Application of Adaptive Neuro-Fuzzy Inference System in Smoothing Transition Autoregressive Models

Authors: Ε. Giovanis

Abstract:

In this paper we propose and examine an Adaptive Neuro-Fuzzy Inference System (ANFIS) in Smoothing Transition Autoregressive (STAR) modeling. Because STAR models follow fuzzy logic approach, in the non-linear part fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation algorithm instead to nonlinear squares. Furthermore, additional fuzzy membership functions can be examined, beside the logistic and exponential, like the triangle, Gaussian and Generalized Bell functions among others. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecasting, Neuro-Fuzzy, Smoothing transition, Time-series

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083757

References:

[1] J. L. M. Aznarte, J. M. Benitez and J. L. Castro, "Smooth transition autoregressive models and fuzzy rule-based systems: Functional equivalence and consequences", Fuzzy Sets and Systems, vol. 158, pp. 2734-2745, 2007
[2] Atsalakis, S.G. and G.I. Atsalakis, "Fruit production forecasting by neuro-fuzzy techniques," Paper prepared for presentation at the 113th EAAE Seminar "A resilient European food industry and food chain in a challenging world", Chania, Crete, Greece, September, pp. 3-6, 2009
[3] Ballini, R., I. Luna, L.M. Lima and R.L.F. da Silveira, "A comparative analysis of neurofuzzy, ANN and ARIMA models for Brazilian stock index forecasting," SCE - Computing in Economics and Finance, 1995
[4] D. Mar─ìek, "Stock Price Forecasting: Autoregressive Modelling and Fuzzy Neural Network," Proceedings of the 1999 EUSFLAT-ESTYLF Joint Conference, Palma de Mallorca, Spain, September, pp. 22-25, 1995
[5] K.S. Chan and H. Tong, "On estimating thresholds in autoregressive models", Journal of Time Series Analysis, vol. 7, pp. 178-190, 1986
[6] T. Teräsvirta, "Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models", Journal of the American Statistical Association, vol. 89, no. 425, 208-218, 1994
[7] T. Teräsvirta and H.M. Anderson, "Characterizing nonlinearities in business cycles using smooth transition autoregressive models", Journal of Applied Econometrics, vol. 7, pp. 119-136, 1992
[8] D. A. Dickey, and W. A. Fuller, "Distribution of the Estimators for Autoregressive Time Series with a Unit Root", Journal of the American Statistical Association. vol. 74, pp. 427-431, 1979
[9] D. Kwiatkowski, P. C. B. Phillips, P. Schmidt and Y. Shin, "Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root", Journal of Econometrics, vol. 54, pp. 159-178, 1992
[10] M. S. Bartlett, "Periodogram analysis and continuous spectra," Biometrika, vol. 37, pp. 1-16, 1950
[11] J.-S.R. Jang, "ANFIS: Adaptive-Network-based Fuzzy Inference Systems," IEEE Trans. on Systems, Man, and Cybernetics, vol. 23, No. 3, pp. 665-685, 1993
[12] J.-S. R. Jang and C.-T. Sun, "Neuro-fuzzy Modeling and Control," Proceedings of the IEEE, vol. 83, no. 3, 378-406, March, 1995
[13] E.H. Moore, "On the reciprocal of the general algebraic matrix," Bulletin of the American Mathematical Society, vol. 26, pp. 394-395, 1920
[14] R. Penrose, "A generalized inverse for matrices," Proceedings of the Cambridge Philosophical Society, vol. 51, pp. 406-413, 1955
[15] M. Petrou, and P. Bosdogianni, Image Processing: The Fundamentals, John Wile & Sons, 2000
[16] L. Khan, S. Anjum and R. Bada, "Standard Fuzzy Model Identification using Gradient Methods," World Applied Sciences Journal, vol. 8, No. 1, pp. 01-09, 2010
[17] M.A. Denai, F. Palis and A. Zeghbib, ANFIS Based Modelling and Control of Non-Linear systems: A Tutorial, IEEE Conf. on Systems, Man, and Cybernetics, vol. 4, pp. 3433-3438, 2004
[18] L.H. Tsoukalas, and R.E. Uhrig, Fuzzy and Neural Approaches in Engineering, First Edition, John Wiley & Sons, 1997, pp. 445-470
[19] J. G. MacKinnon, "Numerical Distribution Functions for Unit Root and Cointegration Tests", Journal of Applied Econometrics, vol. 11, pp. 601-618, 1996