| Abstract [eng] |
Analyzing chaotic time series, it is important to reconstruct it in a phase space for successful reconstruction. Also, it is enough to have time series of one-variable and reconstruction parameters: minimum reconstruction dimension and time delay. For identifying minimum reconstruction dimension there were used two methods: false nearest neighbor method and correlation dimension method. Time delay was identified by the method of mutual information. Moreover, if forecast of time series is made correctly, then reconstruction of time series is also adequate, so for this purpose all-time series were forecasting by neural NARX network and then quality of errors was checked by statistical hypothesis. Minimum reconstruction dimension for Lorenz attractor was better identified by false nearest neighbor method then by correlation dimension method. Time lag was identified by mutual information method and then Lorenz attractor forecast was done correctly for next 16 points by trained neural NARX network. Furthermore, for modeled time series with different phase and amplitude minimum embedding dimension was identified better by false nearest neighbor method. When time lag was identified by mutual information method, this time series forecast was made adequate for 50 points. HP company action prices are minimum embedding dimension was identified better by correlation dimension method. Identified time lag by mutual information method was quite big, but these results are expected when we work with financial time series. For this time series the forecast was mode correct for 25 points ahead by neural NARX network. All in all, all-time series were analyzed, the reconstruction parameters were identified and the reconstruction quality was checked by forecasting time series with neural NARX method and by estimating statistical hypothesis of forecasting errors. |
