In this paper, a randomised pseudolikelihood ratio change point estimator for GARCH model is presented. Derivation of a randomised change point estimator for the GARCH model and its consistency are given. Simulation results that support the validity of the estimator are also presented. It was observed that the randomised estimator outperforms the ordinary CUSUM of squares test, and it is optimal with large variance change ratios.

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.