Modeling Exchange Rate of Naira to Euro with the APLSTAR-GARCH model
Keywords:
ARCH effects, Model evaluation criteria, Nonlinear macroeconomic time series, Parameter estimate, Smooth transition autoregressive modelAbstract
Application of the asymmetric power logistic smooth transition autoregressive (APLSTAR) model proposed by [1] to naira/Euro exchange rate spanning from January, 2006 to April, 2021, which is a nonlinear macroeconomic time series was considered. The APLSTAR model was justifiably fitted to the series and the fit of the APLSTAR model compared with the fits of the competing models revealed that the APLSTAR model fits the data exchange rate of naira to Euro better than the other asymmetric STAR models. Lagrange Multiplier tests for autoregressive conditional heteroscedastic (ARCH) effects were carried out and there was no substantial evidence to reject the presence of ARCH effects in the set of residuals used. Hence, we compared hybrid smooth transition autoregressive-generalized ARCH (STAR-GARCH) models using model evaluation criteria. On balance, the APLSTAR-GARCH (0, 1) model outperforms the other models under consideration.
References
Effiong, B A., Okereke, E.W., Omekara, C. O., Acha, C. K., & Akpan, E. A. A New Family of Smooth Transition Autoregressive (STAR) Models: Properties and Application of its Symmetric Version to Exchange Rates. Communication in Physical Sciences, 9(3), 310-324, 2023.
Terasvirta, T. Specification, Estimation & Evaluation of STAR Models. Journal of
the American Statistical Association, 89(425), 208- 218, 1994.
Box, E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. Time Series Analysis
Forecasting and Control. John Wiley and Sons, Inc. Hoboken, Jersey. 361-370, 2016.
Hamilton, J. D. Time Series Analysis. Princeton University Press, Princeton, 1994.
Tong, H. & Lim, K. S. Threshold autoregressive, Limit Cycles and Cyclical Data. Journal of Royal Statistics Society, 42(3), 245-292, 1980.
Taylor, M. P. & Sarno, L. The Behaviour of Real Exchange Rates during the Post-BrettonWood Period. Journal of International Economies, 46, 261-312, 1998.
Sarantis, N. Modeling Nonlinearities in Real Effective Exchange Rates. Journal of International Money and Finance, 18, 27-45, 1999.
Taylor, M. P. & Peel, D. A. Nonlinear Adjustment, Long-Run Equilibrium and Exchange Rate Fundamentals. Journal of International Money and Finance, 19, 33-53, 2000.
Sarno, l. Real Exchange Rate Behaviour in the Middle East: A ReExamination. Applied Economics Letters, 66, 127-13, 2000.
Baum, C. F., Barkoulas, J. T., & Caglayan, M. Nonlinear Adjustment to purchasing Power Parity in the Post-Bretta Woods Era. Journal of International Money and Finance, 20, 379-399, 2001.
Liew, V. K-S., Baharumslah, A. Z., & Lau, S-H. Forecasting Performance of Logistic STAR Exchange Rate Model: The Original and Reparameterized Versions. MPRAS Paper, No 511, 2003.
Baharumshah, A. Z. & Liew, V. K-S. Forecasting Performance of Exponential Smooth Transition Autoregressive Exchange Rate. Open Economies Review, 17, 235-25, 2006.
Oyewale, A. M. On Evaluating the Volatility of Nigerian Gross Domestic Product Using Smooth Transition Autoregressive-GARCH (STAR - GARCH) Models. American Journal of Applied Mathematics and Statistics, 9(3), 102-106, 2021.
Dijk, D. V., Terasvirta, T. & Franses, P. H. Smooth Transition Autoregressive
models – A survey of Recent Developments. Econometric Reviews, 21(1): 1- 47, 2002.
Jansen, E. S. & Terasvirta, T. Testing Parameter Constancy and Super Exogeity in
Econometric Equations. Oxford Bulletin of Economies and Statistics, 58:735-763, 1996.
Shangodoyin, D.K., Adebille, O. A., & Arnab, R. Specification of Logistic STAR Model: An Alternative Representation of the Transition Function. Journal of Mathematics and Statistics, 54(4): 251-259, 2009.
Engle, R. F. Autoregressive conditional heteroscedasticity with estimates of the Variance of United Kingdom inflation, Econometrica: Journal of the econometric society, 50, 987-1008, 1982.
Tsay, R. S. Analysis of Financial Time Series. John Wiley and Sons, Inc. 605 Third Avenue, New York, 83-87, 2002.
Bollerslev, T. Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307–327, 1986.
Escribano, A. & Jorda, O. Testing nonlinearity. Decision Rules for Selecting between Logistic and Exponential STAR Models. Spanish Economic Review, 3: 193-209, 2001.
Luukkonen, R., Saikkonen, P., & Terasvirta, T. Testing Linearity against STAR Models. Biometrika, 75(3), 491- 499, 1988.
Chan, F. & McAleer, M. Estimating Smooth Transition autoregressive models with GARCH errors in the presence of Extreme Observations and Outliers. Applied Financial Economics, 13(8), 581- 592, 2003.
Yoon, G. Do Real Exchange Rates Really Follow Threshold Autoregressive Model or Exponential Smooth Transition Autoregressive Models? Economic Modeling, 27, 605-612, 2010.
Downloads
Published
Issue
Section
License
Copyright
It is the author's responsibility to ensure that his or her submitted work does not infringe any existing copyright. Authors should obtain permission to reproduce or adapt copyrighted material and provide evidence of approval upon submitting the final version of a manuscript.
