Forecasting overdispersed INAR(1) count time series with negative binomial marginal

2021 ◽  
pp. 1-21
Author(s):  
Manik Awale ◽  
Akanksha S. Kashikar ◽  
T. V. Ramanathan
Keyword(s):  
Time Series ◽  
Negative Binomial ◽  
Count Time Series

SUPERPOSITIONED STATIONARY COUNT TIME SERIES

2019 ◽  
pp. 1-19
Author(s):  
Yisu Jia ◽  
Robert Lund ◽  
James Livsey
Keyword(s):  
Time Series ◽  
Negative Binomial ◽  
Stationary Sequence ◽  
Time Series Models ◽  
Count Time Series ◽  
Marginal Distributions ◽  
Autocovariance Function ◽  
Basic Properties ◽  
Model Class ◽  
Discrete Uniform

Abstract This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

scholarly journals Statistical modeling of COVID-19 deaths with excess zero counts

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Sami Khedhiri
Keyword(s):  
Time Series ◽  
Negative Binomial ◽  
Forecast Accuracy ◽  
Series Data ◽  
Zero Inflation ◽  
Count Time Series ◽  
Forecast Performance ◽  
Intervention Policy ◽  
Auto Regression ◽  
Zero Counts

Abstract Objectives Modeling and forecasting possible trajectories of COVID-19 infections and deaths using statistical methods is one of the most important topics in present time. However, statistical models use different assumptions and methods and thus yield different results. One issue in monitoring disease progression over time is how to handle excess zeros counts. In this research, we assess the statistical empirical performance of these models in terms of their fit and forecast accuracy of COVID-19 deaths. Methods Two types of models are suggested in the literature to study count time series data. The first type of models is based on Poisson and negative binomial conditional probability distributions to account for data over dispersion and using auto regression to account for dependence of the responses. The second type of models is based on zero-inflated mixed auto regression and also uses exponential family conditional distributions. We study the goodness of fit and forecast accuracy of these count time series models based on autoregressive conditional count distributions with and without zero inflation. Results We illustrate these methods using a recently published online COVID-19 data for Tunisia, which reports daily death counts from March 2020 to February 2021. We perform an empirical analysis and we compare the fit and the forecast performance of these models for death counts in presence of an intervention policy. Our statistical findings show that models that account for zero inflation produce better fit and have more accurate forecast of the pandemic deaths. Conclusions This paper shows that infectious disease data with excess zero counts are better modelled with zero-inflated models. These models yield more accurate predictions of deaths related to the pandemic than the generalized count data models. In addition, our statistical results find that the lift of travel restrictions has a significant impact on the surge of COVID-19 deaths. One plausible explanation of the outperformance of zero-inflated models is that the zero values are related to an intervention policy and therefore they are structural.

scholarly journals On robust estimation of negative binomial INARCH models

METRON ◽  
2021 ◽  
Author(s):  
Hanan Elsaied ◽  
Roland Fried
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Robust Estimation ◽  
Negative Binomial ◽  
Scale Parameter ◽  
Real Data ◽  
Count Time Series ◽  
Conditional Mean ◽  
Conditional Maximum ◽  
Methods Of Moments

AbstractWe discuss robust estimation of INARCH models for count time series, where each observation conditionally on its past follows a negative binomial distribution with a constant scale parameter, and the conditional mean depends linearly on previous observations. We develop several robust estimators, some of them being computationally fast modifications of methods of moments, and some rather efficient modifications of conditional maximum likelihood. These estimators are compared to related recent proposals using simulations. The usefulness of the proposed methods is illustrated by a real data example.

scholarly journals Model Selection for Time Series Count Data with Over-Dispersion

2021 ◽  
pp. 60-73
Author(s):  
Saleh Ibrahim Musa ◽  
N. O. Nweze
Keyword(s):  
Time Series ◽  
Count Data ◽  
Negative Binomial ◽  
Time Series Data ◽  
Statistical Modelling ◽  
Information Criteria ◽  
Series Data ◽  
Sample Sizes ◽  
Count Time Series ◽  
Over Dispersion

Time series of count with over-dispersion is the reality often encountered in many biomedical and public health applications.  Statistical modelling of this type of series has been a great challenge. Rottenly, the Poisson and negative binomial distributions have been widely used in practice for discrete count time series data, their forms are too simplistic to accommodate features such as over-dispersion. Unable to account for these associated features while analyzing such data may result in incorrect and sometimes misleading inferences as well as detection of spurious associations. Therefore, the need for further investigation of count time series models suitable to fit count time series with over-dispersion of different level. The study therefore proposed a best model that can fit and forecast time series count data with different levels of over-dispersion and sample sizes Simulation studies were conducted using R statistical package, to investigate the performances of Autoregressiove Conditional Poisson (ACP) and Poisson Autoregressive (PAR) models. The predictive ability of the models were observed at different steps ahead. The relative performance of the models were examined using Akaike Information criteria (AIC) and Hannan-Quinn Information Criteria (HQIC). Conclusively, the best model to fit was ACP at different sample sizes. The predictive abilities of the four fitted models increased as sample size and number of steps ahead were increased

Measuring absolute nanoparticle number concentrations from particle count time series

2013 ◽  
Vol 251 (1) ◽  
pp. 19-26 ◽  
Author(s):  
M. RÖDING ◽  
H. DESCHOUT ◽  
K. BRAECKMANS ◽  
M. RUDEMO
Keyword(s):  
Time Series ◽  
Count Time Series ◽  
Particle Count

Forecasting discrete valued low count time series

2004 ◽  
Vol 20 (3) ◽  
pp. 427-434 ◽  
Author(s):  
R.K. Freeland ◽  
B.P.M. McCabe
Keyword(s):  
Time Series ◽  
Count Time Series

scholarly journals Learning from Nighttime Observations of Gas Flaring in North Dakota for Better Decision and Policy Making

2021 ◽  
Vol 13 (5) ◽  
pp. 941
Author(s):  
Rong Lu ◽  
Jennifer L. Miskimins ◽  
Mikhail Zhizhin
Keyword(s):  
Time Series ◽  
North Dakota ◽  
Policy Making ◽  
Nearest Neighbor ◽  
Negative Binomial ◽  
Infrared Imaging ◽  
Gaussian Mixture Models ◽  
Data Gathering ◽  
Gaussian Mixture ◽  
Estimation Errors

In today’s oil industry, companies frequently flare the produced natural gas from oil wells. The flaring activities are extensive in some regions including North Dakota. Besides company-reported data, which are compiled by the North Dakota Industrial Commission, flaring statistics such as count and volume can be estimated via Visible Infrared Imaging Radiometer Suite nighttime observations. Following data gathering and preprocessing, Bayesian machine learning implemented with Markov chain Monte Carlo methods is performed to tackle two tasks: flaring time series analysis and distribution approximation. They help further understanding of the flaring profiles and reporting qualities, which are important for decision/policy making. First, although fraught with measurement and estimation errors, the time series provide insights into flaring approaches and characteristics. Gaussian processes are successful in inferring the latent flaring trends. Second, distribution approximation is achieved by unsupervised learning. The negative binomial and Gaussian mixture models are utilized to describe the distributions of field flare count and volume, respectively. Finally, a nearest-neighbor-based approach for company level flared volume allocation is developed. Potential discrepancies are spotted between the company reported and the remotely sensed flaring profiles.

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