Article
Computer Science, Interdisciplinary Applications
Cathy W. S. Chen, Chun-Shu Chen, Mo-Hua Hsiung
Summary: The study proposes a new model to investigate the spread of infectious diseases. By considering the neighboring locations of the target series, the model presents a continuous conceptualization of distance and highlights the non-separability of space and time. The proposed model successfully captures the characteristics of spatial dependency, over-dispersion, and a large portion of zeros, providing a comprehensive model for the observed phenomena in the data.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2023)
Article
Economics
Abdelhakim Aknouche, Christian Francq
Summary: This paper studies the estimation problem of conditional mean parameters and compares the properties of Quasi Maximum Likelihood Estimators (QMLEs) and Weighted Least Square Estimators (WLSEs). The results show that when the conditional distribution is misspecified, WLSEs have the same consistency property as QMLEs. Furthermore, when some components of the conditional parameters are null and the variance is well specified, WLSEs have simpler asymptotic distributions and higher efficiency.
JOURNAL OF ECONOMETRICS
(2023)
Article
Mathematics
Lanyu Xiong, Fukang Zhu
Summary: In this paper, a robust estimation method for observation-driven integer-valued time-series models is proposed, with the assumption that the conditional probability mass of current observations follows a negative binomial distribution. The minimum density power divergence estimator is chosen as a robust estimator, and its strong consistency and asymptotic normality are proved under certain conditions. Simulation results and an application to campylobacteriosis infection data demonstrate the effectiveness of the estimator.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2022)
Article
Statistics & Probability
Yuanqi Chu, Keming Yu
Summary: When dealing with time series data with extreme observations, the commonly used approach is to develop models based on heavy-tailed distributions. However, there is less literature on modelling integer-valued time series data with heavy-tailedness. This paper introduces a log-linear version of the beta-negative binomial integer-valued generalized autoregressive conditional heteroscedastic (BNB-INGARCH) model to accommodate both negative and positive serial correlations. Bayesian inference is adopted for better quantifying the uncertainty of unknown parameters, and adaptive Markov chain Monte Carlo sampling schemes are used for parameter estimations and inferences due to the high computational demand. The proposed method's performance is evaluated through a simulation study and empirical applications.
COMPUTATIONAL STATISTICS
(2023)
Article
Statistics & Probability
Ana Martins, Manuel G. Scotto, Christian H. Weiss, Sonia Gouveia
Summary: This paper introduces a new class of space-time integer-valued ARMA models called STINARMA, and focuses on the moving average subclass STINMA. The paper also analyzes the performance of the Poisson STINMA(11) process through a simulation study and by analyzing the daily number of hospital admissions in three Portuguese locations.
ELECTRONIC JOURNAL OF STATISTICS
(2023)
Article
Statistics & Probability
Cathy W. S. Chen, Feng-Chi Liu, Aljo Clair Pingal
Summary: This study proposes integer-valued transfer function models with zero-inflated generalized Poisson and negative binomial distributions to describe overdispersion, a large proportion of zeros, and the influence of exogenous variables. Effective Bayesian estimation and model selection methods are provided for analyzing weekly dengue cases with two meteorological covariates.
STATISTICS & PROBABILITY LETTERS
(2023)
Article
Business, Finance
Yiqun Sun, Hao Ji, Xiurong Cai, Jiangchen Li
Summary: This passage suggests that joint events can play a crucial role in pricing events, helping to mitigate the risk of price spikes and increased expenses. The author Yiqun Sun contributed in conceptualization, methodology, and writing.
FINANCE RESEARCH LETTERS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xiaofei Hu, Beth Andrews
Summary: We introduce a GARCH model for uncorrelated, integer-valued time series with conditional heteroskedasticity, and establish conditions for its stationarity, ergodicity, and moments. Maximum likelihood estimation for model parameters and the limiting distribution of estimators are considered under various scenarios.
JOURNAL OF TIME SERIES ANALYSIS
(2021)
Article
Statistics & Probability
Chenhui Zhang, Dehui Wang, Kai Yang, Han Li, Xiaohong Wang
Summary: This paper introduces a new first-order generalized Poisson integer-valued autoregressive process for modeling integer-valued time series with piecewise structure and overdispersion. It discusses basic probabilistic and statistical properties of the model, derives conditional least squares and conditional maximum likelihood estimators, and establishes the asymptotic properties of the estimators. Additionally, two special cases of the process are discussed, and numerical results of the estimates and a real data example are presented.
JOURNAL OF APPLIED STATISTICS
(2022)
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
Lianyong Qian, Fukang Zhu
Summary: In this article, a more flexible integer-valued GARCH model based on the generalized Conway-Maxwell-Poisson distribution is proposed to model time series of counts. This model offers a unified framework to deal with overdispersed or underdispersed, zero-inflated and heavy-tailed time series of counts.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2023)
Article
Statistics & Probability
Mohammed Alqawba, Norou Diawara
Summary: This paper proposes Markov zero-inflated count time series models based on joint distribution of consecutive observations, addressing zero-inflation and serial dependence. Various copula functions and distributions like ZIP, ZINB, and ZICMP are considered, with likelihood-based inference and asymptotic properties studied. Simulation examples and application to sandstorm counts show advantages over existing models in modeling zero-inflated count time series data.
JOURNAL OF APPLIED STATISTICS
(2021)
Article
Statistics & Probability
Huaping Chen, Qi Li, Fukang Zhu
Summary: This article introduces a new class of beta-binomial integer-valued GARCH models to analyze certain characteristics of integer-valued time series. The performance of conditional maximum likelihood estimates and the asymptotic properties of the estimators are established through simulation studies. Finally, the proposed models are applied to real data sets for further analysis.
ASTA-ADVANCES IN STATISTICAL ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
S. Ramezani, M. Mohammadpour
Summary: In this paper, an integer-valued bilinear model with signed generalized power series thinning operator is proposed for modeling negative integer-valued time series with negative correlation. The strict stationarity and parameter estimation methods are discussed, and the behavior of the estimators is illustrated through numerical results. Additionally, the analysis of three real data sets is presented for demonstrative purposes.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2021)
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)