Analysis of Cryptocurrency Time Series and Forecasting of Volatility Changes Using LSTM Neural Networks and Multifractal Analysis Methods

Abstract

The paper examines the volatility dynamics of Bitcoin, Ether, XRP, and Solana as an indicator of market risk. Cryptocurrency price series are variable and non-stationary, which limits the accuracy of risk forecasting. The methodology combines long-memory estimation, multifractal analysis, and neural network modelling. Using daily data, returns, absolute returns, and 30-day rolling volatility were calculated. Bitcoin showed the lowest average volatility, 0.0326, whereas Solana showed the highest, 0.0554; Ether and XRP reached 0.0428 and 0.0458, respectively. The long-memory parameter of price series ranges from 0.4788 to 0.5420, while volatility series exhibit moderate long memory of 0.2326–0.2964 and confirmed stationarity. XRP showed the widest multifractal volatility spectrum, 1.2651. A distinctive feature of the proposed approach is the use of LSTM models with market, lagged, and dynamic fractal features constructed within a rolling window. Forecasting was performed for 1-, 3-, 7-, and 14-day horizons, and the results were aggregated over 12 repeated training runs. Comparison of LSTM models with and without fractal features showed that their forecasting contribution depends on the feature construction method, while volatility-based features were generally more informative. Comparison with GARCH, ARFIMA, and HAR showed that performance depends on the asset, horizon, and evaluation metric.