Author(s)

George Awiakye-Marfo¹, Joseph Mung’atu², Patrick Weke³

¹Department of Mathematics and Statistics, Pan African University, Nairobi, Kenya.
²Department of Statistics and Actuarial Science, JKUAT, Nairobi, Kenya.
³School of Mathematics, University of Nairobi, Nairobi, Kenya.

In this paper, the randomised pseudolikelihood ratio change point estimator for GARCH models in [1] is employed and its limiting distribution is derived as the supremum of a standard Brownian bridge. Data analysis to validate the estimator is carried out using the United states dollar (USD)-Ghana cedi (GHS) daily exchange rate data. The randomised estimator is able to detect and estimate a single change in the variance structure of the data and provides a reference point for historic data analysis.

GARCH, Randomised, Limiting Distribution, Brownian Bridge, Volatility, CUSUM, IGARCH, Supremum

Awiakye-Marfo, G. , Mung’atu, J. and Weke, P. (2021) Convergence of a Randomised Change Point Estimator in GARCH Models. Journal of Mathematical Finance, 11, 234-245. doi: 10.4236/jmf.2021.112013.