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Threshold-asymmetric volatility models for integer-valued time series
Communications for Statistical Applications and Methods 2019;26:295-304
Published online May 31, 2019
© 2019 Korean Statistical Society.

Deok Ryun Kima,b, Jae Eun Yoona, Sun Young Hwang1,a

aDepartment of Statistics, Sookmyung Women’s University, Korea;
bInternational Vaccine Institute, Korea
Correspondence to: 1Department of Statistics, SookmyungWomen’s University, Cheongpa-ro 47-gil 100, Seoul 04310, Korea.
E-mail: shwang@sookmyung.ac.kr
Received January 9, 2019; Revised February 22, 2019; Accepted March 5, 2019.
 Abstract
This article deals with threshold-asymmetric volatility models for over-dispersed and zero-inflated time series of count data. We introduce various threshold integer-valued autoregressive conditional heteroscedasticity (ARCH) models as incorporating over-dispersion and zero-inflation via conditional Poisson and negative binomial distributions. EM-algorithm is used to estimate parameters. The cholera data from Kolkata in India from 2006 to 2011 is analyzed as a real application. In order to construct the threshold-variable, both local constant mean which is time-varying and grand mean are adopted. It is noted via a data application that threshold model as an asymmetric version is useful in modelling count time series volatility.
Keywords : count data, integer-valued time series, threshold integer-valued ARCH, volatility