American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2021, 9(3), 102-106
DOI: 10.12691/ajams-9-3-4
Open AccessArticle

On Evaluating the Volatility of Nigerian Gross Domestic Product Using Smooth Transition Autoregressive-GARCH (STAR - GARCH) Models

Akintunde Mutairu Oyewale1,

1Department of Statistics, Federal Polytechnic, Ede, Osun State, Nigeria

Pub. Date: October 11, 2021

Cite this paper:
Akintunde Mutairu Oyewale. On Evaluating the Volatility of Nigerian Gross Domestic Product Using Smooth Transition Autoregressive-GARCH (STAR - GARCH) Models. American Journal of Applied Mathematics and Statistics. 2021; 9(3):102-106. doi: 10.12691/ajams-9-3-4

Abstract

STAR-GARCH models are hybrid models that combine the functional form of smooth transition autoregressive models and Generalized autoregressive conditional heteroscedasticity models. The two classes of STAR models considered in this paper are Exponential and Logistic Smooth transition autoregressive models (ESTAR and LSTAR). The functional form of each of this was combined with that of GARCH model and the resulting models becomes ESTAR-GARCH and LSTAR-GARCH models. The derived equations were applied to Nigerian gross domestic product (Real estate) for empirical illustration. Statonarity tests (Unit root test Graphical and correlogrom methods) conducted revealed that the series was stationary at Second difference. The hybrid models equations so derived were used to determine the model that performed better using the information criteria (AIC, SIC and HQIC), variances obtained from the data, performance measure indices (RMSE, MAE, MAPE THEIL U, Bias proportion, variance Bias proportion and covariance Bias proportion) analysis and in - sample forecast accuracy for the models. From all the criteria used it was observed that the duo of LSTAR-GARCH and ESTAR-GARCH models performed far better than classical GARCH model. However, LSTAR-GARCH performs slightly better than ESTAR-GARCH. From these results it is evident that volatility in Nigerian gross domestic product (Real estate) is best captured using Logistic smooth transition GARCH (LSTAR-GARCH) models, it is therefore, recommended for would be forecasters, investors and other end users to make use of LSTAR-GARCH models.

Keywords:
GARCH model STAR model ESTAR-GARCH LSTAR-GARCH performance measure indices volatility

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References:

[1]  African Development Bank (2013). Country Strategy Paper 2013-2017.
 
[2]  Ignite (2013). Fiscal Management Reform Gaining Traction in Nigeria Again.
 
[3]  Osagie, C. (2011). FG Blames Sluggish GDP Growth on Poor Management, This Day, 25 October.
 
[4]  Nwachukwu V.O. (2008). Principles of Statistical Infrence. Zelon Enterprises, Port-Harcourt.
 
[5]  Jeanne, O. and Masson, P. (2000). “Currency Crises, Sunspots, and Markov-Switching Regimes,” Journal of International Economics 50, 327-350.
 
[6]  Cerra, Valerie, and Sweta Chaman Saxena (2005). “Did Output Recover from the Asian Crisis?” IMF Staff Papers 52, 1-23.
 
[7]  Hamilton, J.D. (2005). What’s Real About the Business Cycle? NBER Working Paper, w11161.
 
[8]  Hamilton, James D. (1988). “Rational-Expectations Econometric Analysis of Changes in Regime: An Investigation of the Term Structure of Interest Rates,” Journal of Economic Dynamics and Control 12, 385-423.
 
[9]  Sims, C., Zha, T., (2006). Were there regime switches in US monetary policy? American Economic Review 96, 54-81.
 
[10]  Davig, Troy (2004). “Regime-Switching Debt and Taxation,” Journal of Monetary Economics. 51, 837-859.
 
[11]  Hamilton J.D., (1989). A new approach to the economic analysis of non-stationary time series and the business cycle. Econometrica, 57(2): 357-384.
 
[12]  Chauvet, Marcelle, and James D. Hamilton (2005). “Dating Business Cycle Turning Points,” in Nonlinear Analysis of Business Cycles, edited by Costas Milas, Philip Rothman, and Dick van Dijk.
 
[13]  Teräsvirta, T.and Anderson, H., (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of Applied Econometrics, 7: S119-S136.
 
[14]  Teräsvirta, T., (2006). Univariate nonlinear time series models. In K. Patterson and T. Mills, editors, Palgrave Handbook of Econometrics, volume I. Palgrave Macmillan, New York.
 
[15]  Akintunde, M. O., Shangodoyin, D. K. and Kgosi, P.M. (2013). Smooth Transition Autoregressive-GARCH Model in Forecasting Non-linear Economic Time Series Data. Journal of Statistical and Econometric Methods, vol. 2, no.2, 11-19.