Absolute regularity of semi-contractive GARCH-type processes

Doukhan, Paul; Neumann, Michael H.

doi:10.1017/jpr.2019.8

Cited by 22 publications

(30 citation statements)

References 29 publications

(28 reference statements)

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“…For the related case of Poisson count processes with a GARCH-type structure, absolute regularity has been first proved for contractive IN-GARCH(1,1) processes in Neumann (2011). This has been generalized in Doukhan and Neumann (2019) to semi-contractive models and in Doukhan et al (2020) to the case of possibly non-stationary processes. In all of these papers, the mixing properties were derived by an explicit coupling of two versions of the processes which were tailor-made for the respective properties of the processes.…”

Section: 3mentioning

confidence: 97%

“…The results of our paper are heavily based on the (fully) contractive condition (A1) on the volatility function f . In a related work, Doukhan and Neumann (2019), a weaker so-called semi-contractive condition,…”

Section: 3mentioning

confidence: 99%

“…Mixing properties of such processes have been derived for a first time in Neumann (2011), for INGARCH(1,1) processes under a contractive condition. This has been generalized in Doukhan and Neumann (2019) for the INGARCH(p,q) case and under a weaker semi-contractive condition which resulted in a somewhat unusual subexponential decay of the mixing coefficients. Doukhan et al (2020) proved absolute regularity of the count process again in the INGARCH(1,1) case but allowing a possibly non-stationary (explosive) behavior of the process.…”

Section: Introduction and Notationmentioning

confidence: 99%

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Mixing properties of integer-valued GARCH processes

Doukhan¹,

Khan²,

Neumann³

2021

ALEA

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We consider models for count variables with a GARCH-type structure. Such a process consists of an integer-valued component and a volatility process. Using arguments for contractive Markov chains we prove that this bivariate process has a unique stationary regime. Furthermore, we show absolute regularity (β-mixing) with geometrically decaying coefficients for the count process. These probabilistic results are complemented by a statistical analysis and a few simulations.

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Section: 3mentioning

confidence: 97%

Section: 3mentioning

confidence: 99%

Section: Introduction and Notationmentioning

confidence: 99%

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Mixing properties of integer-valued GARCH processes

Doukhan¹,

Khan²,

Neumann³

2021

ALEA

Self Cite

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“…The first result that we obtain is the stationarity and ergodicity of the process and existence of the first moment under a drift condition and a semicontraction condition. The proof of theorem 1 is based on the approach of Doukhan and Neumann (2019) for semicontractive GARCH‐type processes.…”

Section: Beta–negative Binomial Auto‐regressive Modelsmentioning

confidence: 99%

Beta–Negative Binomial Auto-Regressions for Modelling Integer-Valued Time Series with Extreme Observations

Gorgi

2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary The paper introduces a general class of heavy-tailed auto-regressions for modelling integer-valued time series with outliers. The specification proposed is based on a heavy-tailed mixture of negative binomial distributions that features an observation-driven dynamic equation for the conditional expectation. The existence of a stationary and ergodic solution for the class of auto-regressive processes is shown under general conditions. The estimation of the model can be easily performed by maximum likelihood given the closed form of the likelihood function. The strong consistency and the asymptotic normality of the estimator are formally derived. Two examples of specifications illustrate the flexibility of the approach and the relevance of the theoretical results. In particular, a linear dynamic equation and a score-driven equation for the conditional expectation are studied. The score-driven specification is shown to be particularly appealing as it delivers a robust filtering method that attenuates the effect of outliers. Empirical applications to the series of narcotics trafficking reports in Sydney and the euro–pound sterling exchange rate illustrate the effectiveness of the method in handling extreme observations.

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“…The proof of Theorem 1 in Supplement S4 relies on the results derived byDoukhan & Neumann (2019). Although these authors mainly focus on the case of a conditional Poisson distribution, like we do in Equation (3.1), they point out that the involved stability properties also hold formixed Poisson and compound Poisson distributions (Doukhan & Neumann, 2019, p. 96).…”

mentioning

confidence: 95%

Softplus INGARCH Model

Weiß¹,

Zhu²,

Hoshiyar³

2021

STAT SINICA

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During the last decades, a large variety of models have been proposed for count time series, where the integer-valued autoregressive moving average (ARMA) and integer-valued generalized autoregressive conditional heteroskedasticity (IN-GARCH) models are the most popular ones. However, while both models lead to an ARMA-like autocorrelation function (ACF), the attainable range of ACF values is much more restricted and negative ACF values are usually not possible. The existing log-linear INGARCH model allows for negative ACF values, but the linear conditional mean and the ARMA-like autocorrelation structure are lost. To resolve this dilemma, a novel family of INGARCH models is proposed, which uses the softplus function as a response function. The softplus function behaves approximately linear, but avoids the drawback of not being differentiable in zero. Stochastic properties of the novel model are derived. The proposed model indeed exhibits an approximately linear structure, which is confirmed by extensive simulations, and which makes its model parameters easier to interpret than those of a log-linear INGARCH model. The asymptotics of the maximum likelihood estimators for the parameters are established, and their finite-sample performance is

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Absolute regularity of semi-contractive GARCH-type processes

Cited by 22 publications

References 29 publications

Mixing properties of integer-valued GARCH processes

Mixing properties of integer-valued GARCH processes

Beta–Negative Binomial Auto-Regressions for Modelling Integer-Valued Time Series with Extreme Observations

Softplus INGARCH Model

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