American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2019, 7(4), 138-145
DOI: 10.12691/ajams-7-4-3
Open AccessArticle

### Modelling Change Point in GARCH Models

1Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology

2Department of Statistics and Actuarial Sciences, Dedan Kimathi University of Technology

Pub. Date: June 24, 2019

Cite this paper:
Amon kiregu, Anthony Waititu and Antony Ngunyi. Modelling Change Point in GARCH Models. American Journal of Applied Mathematics and Statistics. 2019; 7(4):138-145. doi: 10.12691/ajams-7-4-3

### Abstract

This research paper use PELT algorithm and GARCH models to conduct volatility change point analysis and to model and forecast change point in volatility of USD/KES data. This study employed simulated data and data from Central Bank of Kenya for the period between January 2005 to December 2018. The estimates and actual values of change points in volatility did not differ after analysis. The USD/KES data exhibited volatility clustering in some time periods. The volatility adjusted GARCH models outperformed plain models. The simulated estimates of GARCH models were almost converging to the parameters from USD/KES data using the same models. The GARCH models that incorporate change points registered better forecasting performance compared to the plain models. The PGARCH, TGARCH and GJRGARCH models had the same forecasting performance measures in absence and presence of change points. The study recognized TGARCH (1,1) as the best model for modelling and forecasting. Banks can use univariate GARCH models in conjunction with PELT algorithm to track loan defaulters. Hospitals can use the same technique to determine the most recurring diseases. Companies can apply the same to determine abnormal profits and losses. The technique can be applied in other sectors like in meteorology.