Application of Adaptive Neuro-Fuzzy Inference System in Smoothing Transition Autoregressive Models
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.
[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
[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
@article{"International Journal of Business, Human and Social Sciences:63859", author = "Ε. Giovanis", title = "Application of Adaptive Neuro-Fuzzy Inference System in Smoothing Transition Autoregressive Models", 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", volume = "4", number = "4", pages = "449-8", }
