Random rounded integer-valued autoregressive conditional heteroskedastic process

Liu, Tianqing; Yuan, Xiaohui

doi:10.1007/s00362-012-0453-2

Cited by 7 publications

(3 citation statements)

References 29 publications

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“…In fact, this does not assume some distributionit is deterministic and simply transforms the data to be discrete. Liu & Yuan (2013) proposed two random rounding operators. Let I(A) be the indicator function for A, (X ) = {z ∈ Z : z ≤ x}, x ∈ R, and…”

Section: 25mentioning

confidence: 99%

Models for Integer Data

Karlis

Khan

2023

Annu. Rev. Stat. Appl.

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Over the past few years, interest has increased in models defined on positive and negative integers. Several application areas lead to data that are differences between positive integers. Some important examples are price changes measured discretely in financial applications, pre- and posttreatment measurements of discrete outcomes in clinical trials, the difference in the number of goals in sports events, and differencing of count-valued time series. This review aims at bringing together a wide range of models that have appeared in the literature in recent decades. We provide an extensive review on discrete distributions defined for integer data and then consider univariate and multivariate time-series models, including the class of autoregressive models, stochastic processes, and ARCH-GARCH– (autoregressive conditionally heteroskedastic–generalized autoregressive conditionally heteroskedastic–) type models. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 10 is March 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Section: 25mentioning

confidence: 99%

Models for Integer Data

Karlis

Khan

2023

Annu. Rev. Stat. Appl.

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“…The first bootstrap method we consider here is the block bootstrap (BB) introduced by Künsch (1989) and Liu and Singh (1992) for time series that are not assumed to have a specific structural form. Their idea is to resample blocks of observations at time.…”

Section: Block Bootstrapmentioning

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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“…Before concluding this section a reference should be made to the two random operators (referred to as first- and second-order random rounding operators) introduced by Liu and Yuan (2013). The usefulness of such operators rely mainly on the fact that the conditional mean and the conditional variance of the process are modelled separately, which implies that no assumptions on the relationship between the conditional mean and variance are needed.…”

Section: Extensions Of the Binomial Thinning Operatormentioning

confidence: 99%

Thinning-based models in the analysis of integer-valued time series: a review

Scotto

Weiß

Gouveia

2015

Statistical Modelling

132

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This article aims at providing a comprehensive survey of recent developments in the field of integer-valued time series modelling, paying particular attention to models obtained as discrete counterparts of conventional autoregressive moving average and bilinear models, and based on the concept of thinning. Such models have proven to be useful in the analysis of many real-world applications ranging from economy and finance to medicine. We review the literature of the most relevant thinning operators proposed in the analysis of univariate and multivariate integer-valued time series with either finite or infinite support. Finally, we also outline and discuss possible directions of future research.

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Random rounded integer-valued autoregressive conditional heteroskedastic process

Cited by 7 publications

References 29 publications

Models for Integer Data

Models for Integer Data

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

Thinning-based models in the analysis of integer-valued time series: a review

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