A Comparison of Two Hölder Regularity Functions to Forecast Stock Indices by ANN Algorithms

Abstract

This study is concerned with local Hölder exponent as a function regularity measure for time series regarding Finance data. The study examines 12 attributes in the Micro, Small and Medium Enterprises (MSME) data for 6 regions (2004–2018). The study has two different approaches. Firstly, (i) multi fractal methods and Brownian motion Hölder regularity functions were used for the identification of the significant and self-similar attributes in the Finance dataset. The steps are: (a) polynomial functions were applied on the Finance dataset and p _ finance dataset was obtained. (b) exponential functions were applied and e _ Finance dataset was obtained. Secondly, (ii) Artificial Neural Network (ANN) algorithms ((Feed Forward Back Propagation (FFBP) and Cascade Forward Back Propagation (CFBP)) were applied on both datasets in a and b. Finally, (iii) classification accuracy rates as per the outcomes obtained from the second stage by the ANN algorithms were compared. Our study has been conducted for the first time in the literature since with the ANN algorithms’ application, it revealed how the most significant attributes are identified in the Finance dataset by Hölder functions (polynomial as well as exponential).