) models

Ghahramani, M.; Thavaneswaran, A.

doi:10.1016/j.econlet.2009.08.018

Cited by 6 publications

(5 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first derivatives of the conditional log likelihood function (7) with respect to Γ ¼ ðg 0 ; g 1 ; . .…”

Section: Estimation Proceduresmentioning

confidence: 99%

“…Heinen derived the properties of his model only for the ACP (1, 1) case. The general case was investigated by Ghahramani and Thavaneswaran [7] who referred to the Heinen paper as the origin of the ACP model. Independently, Ferland et al [1] proposed what was termed the Integer-valued GARCH (INGARCH) process, which is essentially the same as the ACP model of Heinen. The INGARCH model of order (p, q) is defined as follows:…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An integer GARCH model for a Poisson process with time-varying zero-inflation

Isuru

Samaranayake

2023

PLoS ONE

View full text Add to dashboard Cite

A serially dependent Poisson process with time-varying zero-inflation is proposed. Such formulations have the potential to model count data time series arising from phenomena such as infectious diseases that ebb and flow over time. The model assumes that the intensity of the Poisson process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation and allows the zero-inflation parameter to vary over time and be governed by a deterministic function or by an exogenous variable. Both the expectation maximization (EM) and the maximum likelihood estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter estimation methods provide good estimates. Applications to two real-life data sets on infant deaths due to influenza show that the proposed integer-valued GARCH (INGARCH) model provides a better fit in general than existing zero-inflated INGARCH models. We also extended a non-linear INGARCH model to include zero-inflation and an exogenous input. This extended model performed as well as our proposed model with respect to some criteria, but not with respect to all.

show abstract

“…The first derivatives of the conditional log likelihood function (7) with respect to Γ ¼ ðg 0 ; g 1 ; . .…”

Section: Estimation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An integer GARCH model for a Poisson process with time-varying zero-inflation

Isuru

Samaranayake

2023

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…Heinen (2003) introduced an ACP model to deal with time series of count data with serial correlation. Building on Heinen's work, the theoretical properties of the general ACP model were derived by Ghahramani and Thavaneswaran (2009). In brief, the count X t observed during the interval ( t − 1, t ] is considered a realization from a Poisson distribution with a conditional mean that is dependent on past observations and past conditional means.…”

Section: Zero‐inflated Poisson Modelmentioning

confidence: 99%

Predicting lifespan of Drosophila melanogaster: A novel application of convolutional neural networks and zero‐inflated autoregressive conditional Poisson model

Zhang

Samaranayake

Olbricht

et al. 2021

Stat

View full text Add to dashboard Cite

A model to classify the lifespan of Drosophila, the fruit fly, into short-and long-lived categories based on a sleep characteristic, extracted from activity data, is developed using a two-stage process. Stage 1 models the per-minute activity counts of each fly using a zero-inflated autoregressive conditional Poisson model. These probabilities are allowed to vary hourly, reflecting the circadian and other cycles present in a fly's sleep architecture. A 5-day moving window is used to model data allowing the model parameters to vary over the course of the fly's life. The resulting probabilities capture information about changes in sleep patterns with age and are hypothesized to contain features that help categorize flies into short-and long-lived groups. The resulting hourly zero-inflation probabilities over a 24-day period are utilized to create a 'heat map' containing information on the 24-hour daily sleep cycle and its changes across the 24-day observation period. In Stage 2, the heat maps for individual flies are used as inputs to a convolutional neural network to build a classification model. The estimated model provides a reasonably accurate way to group flies into lifespan categories. Grouping flies into such categories would facilitate the discovery of biochemical markers of aging.

show abstract

“…Here, we re-examine some of these models and present simpler derivations of their moment properties using martingale difference. Such martingale difference have been successfully applied to various time series processes, see for example, Thavaneswaran and Abraham (1988) and Ghahramani and Thavaneswaran (2009). These results are very significant for the development of simpler theories on integer-valued time series models, in particular, for estimating the paramaters of the models using the estimating functions method.…”

Section: Introductionmentioning

confidence: 96%

Moment Properties And Quadratic Estimating Functions For Integer-Valued Time Series Models

Mohamed

Najihah

2018

Pak.j.stat.oper.res.

View full text Add to dashboard Cite

Recently, there has been a growing interest in integer-valued time series models. In this paper, using a martingale difference, we prove a general theorem on the moment properties of a class of integer-valued time series models. This theorem not only contains results in the recent literature as special cases but also has the advantage of a simpler proof. In addition, we derive the closed form expressions for the kurtosis and skewness of the models. The results are very useful in understanding the behaviour of the processes involved and in estimating the parameters of the models using quadratic estimating functions (QEF). Specifically, we derive the optimal function for the integer-valued GARCH (p, q) known as INGARCH (p, q) model. Simulation study is carried out to compare the performance of QEF estimates with corresponding maximum likelihood (ML) and least squares (LS) estimates for the INGARCH (1,1) model with different sets of parameters. Results show that the QEF estimates produce smaller standard errors than the ML and LS estimates for small sample size and are comparable to the ML estimates for larger sample size. For illustration, we fit the 108 monthly strike data to INGARCH (1, 1) models via QEF, ML and LS methods, and show the applicability of QEF method in practice.

show abstract

On some properties of Autoregressive Conditional Poisson (ACP) models

Cited by 6 publications

References 8 publications

An integer GARCH model for a Poisson process with time-varying zero-inflation

An integer GARCH model for a Poisson process with time-varying zero-inflation

Predicting lifespan of Drosophila melanogaster: A novel application of convolutional neural networks and zero‐inflated autoregressive conditional Poisson model

Moment Properties And Quadratic Estimating Functions For Integer-Valued Time Series Models

Contact Info

Product

Resources

About