Author(s)

Irene W. Irungu^1*, Peter N. Mwita², Antony G. Waititu³

¹Pan-African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya.
²Machakos University, Machakos, Kenya.
³Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.

The limit theory of a change-point process which is based on the Manhattan distance of the sample autocorrelation function with applications to GARCH processes is examined. The general theory of the sample autocovariance and sample autocorrelation functions of a stationary GARCH process forms the basis of this study. Specifically the point processes theory is utilized to obtain their weak convergence limit at different lags. This is further extended to the change-point process. The limits are found to be generally random as a result of the infinite variance.

Autocorrelation Function, Change-Point, Convergence, GARCH, Manhattan Distance, Model Order, Point Process, Regular Variation, Weak Limit

Irungu, I. , Mwita, P. and Waititu, A. (2018) Limit Theory of Model Order Change-Point Estimator for GARCH Models. Journal of Mathematical Finance, 8, 426-445. doi: 10.4236/jmf.2018.82027.