Estimating time series future optima using a steepest descent methodology as a backtracker

Abstract

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.

Advancing the Backtrack Optimization Technique to Obtain Forecasts of Potential Crisis Periods

“…In [3] was discussed the similarity between a time series and an objective function; based on this realization the usage of calculus tools-such as the local Lipschitz continuity-was extended to time series analysis, too.…”

“…Specifically, the indicator is approximated over a time series constructed from deductions of the local estimations of the Lipschitz constant, and results to the usage of the Lipschitz constant as the sole crisis indicator. The research of the local Lipschitz constant was motivated from previous realizations [3], where it was observed that a time series holds functional properties.…”

“…Recall that the Lipschitz constant is a function's constant that when is used in optimization it enables the acceleration of the optima search [15]; so the concept used in this study [3] was based on the measuring of a time series changes' acceleration in means of changes that the values of the local Lipschitz-made series suffer.…”

“…The findings provided in [17] regarding the different convergence region according to the optimization technique used, motivated researching two techniques for the generation of an interval. The concept of the combinatory application of two techniques was further synthesized with the findings of [3] where the accommodation of time-oriented forecasts was succeeded based on the backtrack technique.…”

“…T T T        . The realization resulted in [3], that any time series may be regarded equivalent to an objective function subject to the factors affecting its price, motivated the research of time series optimization for forecasting. Thus, in [4] the crisis forecasting issue was dealt under the perspective of approximating significant changes of a time series that consists of estimations of the local Lipschitz constant.…”