Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models
In this paper we present, propose and examine
additional membership functions for the Smoothing Transition
Autoregressive (STAR) models. More specifically, we present the
tangent hyperbolic, Gaussian and Generalized bell functions.
Because Smoothing Transition Autoregressive (STAR) models
follow fuzzy logic approach, more fuzzy membership functions
should be tested. Furthermore, fuzzy rules can be incorporated or
other training or computational methods can be applied as the error
backpropagation or genetic algorithm instead to nonlinear squares.
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] K.S. Chan and H. Tong, "On estimating thresholds in autoregressive
models", Journal of Time Series Analysis, vol. 7, pp. 178-190, 1986
[3] T. Teräsvirta, "Specification, Estimation, and Evaluation of Smooth
Transition Autoregressive Models", Journal of the American Statistical
Association, vol. 89, no. 425, 208-218, 1994
[4] 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
[5] 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
[6] M. S. Bartlett, "Periodogram analysis and continuous spectra,"
Biometrika, vol. 37, pp. 1-16, 1950
[7] 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] K.S. Chan and H. Tong, "On estimating thresholds in autoregressive
models", Journal of Time Series Analysis, vol. 7, pp. 178-190, 1986
[3] T. Teräsvirta, "Specification, Estimation, and Evaluation of Smooth
Transition Autoregressive Models", Journal of the American Statistical
Association, vol. 89, no. 425, 208-218, 1994
[4] 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
[5] 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
[6] M. S. Bartlett, "Periodogram analysis and continuous spectra,"
Biometrika, vol. 37, pp. 1-16, 1950
[7] 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:58932", author = "Ε. Giovanis", title = "Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models", abstract = "In this paper we present, propose and examine
additional membership functions for the Smoothing Transition
Autoregressive (STAR) models. More specifically, we present the
tangent hyperbolic, Gaussian and Generalized bell functions.
Because Smoothing Transition Autoregressive (STAR) models
follow fuzzy logic approach, more fuzzy membership functions
should be tested. Furthermore, fuzzy rules can be incorporated or
other training or computational methods can be applied as the error
backpropagation or genetic algorithm instead to nonlinear squares.
We examine two macroeconomic variables of US economy, the
inflation rate and the 6-monthly treasury bills interest rates.", keywords = "Forecast , Fuzzy membership functions, Smoothingtransition, Time-series", volume = "4", number = "4", pages = "418-5", }