Recently it was produced a backtrack technique for the efficient approximation of a time series' future optima. Such an estimation is succeeded based on a selection of sequenced points produced from the repetitive process of the continuous optima finding. Additionally, it is shown that if any time series is treated as an objective function subject to the factors affecting its future values, the use of any optimization technique finally points local optimum and therefore enables accurate prediction making. In this paper the backtrack technique is compiled with a steepest descent methodology towards optimization.

Financial crisis is an unfortunate reality that overshadows any financial system regardless its profitability and the level it functions. The appearance of crises across financial markets, especially during the 1990s that the internationalized markets adopted a rather approachable character, imposed severe costs in financial and social systems. With this paper is proposed the generation of a future interval of time that is vulnerable to enclose the burst of a financial crisis. A time series consisted of approximations of the local Lipschitz constant is examined and in the proposed forecasting approach this constant holds the crisis indicator role. Further the application of two different optimization techniques over the Lipschitz-made time series results to the generation of a future period of time; this interval is likely to envelop the burst of a forthcoming crisis. The usage of a future interval of time empowers the predicting ability of the methodology by providing warning signs priory to the actual crisis burst. To this direction, the obtained results offer strong evidence that the method may be characterized as an Early Warning System (EWS) for financial crisis prediction