This manuscript deals with a parameter estimation of a non-negative integer-valued (NNIV) time series based on the so-called probability generating function (PGF) method. The theoretical background of the PGF estimation technique for a very general,...
In this study, we consider the problem of testing for a parameter change in general integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family when the data are contaminated by outliers. In partic...
Time series analysis is crucial for modeling and forecasting diverse real-world phenomena. Traditional models typically assume continuous-valued data; however, many applications involve integer-valued series, often including negative integers. This p...
Count time series are widely available in fields such as epidemiology, finance, meteorology, and sports, and thus there is a growing demand for both methodological and application-oriented research on such data. This paper reviews recent developments...
In real-life inter-related time series, the counting responses of different entities are commonly influenced by some time-dependent covariates, while the individual counting series may exhibit different levels of mutual over- or under-dispersion or m...
In commerce, economics, engineering and the sciences, quantitative methods based on statistical models for forecasting are very useful tools for prediction and decision. There is an abundance of papers on forecasting for continuous-time series but re...
This paper presents a first-order integer-valued autoregressive time series model featuring observation-driven parameters that may adhere to a particular random distribution. We derive the ergodicity of the model as well as the theoretical properties...
Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-o...
In the realm of time series data analysis, information criteria constructed on the basis of likelihood functions serve as crucial instruments for determining the appropriate lag order. However, the intricate structure of random coefficient integer-va...
The technological keywords extracted from patent documents have much information about a developed technology. We can understand the technological structure of a product by examining the results of patent analysis. So far, much research has been done...
We examine issues of prior sensitivity in a semi-parametric hierarchical extension of the INAR(p) model with innovation rates clustered according to a Pitman–Yor process placed at the top of the model hierarchy. Our main finding is a graphical...
In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive m...
This paper considers the problem of testing for parameter change in random coefficient integer-valued autoregressive models. To overcome some size distortions of the existing estimate-based cumulative sum (CUSUM) test, we suggest estimating function-...
The generalized linear autoregressive moving-average model (GLARMA) has been used in epidemiology to evaluate the impact of pollutants on health. These effects are quantified through the relative risk (RR) measure, which inference can be based on the...
In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we...
This research models and forecasts bounded ordinal time series data that can appear in various contexts, such as air quality index (AQI) levels, economic situations, and credit ratings. This class of time series data is characterized by being bounded...
The incidence of infectious diseases in children may be affected by climate change-related disaster risks that increase as extreme weather events become more frequent. Therefore, this research aims to diagnose the impact of such disaster risks on the...
Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this pa...
The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended b...
A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may...
Modelling the non-stationary unconstrained bivariate integer-valued autoregressive of order 1 (NSUBINAR(1)) model is challenging due to the complex cross-correlation relationship between the counting series. Hence, this paper introduces a novel non-s...
While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified...
The geometric first-order integer-valued autoregressive process (GINAR(1)) can be particularly useful to model relevant discrete-valued time series, namely in statistical process control. We resort to stochastic ordering to prove that the GINAR(1) pr...
We developed a class of bivariate integer-valued time series models using copula theory. Each count time series is modeled as a Markov chain, with serial dependence characterized through copula-based transition probabilities for Poisson and Negative...
Excess zeros is a common phenomenon in time series of counts, but it is not well studied in asymmetrically structured bivariate cases. To fill this gap, we first considered a new first-order, bivariate, random coefficient, integer-valued autoregressi...
A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties...
Recently, there has been a growing interest in integer-valued time series models, especially in multivariate models. Motivated by the diversity of the infinite-patch metapopulation models, we propose an extension to the popular bivariate INAR(1) mode...
In view of the complexity and asymmetry of finite range multi-state integer-valued time series data, we propose a first-order random coefficient multinomial autoregressive model in this paper. Basic probabilistic and statistical properties of the mod...
In many real-life instances, time series of counts are often exposed to the dispersion phenomenon while at the same time being influenced by some explanatory variables. This paper takes into account these two issues by assuming that the series of cou...
This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and corr...
In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its effic...
The novel circumstance-driven bivariate integer-valued autoregressive (CuBINAR) model for non-stationary count time series is proposed. The non-stationarity of the bivariate count process is defined by a joint categorical sequence, which expresses th...
This paper proposes a new time-varying integer-valued autoregressive (TV-INAR) model with a state vector following a logistic regression structure. Since the autoregressive coefficient in the model is time-dependent, the Kalman-smoothed method is app...
This study considers support vector regression (SVR) and twin SVR (TSVR) for the time series of counts, wherein the hyper parameters are tuned using the particle swarm optimization (PSO) method. For prediction, we employ the framework of integer-valu...
This paper considers the periodic self-exciting threshold integer-valued autoregressive processes under a weaker condition in which the second moment is finite instead of the innovation distribution being given. The basic statistical properties of th...
The significance of count data modeling and its applications to real-world phenomena have been highlighted in several research studies. The present study focuses on a two-parameter discrete distribution that can be obtained by compounding the Poisson...
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 Poisso...
Intra-day transactions of stocks from competing firms in the financial markets are known to exhibit significant volatility and over-dispersion. This paper proposes some bivariate integer-valued auto-regressive models of order 1 (BINAR(1)) that are us...
This article discusses the class of Periodic Generalized Poisson Integer-Valued Generalized Autoregressive Conditional Heteroscedastic PGPINGARCH models. The model, in addition to properly capture the periodic feature in the autocovariance structure,...
In this paper, the authors introduce the transmuted geometric integer-valued autoregressive model with periodicity, designed specifically to analyze epidemiological and public health time series data. The model uses a transmuted geometric distributio...
Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focus...
This article introduces a flexible time series regression model known as the Mixture of Integer-Valued Generalized Autoregressive Conditional Heteroscedasticity (MINGARCH). Mixture models provide versatile frameworks for capturing heterogeneity in co...
Several pieces of research have spotlighted the importance of count data modelling and its applications in real-world phenomena. In light of this, a novel two-parameter compound-Poisson distribution is developed in this paper. Its mathematical functi...
The Asian rice gall midge (Orseolia oryzae (Wood-Mason)) is a major insect pest in rice cultivation. Therefore, development of a reliable system for the timely prediction of this insect would be a valuable tool in pest management. In this study, occu...
This investigation explores the effects of applying fuzzy time series (FTSs) based on neural network models for estimating a variety of spectral functions in integer time series models. The focus is particularly on the skew integer autoregressive of...
Knowledge of causal relationships is fundamental for understanding the dynamic mechanisms of ecological systems. To detect such relationships from multivariate time series, Granger causality, an idea first developed in econometrics, has been formulat...
In the present work, a neotype chaotic product trigonometric map (PTM) system is proposed. We demonstrate the chaotic characteristics of a PTM system by using a series of complexity criteria, such as bifurcation diagrams, Lyapunov exponents, approxim...
Several models for time series with integer values have been published as a result of the substantial demand for the description of process stability having discrete marginal distributions. One of these models is the mixed count geometric integer aut...
The paper concerns the solution of the ordinary differential equation y″±xmy=0, which may be designated the generalized Airy equation, since the original Airy equation corresponds to the particular case m=1 with the + sign. The solutions...
Symmetry performs an essential function in finding the correct techniques for solutions to time space fractional differential equations (TSFDEs). In this article, we present the Novel Analytic Method (NAM) for approximate solutions of the linear and...
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