Long Memory Conditional Heteroscedasticity in Count Data

Segnon Mawuli, Stapper Manuel

Abstract

This paper introduces a new class of integer-valued long memory processesthat are adaptations of the well-known FIGARCH(p, d, q) process of Baillie (1996) andHYGARCH(p, d, q) process of Davidson (2004) to a count data setting. We derive thestatistical properties of the models and show that reasonable parameter estimates areeasily obtained via conditional maximum likelihood estimation. An empirical application with financial transaction data illustrates the practical importance of the models.