Novel techniques and algorithms for the segmentation and prediction of the univariate and multivariate time-series will be constructed during the project. Mathematical model based on the interpolation of the univariate time-series with Chebyshev polynomials within a non-uniform time-grid will be proposed. Such a model estimates the fact that values of the time-series near the present time moment have more influence on the future value than older ones. The model builds the ground for the algorithm of the prediction of signals with a high noise level. The implementation of such an algorithm runs into the ill-conditioned optimization problem which requires a construction of novel non-standard cost functions optimized employing adaptive evolutionary optimization algorithms. Moreover, novel segmentation techniques and algorithms, which enable to improve the quality of the prediction of the isolated scalar time-series, employing reconstructed near optimal mathematical models of the related time-series, will be proposed.
Project funding:
KTU Research and Innovation Fund
Project results:
Mathematical model for the interpolation of time-series with Chebyshev polynomials was constructing. The model exploits the non-uniform distribution of the roots of Chebyshev polynomial, taking into account that values of the time-series near the present time moment have more influence on the future value than older ones. Algorithms for the prediction of noisy signals were constructed. Technique for the evaluation of the non-linear dynamics of the time-series based on the relationship between MPE and MWPE and optimal non-uniform embedding was proposed. Technique for the evaluation of the 2D signals based on the weighted and truncated Shannon entropy was proposed. Results of the proposed forecasting algorithm were compared with the results of other classical and state of the art forecasting techniques. The results were published in 1 paper, presented at 2 conferences and at the meeting of Lithuanian young mathematicians.
Period of project implementation: 2020-04-14 - 2020-12-31
