Adaptive forecasting of wave non-periodic time series.

The forecasting problem of wave financial time series is considered. In practice of econometric forecasting of financial processes, real time series are of a complex structure described by the composition of non-periodic oscillating functions. The proposed approach for adaptive wave forecasting

uses the idea of harmonic structure analysis of wave time series represented as a number of harmonic superposition with tuning frequencies. The proposed forecasting method is based on the special autoregressive representation of wave time series and both frequencies and amplitudes of partial harmonics estimation. The peculiarities of the method are the initial time-series decomposition on the trend and oscillatory components. The special adaptive technique and corresponding recurrent identification algorithm with tuning parameters is used for model updating with the combination of detection the moments when the time series change its properties. In such a case, the identification algorithm also ensures non-stationary wave component frequencies real-time tracking. The proposed technique can be treated as the development of structural approach for time series spectral analysis. The developed method is applied for the problem of stock prices and stock market indexes forecasting. (JEL C10)

LEONID M. LYUBCHYK, GALINA M. GRINBERG, AND ARKADY RIVTIS

National Technical University--U.S.A.