Fraktalna analiza finansowych szeregów czasowych z wykorzystaniem wymiaru fraktalnego oraz punktowych wykładników Höldera

Abstract

A b s t r a c t. This paper presents a fractal analysis application to the verification of assumptions of Fractal Market Hypothesis and the presence of fractal properties in financial time series. In this research, the box-counting dimension and pointwise Hölder exponents are used. Achieved results lead to interesting observations related to nonrandomness of price series and occurrence of relationships binding fractal properties and variability measures with the presence of trends and influence of the economic situation on financial instruments' prices. K e y w o r d s: fractal analysis, fractal dimension, box-counting dimension, pointwise Hölder exponents, Hurst exponent.

The (In)Efficiency of Emerging and Developed Markets: An Analysis from Fractal Theory

“…In times of market stress, there is a tendency to reduce the randomness of returns, which implies a reduction in market efficiency, which is later reestablished. This finding is consistent with previous studies, such as Lahmiri and Bekiros (2020) and Kapecka (2013).…”

“…The oscillatory behavior and the values of the index prices reflect a loss of informational efficiency. The oscillatory behavior and values of the EIs were also found in previous studies, such as those of Kristoufek and Vosvrda (2014) and Kapecka (2013). In addition, although not very expressively, it is possible to identify that, in general, the BRICS countries have a higher concentration of EI < 0,2.…”

A Comparative Study of Financial Crises: Fractal Dissection of Investor Rationality

“…The long memory was found for the sample period of study. An important observation supporting the non-randomness of the markets was revealed by Kapecka (2013) wherein they established a relationship between fractal properties of the investigated time series and the underlying economic situation.…”

Application of the Surface Division Method to Segregate Investments in Capital Markets for Shares‘ Portfolio

“…Today, the fractal dimension is used to describe many natural phenomena (Cervantes-De la Torre, González-Trejo, Real-Ramírez and Hoyos-Reyes, 2013), spatial planning (Guoqiang, 2002;Chen, 2013), medical problems (Gómez, Mediavilla , Hornero, Abásolo and Fernández, 2009;Harne, 2014) or economic (Bhatt, Dedania and Shah, 2015;Kapecka, 2013). The methodology of estimating the fractal dimension is also being developed (Sy-Sang and Feng-Yuan, 2009).…”