Analysis of univariate time series with connectionist nets: A case study of two classical examples

Abstract We briefly report on a parsimonious feedforward connectionist net approach for modelling and forecasting univariate time series. The methodology includes all stages of a time series analysis: model identification, model building and diagnosis checking. Within our approach we have modeled and forecasted quite a large number of deterministic and stochastic time series models. As two examples we present here the analysis of the sunspots activity data and of a deterministic chaotic time series. As the results show, in the forecasting process the principle of parsimony becomes evident, indicating that models with less parameters generally produce better results. Thus the idea of parsimony gives our modelling procedure a strong practical orientation.

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

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

[3]  A. Izenman.  J. R. Wolf and the zürich sunspot relative numbers , 1985 .

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

[5]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[6]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[7]  G. Kitagawa,et al.  Akaike Information Criterion Statistics , 1988 .

[8]  T. W. Anderson,et al.  Statistical analysis of time series , 1972 .

[9]  G. Yule.  On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers , 1927 .

[10]  Philip E. Gill,et al.  Practical optimization , 1981 .

[11]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

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

[13]  G. Hartmann,et al.  Parallel Processing in Neural Systems and Computers , 1990 .

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

[15]  Mahmoud M. Gabr,et al.  THE ESTIMATION AND PREDICTION OF SUBSET BILINEAR TIME SERIES MODELS WITH APPLICATIONS , 1981 .

[16]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

[17]  M. J. Morris.  Forecasting the Sunspot Cycle , 1977 .

[18]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

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

[20]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[21]  Per Hokstad,et al.  A METHOD FOR DIAGNOSTIC CHECKING OF TIME SERIES MODELS , 1983 .

[22]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[23]  M. B. Priestley,et al.  Non-linear and non-stationary time series analysis , 1990 .

[24]  C. Granger,et al.  Forecasting Economic Time Series. , 1988 .

[25]  T. Ozaki.  2 Non-linear time series models and dynamical systems , 1985 .

[26]  P. A. P. Moran.  Some Experiments on the Prediction of Sunspot Numbers , 1954 .