Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models

Authors: Ε. Giovanis

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1073587

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] 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