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) |
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Pages (from-to) | 737-751 |
Number of pages | 15 |
Journal | Journal of Time Series Analysis |
Volume | 42 |
Issue number | 5-6 |
DOIs | |
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