Model-free forecasting for nonlinear time series (with application to exchange rates)

Abstract The first step in nonlinear model construction is data identification. While the major drawback with most of the nonlinear tests is that they are designed to test a parametric null against certain parametric alternatives and are therefore inconsistent against all possibile alternatives. In this paper, by incorporating the neurocomputing technique, the intriguing model construction and forecast problems such as how to find a best fitted model and to obtain a more appropriate prediction performance are addressed. The dynamic abilities of this approach lies in the fact that the multilier feed forward networks are functional approximators for any functions. Simulations verify that the neural networks perform a robust forecast for some nonlinear time series. Finally, we use the data of the exchange rates of Taiwan to compare the predictive performances of neural networks with ARIMA models.

[1]  David A. Jones.  Time series analysis in water resources , 1987 .

[2]  M. Hinich.  Testing for Gaussianity and Linearity of a Stationary Time Series. , 1982 .

[3]  J. Gooijer,et al.  Some recent developments in non-linear time series modelling, testing, and forecasting☆ , 1992 .

[4]  Robert M. Farber,et al.  How Neural Nets Work , 1987, NIPS.

[5]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[6]  M. Priestley.  STATE‐DEPENDENT MODELS: A GENERAL APPROACH TO NON‐LINEAR TIME SERIES ANALYSIS , 1980 .

[7]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[8]  Bart Kosko,et al.  Neural networks for signal processing , 1992 .

[9]  S. Grossberg.  Studies of mind and brain : neural principles of learning, perception, development, cognition, and motor control , 1982 .

[10]  R. Luukkonen,et al.  Lagrange multiplier tests for testing non-linearities in time series models , 1988 .

[11]  Andrew A. Weiss,et al.  ARCH and Bilinear Time Series Models: Comparison and Combination , 1986 .

[12]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[13]  M. Hashem Pesaran,et al.  Nonlinear Dynamics and Econometrics: An Introduction , 1992 .

[14]  D. Tjøstheim.  SOME DOUBLY STOCHASTIC TIME SERIES MODELS , 1986 .

[15]  John F. Kolen,et al.  Learning in parallel distributed processing networks: Computational complexity and information content , 1991, IEEE Trans. Syst. Man Cybern..

[16]  H. White.  Consequences and Detection of Misspecified Nonlinear Regression Models , 1981 .

[17]  T. Rao,et al.  An Introduction to Bispectral Analysis and Bilinear Time Series Models , 1984 .

[18]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[19]  C. Granger,et al.  An introduction to bilinear time series models , 1979 .

[20]  Dominique Guegan,et al.  Power of the score test against bilinear time series models , 1992 .

[21]  Berlin Wu,et al.  On the identification problem for bilinear time series models , 1992 .

[22]  A. Lapedes,et al.  Nonlinear signal processing using neural networks: Prediction and system modelling , 1987 .

[23]  Roger W. Brockett.  Volterra series and geometric control theory , 1976, Autom..

[24]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[25]  Clive W. J. Granger,et al.  Developments in the Nonlinear Analysis of Economic Series , 1991 .

[26]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[27]  Ed. McKenzie,et al.  SOME SIMPLE MODELS FOR DISCRETE VARIATE TIME SERIES , 1985 .

[28]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..