Minification processes with discrete marginals

Vipul, Kalamkar

doi:10.1017/s0021900200103146

Cited by 2 publications

(3 citation statements)

References 7 publications

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“…Alternative integer-valued processes based on non-additive innovation through maximum and minimum operations were proposed by Littlejohn (1992), Littlejohn (1996), Kalamkar (1995), Scotto et al (2016), and Aleksić and Ristić (2021). For the count processes {X t } t∈N considered in these works, a certain nonlinearity is induced in the sense that the conditional expectation E(X t |X t−1 ) is non-linear on X t−1 (and also the conditional variance) in contrast with (3).…”

Section: Introductionmentioning

confidence: 99%

Modified Galton-Watson processes with immigration under an alternative offspring mechanism

Barreto‐Souza¹,

Ndreca²,

B.³

et al. 2022

Preprint

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We propose a novel class of count time series models alternative to the classic Galton-Watson process with immigration (GWI) and Bernoulli offspring. A new offspring mechanism is developed and its properties are explored. This novel mechanism, called geometric thinning operator, is used to define a class of modified GWI (MGWI) processes, which induces a certain non-linearity to the models. We show that this non-linearity can produce better results in terms of prediction when compared to the linear case commonly considered in the literature. We explore both stationary and non-stationary versions of our MGWI processes. Inference on the model parameters is addressed and the finite-sample behavior of the estimators investigated through Monte Carlo simulations. Two real data sets are analyzed to illustrate the stationary and non-stationary cases and the gain of the non-linearity induced for our method over the existing linear methods. A generalization of the geometric thinning operator and an associated MGWI process are also proposed and motivated for dealing with zero-inflated or zero-deflated count time series data.

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Section: Introductionmentioning

confidence: 99%

Modified Galton-Watson processes with immigration under an alternative offspring mechanism

Barreto‐Souza¹,

Ndreca²,

B.³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…where the set of natural numbers N also includes zero. The discrete minification model, as an extension to the continuous minification model, has been proposed and studied to model count data for many years; see Lewis & Mckenzie (1991), Littlejohn (1992), Kalamkar (1995) This paper is organised as follows. Section 2 proposes a new min-INAR(1) process driven by explanatory variables and studies its basic properties.…”

Section: Introductionmentioning

confidence: 99%

“…random variables with the following probability mass function (pmf)

\Pr (G_{i} = x) = \frac{α^{x}}{{false(1 + α false)}^{x + 1}}, x \in N,

where the set of natural numbers

double-struckN

also includes zero. The discrete minification model, as an extension to the continuous minification model, has been proposed and studied to model count data for many years; see Lewis & Mckenzie (1991), Littlejohn (1992), Kalamkar (1995), among others. Aleksić & Ristić (2021) indicated that both the max‐INAR and min‐INAR models can account for the time series with extreme counts.…”

Section: Introductionmentioning

confidence: 99%

A new minification integer‐valued autoregressive process driven by explanatory variables

Qian

Zhu

2022

Aus NZ J of Statistics

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Summary The discrete minification model based on the modified negative binomial operator, as an extension to the continuous minification model, can be used to describe an extreme value after few increasing values. To make this model more practical and flexible, a new minification integer‐valued autoregressive process driven by explanatory variables is proposed. Ergodicity of the new process is discussed. The estimators of the unknown parameters are obtained via the conditional least squares and conditional maximum likelihood methods, and the asymptotic properties are also established. A testing procedure for checking existence of the explanatory variables is developed. Some Monte Carlo simulations are given to illustrate the finite‐sample performances of the estimators under specification and misspecification and the test, respectively. A real example is applied to illustrate the performance of our model.

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Minification processes with discrete marginals

Cited by 2 publications

References 7 publications

Modified Galton-Watson processes with immigration under an alternative offspring mechanism

Modified Galton-Watson processes with immigration under an alternative offspring mechanism

A new minification integer‐valued autoregressive process driven by explanatory variables

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