Mixtures of Nonlinear Poisson Autoregressions

Doukhan, Paul; Fokianos, Konstantinos

doi:10.1111/jtsa.12558

Cited by 10 publications

(18 citation statements)

References 54 publications

(101 reference statements)

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“…Thus a necessary and sufficient condition for the stationarity and ergodicity of (Y t ) is that (3.4) holds. If in particular This condition improves those proposed byAknouche and Demmouche (2019),Doukhan et al (2021) andMao et al (2019) for the Poisson mixture INGARCH model.If X s ∼  (𝜆) then (3.8) holds with a sj (i) =…”

supporting

confidence: 77%

“…Hence 𝛼 si = 𝛼 s,i and 𝛽 sj = 𝛽 s,j denote the values of the coefficients 𝛼 Δ t ,i and 𝛽 Δ t ,j when the Markov chain Δ t is in state s. This kind of equation has been considered for the volatility of MS-GARCH models (see for instance Francq and Zakoian, 2005). For MS-INGARCH models with independent switching, representation (3.1) was considered by Aknouche and Demmouche (2019), Doukhan et al (2021), and Mao et al (2019). Since 𝜆 t depends on the present and past regimes {Δ t−u , u ≥ 0}, we can call it the past-regime dependent switching.…”

Section: The Past-regime Dependent Switchingmentioning

confidence: 99%

“…Hujer et al ., 2002,2003; De Luca and Zuccolotto, 2006; Hujer and Vuletic, 2007; Hautsch, 2012; Chen et al ., 2013). Recently, Markov‐switching INGARCH (MS‐INGARCH) models have also been introduced in the context of count time series (Zhu et al ., 2010; Berentsen et al ., 2018; Lee and Hwang, 2018; Doukhan et al ., 2021; Aknouche and Demmouche, 2019). The Markov switching count and duration models have a similar conditional mean specification as MS‐GARCH models, but unlike the latter, they are generally not MEM and therefore their ergodic properties are not easily obtained using the SRE theory.…”

Section: Introductionmentioning

confidence: 99%

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Stationarity and ergodicity of Markov switching positive conditional mean models

Aknouche

Francq

2021

Journal Time Series Analysis

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A general Markov-Switching autoregressive conditional mean model, valued in the set of nonnegative numbers, is considered. The conditional distribution of this model is a finite mixture of nonnegative distributions whose conditional mean follows a GARCHlike dynamics with parameters depending on the state of a Markov chain. Three different variants of the model are examined depending on how the lagged-values of the mixing variable are integrated into the conditional mean equation. The model includes, in particular, Markov mixture versions of various well-known nonnegative time series models such as the autoregressive conditional duration (ACD) model, the integer-valued GARCH (INGARCH) model, and the Beta observation driven model. Under contraction in mean conditions, it is shown that the three variants of the model are stationary and ergodic when the stochastic order and the mean order of the mixing distributions are equal. The proposed conditions match those already known for * I am grateful to the Agence Nationale de la Recherche (ANR), which supported this work via the Project MultiRisk (ANR-16-CE26-0015-02). I also thanks the labex ECODEC.1Markov-switching GARCH models. We also give conditions for finite marginal moments. Applications to various mixture and Markov mixture count, duration and proportion models are provided.

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supporting

confidence: 77%

Section: The Past-regime Dependent Switchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stationarity and ergodicity of Markov switching positive conditional mean models

Aknouche

Francq

2021

Journal Time Series Analysis

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“…For instance, Al-Osh and Alzaid (1987) proposes several methods for estimating so-called first order integer-valued autoregressive (INAR(1)) models, while Pedeli et al (2015) suggest saddlepoint approximation methods for estimating INAR(p) models, and Fokianos (2016) considers a GLM perspective on estimation. Recently, spectral estimation and indirect inference have been pursued in Doukhan et al (2020) and Davis et al (2020), respectively, while Doukhan et al (2021) estimates Markov switching integer-valued ARCH models using maximum likelihood methods. For extensive treatments of count-valued time series, we refer to Davis et al (2016) and Karlis (2016).…”

Section: Introductionmentioning

confidence: 99%

Inference and forecasting for continuous-time integer-valued trawl processes

Bennedsen¹,

Lunde²,

Shephard³

et al. 2021

Preprint

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This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integervalued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model, and we prove consistency and asymptotic normality of this estimator. The same methods allow us to develop probabilistic forecasting methods, which can be used to construct the predictive distribution of integer-valued time series. In a simulation study, we document good finite sample performance of the likelihood-based estimator and the associated model selection procedure. Lastly, the methods are illustrated in an application to modelling and forecasting financial bid-ask spread data, where we find that it is beneficial to carefully model both the marginal distribution and the autocorrelation structure of the data. We argue that integer-valued trawl processes are especially well-suited in such situations.

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“…Larges classes of examples including ARCH, GARCH-type models or integer valued GLM models possibly integer valued may be found both in [11] and in [10], see also e.g. [13], [20] and [17] for more models. Note that those classes of models and many others may easily seen to fit the conditions in the current results, which gives sense to our settings and to our results.…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Taylor's Law

De la Pena,

Doukhan,

Salhi

2020

Preprint

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Taylor's power law (or fluctuation scaling) states that on comparable populations, the variance of each sample is approximately proportional to a power of the mean of the population. It has been shown to hold by empirical observations in a broad class of disciplines including demography, biology, economics, physics and mathematics. In particular, it has been observed in the problems involving population dynamics, market trading, thermodynamics and number theory. For this many authors consider panel data in order to obtain laws of large numbers and the possibility to fit those expressions; essentially we aim at considering ergodic behaviors without independence. Thus we restrict the study to stationary time series and we develop different Taylor exponents in this setting. From a theoretic point of view, there has been a growing interest on the study of the behavior of such a phenomenon. Most of these works focused on the so-called static Taylor related to independent samples. In this paper, we introduce a dynamic Taylor's law for dependent samples using self-normalised expressions involving Bernstein blocks. A central limit theorem (CLT) is proved under either weak dependence or strong mixing assumptions for the marginal process. The limit behavior of such a new index involves the series of covariances unlike the classic framework where the limit behavior involves the marginal variance. We also provide an asymptotic result for for a goodness-of-fit testing suited to check whether the corresponding dynamical Taylor's law holds in empirical studies. Moreover, we also obtain a consistent estimation of the Taylor's exponent.

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Mixtures of Nonlinear Poisson Autoregressions

Cited by 10 publications

References 54 publications

Stationarity and ergodicity of Markov switching positive conditional mean models

Stationarity and ergodicity of Markov switching positive conditional mean models

Inference and forecasting for continuous-time integer-valued trawl processes

A Dynamic Taylor's Law

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