TIME SERIES ANALYSIS USING FRACTAL THEORY

Abstract

Davit Aludauri E-mail: davit.aludauri@gmail.com PhD student , Ivane Javakhishvili Tbilisi State University Tbilisi, Georgia https://orcid.org/0009-0000-7960-9668 Givi Bedianashvili E-mail: givi.bedianashvili@tsu.ge Doctor of Economic Sciences, associate professor Ivane Javakhishvili Tbilisi State University Tbilisi, Georgia https://orcid.org/0000-0003-4521-737X Giorgi Rakviashvili E-mail: giorgi.rakviashvili@iliauni.edu.ge Doctor of Mathematics, Associate Professor Ilia State University Tbilisi, Georgia https://orcid.org/0009-0003-3888-5019 Abstract. Financial markets have become a center of attention and a field of study for over a century, especially nowadays when there is an abundance of data about them, however, behavior of financial markets still stays as mystery and a field that is rife with unpredictability and uncertainty. There are many methods and techniques for analyzing time series data. Due to the fact that prices are formed by decisions made by millions of people across the planet the price in itself holds the reflection of all of those decisions which itself is a natural process. Therefore, we can look at the financial data as a fractal object and analyze them. Method that has been primarily used to analyze time series is fractal dimension which we can use to measure of the time series, in other words, we can measure how correlated is the time series and thus have an opinion about its future behavior. As we later find out, fractal dimension provides interesting insights into the time series and most importantly, it is a method that can analyze pictures and thus it is not restricted by data formats. Keywords: Uncertainty, Time series, Fractals, Fractal Dimension, Autocorrelation, Hurst Exponent JEL classification: C1, C22, C32, D81