Time-series analysis using orthogonal polynomials

Advances in the study of non-linear dynamics have encouraged the construction of models and simulators of non-linear time-series. Researchers in the field of both science and statistics have come up with innovative methods that are useful in extracting information from systems that exhibit non-linear dynamics. Time-series, as we all know, is the sequence x1, x2, x3,…x11 observed in time. Time-series analysis depends on the fact that data points taken over time may have internal structure such as autocorrelation, trend or seasonal variation. It is these properties that make model construction possible.

As part of this research, the Measure Based approach to reconstruction, proposed by Giona [1], is investigated. This method is based on the Fourier expansion of the polynomial system 11 orthonormal to the invariant measures. Programs have been written based on the MB approach and these programs were tested on various one dimensional time-series like the sine map, the tent map and the logistic map. This approach to reconstruction furnishes good results when applied to chaotic one dimensional time-series.