A geometric minification integer-valued autoregressive model

Aleksić, Milena S.; Ristić, Miroslav M.

doi:10.1016/j.apm.2020.08.047

Cited by 11 publications

(11 citation statements)

References 20 publications

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“…For common types of count DGPs, the ML estimatorθ ML behaves in a unique way, see [2,4], for example.θ ML is consistent, and √ T (θ ML − θ ) is asymptotically normally distributed according to N(0, I −1 (θ)), where 0 denotes the zero vector, and I(θ ) the expected Fisher information per observation. The mean observed Fisher information 1 T J(θ ), in turn, where J(θ ) is the Hessian of the log-likelihood function, approximates I(θ ). This asymptotic distribution can now be used to assess the variability of the parameter estimates, in analogy to [5].…”

Section: Resampling Of Coherent Forecastsmentioning

confidence: 99%

“…For example, there are models using different thinning operations, such as the so-called 'NGINAR(1) model' by Ristić et al [19] relying on negative-binomial thinning, and there are also regression-type models for time series consisting of bounded counts, such as the so-called 'BINARCH models' by Ristić et al [20]. Generally, one may also consider models with a non-linear conditional mean, although problems might occur if the log-likelihood function has multiple local maxima, such as for the minification INAR model of [1]. To not make our comparisons unnecessarily complex, we restrict to the models in Appendix 1.…”

Section: Comparison To Other Types Of Dgpmentioning

confidence: 99%

“…[ 20 ]. Generally, one may also consider models with a non-linear conditional mean, although problems might occur if the log-likelihood function has multiple local maxima, such as for the minification INAR model of [ 1 ]. To not make our comparisons unnecessarily complex, we restrict to the models in Appendix 1.…”

Section: Simulation Studymentioning

confidence: 99%

See 2 more Smart Citations

Efficient accounting for estimation uncertainty in coherent forecasting of count processes

Weiß

Homburg

Alwan

et al. 2021

Journal of Applied Statistics

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Coherent forecasting techniques for count processes generate forecasts that consist of count values themselves. In practice, forecasting always relies on a fitted model and so the obtained forecast values are affected by estimation uncertainty. Thus, they may differ from the true forecast values as they would have been obtained from the true data generating process. We propose a computationally efficient resampling scheme that allows to express the uncertainty in common types of coherent forecasts for count processes. The performance of the resampling scheme, which results in ensembles of forecast values, is investigated in a simulation study. A real-data example is used to demonstrate the application of the proposed approach in practice. It is shown that the obtained ensembles of forecast values can be presented in a visual way that allows for an intuitive interpretation.

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Section: Resampling Of Coherent Forecastsmentioning

confidence: 99%

Section: Comparison To Other Types Of Dgpmentioning

confidence: 99%

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Efficient accounting for estimation uncertainty in coherent forecasting of count processes

Weiß

Homburg

Alwan

et al. 2021

Journal of Applied Statistics

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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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“…(2018), the discrete minification model of the form X t =min{ α ∘ X t −1 , ε t } would become zero once the first zero occurred. To solve this problem, Aleksić & Ristić (2021) constructed a discrete minification INAR (min‐INAR) model via the modified negative binomial operator. The min‐INAR(1) process is defined by

X_{t} = \min false{α ⋄ X_{t - 1}, ε_{t} false}, α > 0,

where

α ⋄ X = \sum_{i = 1}^{X + 1} G_{i}

, G i is a sequence of i.i.d.…”

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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A geometric minification integer-valued autoregressive model

Cited by 11 publications

References 20 publications

Efficient accounting for estimation uncertainty in coherent forecasting of count processes

Efficient accounting for estimation uncertainty in coherent forecasting of count processes

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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