Time series with discrete semistable marginals

Bouzar, Nadjib; Jayakumar, K.

doi:10.1007/s00362-006-0040-5

Cited by 13 publications

(5 citation statements)

References 13 publications

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“…The next proposition states that equation ( 4) is a sufficient condition for the existence of stationary INAR (1) processes. For a proof see for example Bouzar and Jayakumar (2008) or, in a more general setting, Aly and Bouzar (1994).…”

Section: Introductionmentioning

confidence: 99%

Stationary underdispersed INAR(1) models based on the backward approach

Aly,

Bouzar

2021

Preprint

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Most of the stationary first-order autoregressive integer-valued (INAR(1)) models were developed for a given thinning operator using either the forward approach or the backward approach. In the forward approach the marginal distribution of the time series is specified and an appropriate distribution for the innovation sequence is sought. Whereas in the backward setting, the roles are reversed. The common distribution of the innovation sequence is specified and the distributional properties of the marginal distribution of the time series are studied. In this article we focus on the backward approach in presence of the Binomial thinning operator. We establish a number of theoretical results which we proceed to use to develop stationary INAR(1) models with finite mean. We illustrate our results by presenting some new INAR (1) models that show underdispersion.

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Section: Introductionmentioning

confidence: 99%

Stationary underdispersed INAR(1) models based on the backward approach

Aly,

Bouzar

2021

Preprint

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“…While theoretical properties of INAR models with Poisson innovations have been extensively studied in the literature (see, for instance, Freeland and McCabe 2004a;, and the references therein), relatively few contributions discuss the development of methods for INAR models with innovations distributed differently from the Poisson. Among the others, Bouzar and Jayakumar (2008) propose INAR models with discrete semistable marginals and related distributions, Weiß (2013) works on models for counts showing underdispersion, Weiß et al (2016) introduce a test for departures from Poissonity.…”

Section: Introductionmentioning

confidence: 99%

Model-based INAR bootstrap for forecasting INAR(p) models

Bisaglia

Gerolimetto

2019

Comput Stat

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In this paper we analyse some bootstrap techniques to make inference in INAR( p) models. First of all, via Monte Carlo experiments we compare the performances of these methods when estimating the thinning parameters in INAR( p) models; we state the superiority of model-based INAR bootstrap approaches on block bootstrap in terms of low bias and Mean Square Error. Then we adopt the model-based bootstrap methods to obtain coherent predictions and confidence intervals in order to avoid difficulty in deriving the distributional properties. Finally, we present an empirical application.

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“…In this connection, we note that for both the INAR and PAR models, a typical example of distributional law involves the Poisson distribution. Recently, however, there have been proposed several alternatives or more general specifications; see, for instance, Jazi et al (), Bouzar & Jayakumar (), Bourguinon & Vasconcellos (), Goncalves et al (), Schweer & Weiss (), Zhu () and Fokianos (). One major aspect that might lead to non‐Poisson specifications is (marginal or conditional) overdispersion or underdispersion of the data at hand, and it is conceivable to expect that such a feature might manifest itself only beyond a certain point in time, thus signalling a structural change in the observations that cannot be accommodated by a potential change in the parameters as long as the (equidispersed) Poisson law remains in place.…”

Section: Introductionmentioning

confidence: 99%

Tests for Structural Changes in Time Series of Counts

Hudecová¹,

Hušková²,

Meintanis

2017

Scandinavian J Statistics

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We propose methods for detecting structural changes in time series with discretevalued observations. The detector statistics come in familiar L2-type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.

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Time series with discrete semistable marginals

Abstract: Autoregressive process, Moving average process, Stationarity, Probability generating functions, Discrete semistable distribution,

Cited by 13 publications

References 13 publications

Stationary underdispersed INAR(1) models based on the backward approach

Stationary underdispersed INAR(1) models based on the backward approach

Model-based INAR bootstrap for forecasting INAR(p) models

Tests for Structural Changes in Time Series of Counts

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