In this paper we present a novel similarity measure method for financial data in automatic trading context. The differences in length of compared ranks, the occurrence of delays, inactive sessions, random fluctuations and noises included in trends cause that method based on second order statistics or metric distance often give improper results and require rather human insight or individual supervision.

In our approach, we propose assessment of the similarity in a coherent, hierarchical and multi-faceted way, following the general scheme where various detailed basic measures may be used. Our method allows to assess the similarity between the individual signals as well as their groups. Such approach shows data similarity in a flexible way close to human perception and allows the direct calculation, does not require learning (optimization) on specific prototypes which is typical for methods of artificial intelligence.

As the basic measures we apply divergence functions like the Fermi-Dirac divergence and Bose-Einstein divergence which allow us to explore symmetric properties of signals. Those properties are crucial elements of our general scheme where mutual and self-similar signals characteristics are interpreted in terms of symmetricity.   

We also propose a new basis measure based on a concept of self and mutual signal smoothness which in some sense can be interpreted as an effect of the point-to-point shifts in the phase space. In our general similarity scheme this measure can be an alternative to divergence functions.  

From applicative point of view a special attention is paid to the resemblance to random noise which is often a difficult task in terms of financial signals due to the fact that typical returns are often close to mathematical white noise models. The whole concept is illustrated with computer research on both simulated data and practical data from financial markets.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/31824 must be provided.

1. Analysis of financial time series morphology with AMUSE algorithm and its extensions