Article
Physics, Multidisciplinary
Zhengwei Liu, Fukang Zhu
Summary: In this paper, a new integer-valued autoregressive model is introduced based on the extended binomial thinning operator, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares estimation and conditional maximum likelihood estimation methods are proposed for the model. Moreover, the asymptotic property of the two-step conditional least squares estimator is also obtained, and the proposed model is demonstrated to have superior performance through the analysis of real data sets with different dispersion levels.
Article
Mathematics
Wooi Chen Khoo, Seng Huat Ong, Biswas Atanu
Summary: This paper studies a flexible forecasting method based on the method of mixtures, specifically considering time series of counts. Through numerical experiments and comparative analysis, the advantages of the mixture model in forecasting performance are demonstrated and validated with two sets of real data.
Article
Engineering, Multidisciplinary
Milena S. Aleksic, Miroslav M. Ristic
Summary: In this paper, a new minification integer-valued autoregressive model is proposed to address the issue of potential constant zero values over time when using binomial or negative binomial thinning operators. Various estimation methods are considered, and the model's applicability is demonstrated on real data sets through simulations. The model's adequacy is further confirmed using the parametric bootstrap approach.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Multidisciplinary Sciences
Zohreh Mohammadi, Zahra Sajjadnia, Maryam Sharafi, Naushad Mamode Khan
Summary: This paper introduces a new stationary first-order integer-valued autoregressive process (INAR) with zero-and-one-inflated geometric innovations, which is useful for modeling medical practical data. The basic probabilistic and statistical properties of the model are discussed. The proposed model is applied to analyze two medical series and compared with other competing models based on goodness-of-fit statistics and selection criteria.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
(2022)
Article
Mathematics
Rehan Ahmad Khan Sherwani, Sadia Iqbal, Shumaila Abbas, Muhammad Aslam, Ali Hussein AL-Marshadi
Summary: This research introduces the neutrosophic negative binomial distribution to address issues related to interval-valued data under the negative binomial distribution, including derivations of various properties of the proposed distribution and discussions on its applications in real data scenarios.
JOURNAL OF MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Bing Su, Fukang Zhu
Summary: This paper reviews the relationship between the bivariate integer-valued autoregressive model of order 1 (BINAR(1)) and the bivariate negative binomial (BNB) distribution, compares the performances of BINAR(1) models with explanatory variables in the survival probability under different BNB distributions, and evaluates the parameter estimation method using conditional maximum likelihood through Monte Carlo simulations. Sales counts are used for model performance comparison, leading to interesting conclusions.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2021)
Article
Mathematics, Applied
Bogdan A. Pirkovic, Petra N. Laketa, Aleksandar S. Nastic
Summary: The paper investigates the behavior of a generalized random environment integer-valued autoregressive model with geometric marginal distribution and negative binomial thinning operator. It proposes a new estimation method that includes data transformation to reduce information loss, and compares this new approach with the traditional method on simulated and real-life data, highlighting the benefits of the new method.
Article
Multidisciplinary Sciences
Ashwinee Devi Soobhug, Homeswaree Jowaheer, Naushad Mamode Khan, Neeshti Reetoo, Kursheed Meethoo-Badulla, Laurent Musango, Celestin C. Kokonendji, Azmi Chutoo, Nawel Aries
Summary: This paper proposes a high-ordered integer-valued auto-regressive time series model for situations with excess zeros and non-stationary trend. The model is tested on SARs-CoV-2 series in Mauritius and shows its suitability, as well as identifies vaccination events and COVID-19 stringency index as the most influential factors in reducing locally acquired COVID-19 cases.
Article
Engineering, Multidisciplinary
Naushad Mamode Khan, Hassan S. Bakouch, Ashwinee Devi Soobhug, Manuel G. Scotto
Summary: The COVID-19 pandemic has severely disrupted global economic and social activities, especially impacting vulnerable economies like Small Island Developing States. Through the development of a new integer-valued time series model for COVID-19 infections, this research has made progress in modeling and forecasting the pandemic, with the INAR-WCG model showing slightly better performance in terms of RMSEs compared to other models.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Statistics & Probability
Bader S. Almohaimeed
Summary: This paper establishes the strong consistency and asymptotic normality of the negative binomial quasi-maximum likelihood estimator (NBQMLE) for a general class of integer-valued time series models with periodic time-varying parameters. Specific models, including the Poisson periodic INGARCH model, negative binomial periodic INGARCH model, and periodic INAR(1) model, are used for illustration. The performance of the NBQMLE is evaluated through simulation study and applied to a real dataset.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2022)
Article
Mathematics, Applied
Dan-shu Sheng, De-hui Wang, Kai Yang, Zi-ang Wu
Summary: This paper introduces a quantile regression estimation method for first-order integer-valued autoregressive models by defining a smoothing process, and derives estimators for the autoregressive coefficient and quantile of innovations using jittering method. The consistency and asymptotic normality of the estimators are established, and their performance is evaluated through Monte Carlo simulations, showing good performance in both simulations and real data applications.
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
(2021)
Article
Statistics & Probability
Wagner Barreto-Souza, Sokol Ndreca, Rodrigo B. Silva, Roger W. C. Silva
Summary: We propose a novel class of INAR(1) models based on the geometric thinning operator, which introduces non-linearity to the models. The non-linear INAR(1) processes, named NonLINAR(1), are shown to produce better prediction results compared to the linear case. Stationary and non-stationary versions of the NonLINAR processes are explored, and model parameter inference and finite-sample behavior are investigated.
Article
Physics, Multidisciplinary
Kaizhi Yu, Tielai Tao
Summary: This paper introduces a first-order integer-valued autoregressive time series model with observation-driven parameters that may follow a specific random distribution. The ergodicity of the model and the theoretical properties of point estimation, interval estimation, and parameter testing are derived. These properties are verified through numerical simulations. Finally, the application of this model is demonstrated using real-world datasets.
Article
Environmental Sciences
Maria Bugallo, Maria Dolores Esteban, Manuel Francisco Marey-Perez, Domingo Morales
Summary: In recent decades, there have been changes in the occurrence of wildfires. It is necessary to develop accurate predictive models on a country scale to efficiently allocate firefighting resources. Mediterranean countries experience a high number of wildfires, mainly concentrated in the summer months. Zero-inflated negative binomial mixed models are suitable for analyzing this type of data and can provide useful prediction tools by considering both the occurrence and non-occurrence of fires. Additionally, a parametric bootstrap method is applied to estimate mean squared errors and construct prediction intervals.
JOURNAL OF ENVIRONMENTAL MANAGEMENT
(2023)
Article
Statistics & Probability
Yao Kang, Dehui Wang, Feilong Lu, Shuhui Wang
Summary: This paper develops two classes of INAR(1) processes to model different characteristics of count data. Estimation methods and properties of the model parameters are derived, and the flexibility and usefulness of the proposed models are demonstrated through real examples.
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
(2022)
Article
Statistics & Probability
Aleksandar S. Nastic, Miroslav M. Ristic, Ana V. Miletic Ilic
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2017)
Article
Statistics & Probability
Bozidar V. Popovic, Miroslav M. Ristic, Narayana Balakrishna
STATISTICAL PAPERS
(2017)
Article
Mathematics, Applied
Aleksandar S. Nastic, Miroslav M. Ristic, Ana D. Janjic
Article
Computer Science, Interdisciplinary Applications
Ana V. Miletic Ilic, Miroslav M. Ristic, Aleksandar S. Nastic, Hassan S. Bakouch
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2018)
Article
Mathematics, Applied
Petra N. Laketa, Aleksandar S. Nastic, Miroslav M. Ristic
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2018)
Article
Statistics & Probability
Miroslav M. Ristic, Marcelo Bourguignon, Aleksandar S. Nastic
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2019)
Article
Statistics & Probability
Miroslav M. Ristic, Yuvraj Sunecher, Naushad Mamode Khan, Vandna Jowaheer
Article
Engineering, Multidisciplinary
Bozidar V. Popovic, Miroslav M. Ristic, Ali I. Genc
APPLIED MATHEMATICAL MODELLING
(2020)
Article
Statistics & Probability
Bozidar V. Popovic, Miroslav M. Ristic, Konstantinos Zografos
Summary: This article studies an integral transformation of the copula function and proves that under certain conditions, the studied transformation remains a copula function. The article also explores properties of the integral transformation and derives bounds for Kendall's tau and Spearman's rho.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Medicine, General & Internal
Lidija Popovic Dragonjic, Maja Jovanovic, Miodrag Vrbic, Aleksandar Nastic, Miodrag Djordjevic, Milica Veljkovic
Summary: This study evaluated a rarely reported complication of measles, acute morbillous pancreatitis (AMP), which was diagnosed in 14% of the studied patients. The patients with AMP had higher levels of ALT and vomited more frequently. Only slight differences in measles duration, changes in RBC count, and CRP levels were found between male and female patients with AMP.
MEDICINA-LITHUANIA
(2022)
Article
Mathematics, Applied
Bogdan A. Pirkovic, Petra N. Laketa, Aleksandar S. Nastic
Summary: The paper investigates the behavior of a generalized random environment integer-valued autoregressive model with geometric marginal distribution and negative binomial thinning operator. It proposes a new estimation method that includes data transformation to reduce information loss, and compares this new approach with the traditional method on simulated and real-life data, highlighting the benefits of the new method.
Article
Operations Research & Management Science
Predrag M. Popovic, Petra N. Laketa, Aleksandar S. Nastic
SORT-STATISTICS AND OPERATIONS RESEARCH TRANSACTIONS
(2019)
Article
Statistics & Probability
Aleksandar S. Nastic, Petra N. Laketa, Miroslav M. Ristic
REVSTAT-STATISTICAL JOURNAL
(2019)
Article
Statistics & Probability
Predrag M. Popovic, Aleksandar S. Nastic, Miroslav M. Ristic
REVSTAT-STATISTICAL JOURNAL
(2018)
