Negative Binomial Quasi‐Likelihood Inference for General Integer‐Valued Time Series Models

Aknouche, Abdelhakim; Bendjeddou, Sara; Touche, Nassim

doi:10.1111/jtsa.12277

Cited by 21 publications

(16 citation statements)

References 45 publications

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“…Corollary 3.1 is a direct consequence of Theorem 3.1 and Section 2.4. This result has been conjectured by Aknouche, Bendjeddou, and Touche (2018) but, to the best of our knowledge, it had not yet been formally proven.…”

Section: Remark 33 (Joint Stationarity With the Exogenous Variables)mentioning

confidence: 68%

Count and Duration Time Series With Equal Conditional Stochastic and Mean Orders

Aknouche

Francq

2020

Econom. Theory

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We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. We give conditions for consistency and asymptotic normality of the Exponential Quasi-Maximum Likelihood Estimator of the conditional mean parameters. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in this paper.

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Section: Remark 33 (Joint Stationarity With the Exogenous Variables)mentioning

confidence: 68%

Count and Duration Time Series With Equal Conditional Stochastic and Mean Orders

Aknouche

Francq

2020

Econom. Theory

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“…Theorem 2.2 Under H 1 with θ * 1 and θ * 2 belonging to • Θ, assume that (A1)-(A4) hold for (Y (1) , θ * 1 ) and (Y (2) , θ * 2 ). If Assumption B is satisfied, then…”

Section: Change-point Test and Asymptotic Resultsmentioning

confidence: 99%

A general procedure for change-point detection in multivariate time series

Diop¹,

Kengne²

2021

Preprint

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We consider the change-point detection in multivariate continuous and integer valued time series.We propose a Wald-type statistic based on the estimator performed by a general contrast function; which can be constructed from the likelihood, a quasi-likelihood, a least squares method, etc. Sufficient conditions are provided to ensure that the statistic convergences to a well-known distribution under the null hypothesis (of no change) and diverges to infinity under the alternative; which establishes the consistency of the procedure. Some examples are detailed to illustrate the scope of application of the proposed procedure. Simulation experiments are conducted to illustrate the asymptotic results.

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“…Theoretical results on negative binomial QML were derived in Aknouche et al . (2018), where a two‐stage QML estimator was considered. In contrast, BNB–GAS and NB–GAS do not have the same specification for λ t and only the conditional mean of BNB–GAS is robust against outliers.…”

Section: Empirical Applicationsmentioning

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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Negative Binomial Quasi‐Likelihood Inference for General Integer‐Valued Time Series Models

Cited by 21 publications

References 45 publications

Count and Duration Time Series With Equal Conditional Stochastic and Mean Orders

Count and Duration Time Series With Equal Conditional Stochastic and Mean Orders

A general procedure for change-point detection in multivariate time series

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

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