A New Family of Smooth Transition Autoregressive (STAR) Models: Properties and Application of its Symmetric Version to Exchange Rates
Keywords:
Regime shifts, Time series, Nonstationarity, Power logistic function, smooth transition autoregressive modelAbstract
Communication in Physical Sciences, 2023, 9(3):310-324
Authors: Benjamin* Asuquo Effiong, Emmanuel Wilfred Okereke, Chukwuemeka Onwuzuruike Omekara, Chigozie Kelechi Acha and Emmanuel Alphonsus Akpan
Received: 12 May 2023/Accepted 08 July 2023
A good number of economic variables undergo the process of regime shifts. In modeling such variables, it is necessary to consider a model that has provision for the regime form of nonstationarity. The smooth transition autoregressive (STAR) model is a choice model for time series with regime shifts. Given the role of transition functions in the performance of STAR models, this study introduced a family of transition functions by modifying the conventional logistic function. This new family, called the power logistic transition function, has the symmetric transition function and asymmetric transition function as special cases, making it useful in constructing both symmetric and asymmetric STAR models. The symmetric form of the family and the associated STAR model are extensively explained. The performance of the symmetric version of the power logistic smooth transition autoregressive model was illustrated with a monthly exchange rate of naira to United States dollar and African Financial Community Franc spanning from January 2004 to April 2021, which were extracted from Central Bank of Nigeria statistical bulletin. The numerical results obtained show that the symmetric power logistic smooth transition autoregressive model outperforms the linear autoregressive model and other existing symmetric smooth transition autoregressive models.
Downloads
References
Anderson, H.M. (1997). Transaction Costs and Nonlinear Adjustment towards Equilibrium in the
US Treasuring Bill Market. Oxford Bulletin of Economics and Statistics, 59(4):465-484.
Ajm, A. N. and El-Montasser, G. (2012). Seasonal Bi- parameter Smooth Transition Autoregressive Model for the UK Industrial Production Index. Applied Mathematical
Sciences, 6, 32, , pp. 1541 – 1562.
Bacon, D. W. $. & Watts, D. C. (1971). Estimating the Transition between Two Intersecting
Straight Lines. Biometrika, 58, pp. 525-534.
Baum, C. F., Barkoulas, J. T. & Caglayan, M (2001). Nonlinear Adjustment to purchasing Power Parity in the Post-Bretta Woods Era. Journal of International Money and Finance, 20, pp. 379-399.
Chan, K. S. & Tong, H. (1986). On Estimating Threshold Autoregressive Models. Journal of
Time Series Analysis, 7, pp. 179-190.
Dijk, D. V., Terasvirta, T. & Franses, P. H. (2002). Smooth Transition Autoregressive models
– A survey of Recent Developments. Econometric Reviews, 21, 1, , pp. 1-47.
Escribano, A. & Jorda, o. (2001). Testing nonlinearity. Decision Rules for Selecting between Logistic and Exponential STAR Models. Spanish Economic Review, 3, pp. 193-209.
Haggan, V. & Ozaki, T. (1981). Modeling Nonlinear Random Vibration Using an Amplitude-Dependent Autoregressive Time Series Models. Biometrika, 68, pp. 189-196.
Liew, V. K-S., Baharumslah, A. Z. & Lau, S-H. (2003). Forecasting Performance of Logistic STAR Exchange Rate Model: The Original and Reparameterized Versions, MPRAS Paper, No 511.
Luukkonen, R., Saikkonen, P. & Terasvirta, T. (1988). Testing Linearity against STAR Models, Biometrika, 75, 3, , pp. 491- 499.
Sarantis, N. (1999). Modeling Nonlinearities in Real Effective Exchange Rates. Journal of International Money and Finance, 18, pp. 27-45.
Sarno, l. (2000). Real Exchange Rate Behaviour in the Middle East: A Re-Examination. Applied
Economics Letters, 66, pp. 127-136.
Shangodoyin, D.K., Adebille, O. A. & Arnab, R. (2009). Specification of Logistic STAR Model: An Alternative Representation of the Transition Function. Journal of Mathematics and Statistics, 54, 4, pp. 251-259.
Siliverstovs, B. (2005). The Bi- parameter smooth transition autoregressive model. Economic Bulletin, 3, 22, pp. 1-11.
Taylor, M. P. & Sarno, L. (1998). The Behaviour of Real Exchange Rates during the Post-Bretton Wood Period. Journal of International Economies, 46, pp. 261-312.
Taylor, M. P. & Peel, D. A. (2000). Nonlinear Adjustment, Long-Run Equilibrium and Exchange Rate Fundamentals. Journal of International Money and Finance, 19, pp.33-53.
Terasvirta, T. (1994). Specification, Estimation and Evaluation of STAR Models. Journal of the American Statistical Association, 89, 425, pp. 208- 218.
Tong, H. & Lim, K. S.(1980). Threshold autoregressive, Limit Cycles and Cyclical Data. Journal of Royal Statistics Society, 42, 3, pp. 245-292.
Tong, H. (1983). Threshold Models in Nonlinear Time Series Analysis. Lecture notes in Statistics. 21, Springer- Verlag, New York.
Tong, H. (1990). Linear Time Series. A dynamical system approach. Oxford University Press, Oxford.
Yaya, O. S. & Shittu, O. I. (2016). Symmetric variants of logisticsmooth transition autoregressive models: Monte Carlo Evidences. Journal of Modern Applied Statistical Methods, 15, 1, pp. 711- 737.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Journal and Author
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
