| Abstract [eng] |
The examination of financial markets behaviour crucial part of the financial investments theory. The methods for analyzing the financial, markets established in the 1960's and 1970's, were valid only during periods of stable market conditions. They are based on the assumption that the financial market's behaviour is subject to the normal distribution law. In the nineties began to look at this problem from the point of view of fractal analysis. It was observed that financial time series have the property of self-similarity. In this paper, we have tested long memory property for the five biggest cryptocurrencies: Bitcoin, Ethereum, Binance Coin, XRP, and Cardano. This thesis studies persistence and volatility using R/S analysis was carried out. Our findings show that four out of five cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) extensions as a suitable modeling technique. In this paper, the Fractionally Integrated GARCH (FIGARCH) models, with skewed student distribution, were produced and compared with GARCH models. Models were compared using Akaike information criteria, which indicated the improvement of the model's fitness. The paper ends with some concluding remarks and future directions of research. |
