W. Rogoza, G. Ishchenko
The article investigates the problem of forecasting time series in the conditions of a small amount of experimental data. The latter are presented in the form of samples that contain the values of the parameters of the object of study. To create predictive mathematical models, it is proposed to use second-order Kolmogorov-Gabor polynomials, the coefficients of which are calculated according to certain rules on the basis of experimental data (the stage of calculating these coefficients can be interpreted as model training). Because there is a small amount of experimental data, it is not possible to establish statistical characteristics of changes in the parameters of the object, so in these conditions, classical forecasting methods become inappropriate, and the reliability and accuracy of mathematical models is crucial. The article proposes an approach to building mathematical predictive models based on the principles of system identification, i,e, the object of research is considered as a "black box", data known from experiments - as input parameters, and predicted parameters - as output parameters of the conditional multiport. To predict the magnitude of each parameter of the object in future moments of time, several alternative mathematical models are created, called particular prediction models. To enhance the probability of a reliable prediction, among the alternative models are selected those models that meet certain conditions of reliability. of the proposed method.
time series, time-limited forecasting, small number of experimental samples, system identification.
- Russel, S.T. and Norvig, P. (2003), Artificial Intelligence. A Modern Approach, Prentice Hall, New Jersey, USA.
- Witten, I.H. and Frank, E. (2005), Data Mining: Practical machine learning tools and techniques, Morgan Kaufmann, Prentice Hall, USA.
- Box, G. and Jenkins, G. (1970), Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco, USA.
- Ljung, L. (1999), System Identification - Theory For the User. Prentice Hall, N.J., USA.
- Kalman, R.E. (1960), “A new approach to linear filtering and prediction problems”, Journal of Basic Engineering, Vol. 82, no. 1, pp. 35-45.
- Ivakhnenko, A.G. (1982), Induktivny metod samoorganizacii modeley slozhnyh system [Inductive method of self-organization of complex systems], Naukova Dumka, Kyiv, Ukraine.
- Rogoza, W. (2019), “Method for the prediction of time series using small sets of experimental samples”, Applied Mathematics and Computation, Vol. 355, pp. 108-122.