A geometric time series model with dependent Bernoulli counting series

Ristić, Miroslav M.; Nastić, Aleksandar S.; Ilić, Ana V. Miletić

doi:10.1111/jtsa.12023

Cited by 57 publications

(29 citation statements)

References 38 publications

(55 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other works that have recently appeared in the literature dealing with INAR processes are those of Barczy et al (), Nastić (), Nastić & Ristić (), Ristić et al (), Weiß (), Weiß & Kim (), Meintanis & Karlis (), Schweer & Weiß () and Bisaglia & Canale () just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

Barreto‐Souza

2015

Journal Time Series Analysis

View full text Add to dashboard Cite

In this article, we propose a first‐order integer‐valued autoregressive [INAR(1)] process for dealing with count time series with deflation or inflation of zeros. The proposed process has zero‐modified geometric marginals and contains the geometric INAR(1) process as a particular case. The proposed model is also capable of capturing underdispersion and overdispersion, which sometimes are caused by deflation or inflation of zeros. We explore several statistical and mathematical properties of the process, discuss point estimation of the parameters and find the asymptotic distribution of the proposed estimators. We also propose a test based on our model for checking if the count time series considered is deflated or inflated of zeros. Two empirical illustrations are presented in order to show the potential for practice of our zero‐modified geometric INAR(1) process. This article contains a Supporting Information.

show abstract

Section: Introductionmentioning

confidence: 99%

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

Barreto‐Souza

2015

Journal Time Series Analysis

View full text Add to dashboard Cite

show abstract

“…Example 3 (Dependent counting INAR(1) process). Ristić et al (2013) proposed a geometrically distributed time series generated by dependent Bernoulli count series, called DCINAR(1) process. The DCINAR(1) process is based on new generalized binomial thinning operator α• θ and satisfies the following equation: α).…”

Section: Remark 23 (Alternative Approach) the Innovation Pmf Can Bementioning

confidence: 99%

Fractional approaches for the distribution of innovation sequence of INAR(1) processes

Rodrigues

Bourguignon

Santos‐Neto

2019

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

In this paper, we present a fractional decomposition of the probability generating function of the innovation process of the first-order non-negative integer-valued autoregressive [INAR(1)] process to obtain the corresponding probability mass function. We also provide a comprehensive review of integer-valued time series models, based on the concept of thinning operators, with geometric-type marginals. In particular, we develop four fractional approaches to obtain the distribution of innovation processes of the INAR(1) model and show that the distribution of the innovations sequence has geometric-type distribution. These approaches are discussed in detail and illustrated through a few examples. Finally, using the methods presented here, we develop four new first-order non-negative integer-valued autoregressive process for autocorrelated counts with overdispersion with known marginals, and derive some properties of these models.

show abstract

“…Extensions of binomial thinning based on Bernoulli-distributed dependent r.v's were proposed by Brännäs and Hellström (2001), and more recently by Ristić et al (2013) who assume that the variables in (1.1) take the form…”

Section: Thinning Operators With Dependence Structurementioning

confidence: 99%

Thinning-based models in the analysis of integer-valued time series: a review

Scotto

Weiß

Gouveia

2015

Statistical Modelling

127

View full text Add to dashboard Cite

This article aims at providing a comprehensive survey of recent developments in the field of integer-valued time series modelling, paying particular attention to models obtained as discrete counterparts of conventional autoregressive moving average and bilinear models, and based on the concept of thinning. Such models have proven to be useful in the analysis of many real-world applications ranging from economy and finance to medicine. We review the literature of the most relevant thinning operators proposed in the analysis of univariate and multivariate integer-valued time series with either finite or infinite support. Finally, we also outline and discuss possible directions of future research.

show abstract

A geometric time series model with dependent Bernoulli counting series

Cited by 57 publications

References 38 publications

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

Fractional approaches for the distribution of innovation sequence of INAR(1) processes

Thinning-based models in the analysis of integer-valued time series: a review

Contact Info

Product

Resources

About