Integer-valued asymmetric garch modeling

Xiaofei Hu; Beth Andrews

doi:10.1111/jtsa.12605

Integer-valued asymmetric garch modeling

Xiaofei Hu, Beth Andrews^*

^*Corresponding author for this work

Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We propose a GARCH model for uncorrelated, integer-valued time series that exhibit conditional heteroskedasticity. Conditioned on past information, these observations have a two-sided Poisson distribution with time-varying variance. Positive and negative observations can have an asymmetric impact on conditional variance. We give conditions under which the proposed integer-valued GARCH process is stationary, ergodic, and has finite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its parameter space, and when some GARCH coefficients are zero.

Original language	English (US)
Pages (from-to)	737-751
Number of pages	15
Journal	Journal of Time Series Analysis
Volume	42
Issue number	5-6
DOIs	https://doi.org/10.1111/jtsa.12605
State	Published - Sep 1 2021

Funding

This article is an extension of part of Xiaofei Hu's PhD dissertation, which was written while he was a student at Northwestern University. We are indebted to two referees and an editor whose comments led to considerable improvements in the manuscript.

Keywords

Asymmetric GARCH
Poisson
integer-valued
maximum likelihood

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1111/jtsa.12605

Cite this

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abstract = "We propose a GARCH model for uncorrelated, integer-valued time series that exhibit conditional heteroskedasticity. Conditioned on past information, these observations have a two-sided Poisson distribution with time-varying variance. Positive and negative observations can have an asymmetric impact on conditional variance. We give conditions under which the proposed integer-valued GARCH process is stationary, ergodic, and has finite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its parameter space, and when some GARCH coefficients are zero.",

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N2 - We propose a GARCH model for uncorrelated, integer-valued time series that exhibit conditional heteroskedasticity. Conditioned on past information, these observations have a two-sided Poisson distribution with time-varying variance. Positive and negative observations can have an asymmetric impact on conditional variance. We give conditions under which the proposed integer-valued GARCH process is stationary, ergodic, and has finite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its parameter space, and when some GARCH coefficients are zero.

AB - We propose a GARCH model for uncorrelated, integer-valued time series that exhibit conditional heteroskedasticity. Conditioned on past information, these observations have a two-sided Poisson distribution with time-varying variance. Positive and negative observations can have an asymmetric impact on conditional variance. We give conditions under which the proposed integer-valued GARCH process is stationary, ergodic, and has finite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its parameter space, and when some GARCH coefficients are zero.

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KW - maximum likelihood

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Integer-valued asymmetric garch modeling

Abstract

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Keywords

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