Abstract
In this paper, we undertake the problem of evaluating interrelation among time series. Interrelation is measured using a similarity index. In this paper, we suggest a new one based on the known fuzzy transform (F-transform), which has been proven to remove higher frequencies than a given threshold and reduce the random noise significantly. The F-transform also provides an estimation of the slope of time series in a given imprecisely delineated time. We prove some of the suggested index properties and show its ability to measure similarity (and thus the interrelation) on a selection of several real financial time series. The method is well interpretable and easy to adjust.
Highlights
Time series form a topic of research that has been widely studied for many years
Analysis of time series in theoretical and practical aspects is an crucial part of the study of stock markets
In recent decades, worldwide economies have become increasingly related to each other. Various phenomena such as politics, social media platforms, and even pandemics can influence a set of financial time series
Summary
Time series form a topic of research that has been widely studied for many years (for some recent references, see [1,2,3,4,5]). Many researchers aim to improve his method concerning the clustering algorithm or the distance measure itself in continuation of his work. This can be briefly described as follows. The similarity between two-time series should not be computed based on their values only and based on the corresponding slopes This is important in the stock market because relative variations in the price values affect the trading performance. The parameters of the F-transform can be set in such a way that the approximating function fhas the desired properties These properties make the F-transform suitable for applications in various tasks when processing time series. More about F-transform and its applications can be found in [24]
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