Modelling Change Point in GARCH Models

Amon kiregu^1, , Anthony Waititu¹ and Antony Ngunyi²

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

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

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.

Keywords:
change point PGARCH TGARCH GJRGARCH volatility

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References:

[1]	Johansson, P. (2019). Volatility forecasting using the GARCH framework on the OMXS30 and MIB30 stock indices.
[2]	Verma, P., & Ghosh, S. K. (2019). Trend Analysis of Climatic Research Unit Temperature dataset for Gangotri Glacier, India. Dynamics of Atmospheres and Oceans.
[3]	Singh, S., & Tripathi, L. K. (2016). Modelling Stock Market Return Volatility: Evidence from India. Research Journal of Finance and Accounting, 7(13), 93-101.
[4]	Włodarczyk, A., & Kadłubek, M. (2018). Use of Mulifactor Models with Garch Structure in Carbon Emissions Risk Management. Multidisciplinary Aspects of Production Engineering, 1(1), 407-413.
[5]	Dutta, A. (2019). Forecasting ethanol market volatility: new evidence from the corn implied volatility index. Biofuels, Bioproducts and Biorefining, 13(1), 48-54.
[6]	Stoykova, A., & Paskaleva, M. (2019). Southeast European Capital Markets: Dynamics, Relationship and Sovereign Credit Risk. Walter de Gruyter GmbH & Co KG.
[7]	Sarwar, G. (2019). Transmission of Risk between US and Emerging Equity Markets. Emerging Markets Finance and Trade, 55(5), 1171-1183.
[8]	Sarwar, G., & Khan, W. (2019). Interrelations of US market fears and emerging markets returns: Global evidence. International Journal of Finance & Economics.
[9]	Jiang, T., & Hua, Q. (2019). Option Pricing for TGARCH-M with GED Based on Improved EEMD. Emerging Markets Finance and Trade, 1-20.
[10]	Mozumder, S., Kabir, M. H., & Dempsey, M. (2018). Pricing and hedging options with GARCH-stable proxy volatilities. Applied Economics, 50(56), 6034-6046.
[11]	Chun, D., Cho, H., & Ryu, D. (2019). Forecasting the KOSPI200 spot volatility using various volatility measures. Physica A: Statistical Mechanics and its Applications, 514, 156-166.
[12]	Bedoui, R., Braiek, S., Guesmi, K., & Chevallier, J. (2019). On the Conditional Dependence Structure between Oil, Gold and USD Exchange rates: Nested Copula based GJR-GARCH Model. Energy Economics.
[13]	Jamel, L., & Mansour, S. (2019). Co-movements in volatility of dependency between US dollar and euro: analysing by conditional heteroscedasticity models. International Journal of Management and Enterprise Development, 18(1-2), 1-19.
[14]	Allen, D. E., McAleer, M., Powell, R. J., & Singh, A. K. (2018). Non-Parametric Multiple Change Point Analysis of the Global Financial Crisis. Annals of Financial Economics, 13(02), 1850008.
[15]	Pereira, P. F., & Ramos, N. M. (2018). Detection of occupant actions in buildings through change point analysis of in-situ measurements. Energy and Buildings, 173, 365-377.
[16]	Ding, Z., C. W. Granger, and R. F. Engle (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance 1, 83-106.
[17]	Glosten,L, R., Jagannathan, R, &Runkle,D.E.(1993). On the relation between the expected value amd the volatility of the nominal excess return on stocks. The Journal of finance, 48(5), 1779-1801.
[18]	Zakoian, J.M. (1994). Threshold heteroskedastic models. Journal of Ecconomic Dynamics and control, 18(5), 931-955.