Strict stationarity of Poisson integer-valued ARCH processes of order infinity
Abstract
This paper establishes necessary and sufficient conditions for the existence of a unique strictly stationary and ergodic solution for integer-valued autoregressive conditional heteroscedasticity (INARCH) processes. We also provide conditions that guarantee existence of higher order moments. The results apply to integer-valued GARCH model, and its long-memory versions with hyperbolically decaying coefficients and turn out to be instrumental on deriving large sample properties of the maximum likelihood estimators of the model parameters.
Keywords
INARCH processes; Stationarity; Ergodicity; Lyapunov exponent; Maximum likelihood estimation
Cite as
Segnon, M. (2022). Strict stationarity of Poisson integer-valued ARCH processes of order infinity. In Center, f. Q. E. (. (Ed.), CQE Working Papers: Vol. 102/2022. University of Muenster.Details
Publication type
Working paper
Peer reviewed
No
Publication status
Published
Year
2022
Editor
Center for Quantitative Economics (CQE)
Number of pages
22
Volume
102/2022
Title of series
CQE Working Papers
Place
University of Muenster
Language
English
Full text