This study investigates the application of the Light Gradient Boosting Machine (LGBM) model for both deterministic and probabilistic forecasting of Bitcoin realized volatility. Utilizing a comprehensive set of 69 predictors -- encompassing market, behavioral, and macroeconomic indicators -- we evaluate the performance of LGBM-based models and compare them with both econometric and machine learning baselines. For probabilistic forecasting, we explore two quantile-based approaches: direct quantile regression using the pinball loss function, and a residual simulation method that transforms point forecasts into predictive distributions. To identify the main drivers of volatility, we employ gain-based and permutation feature importance techniques, consistently highlighting the significance of trading volume, lagged volatility measures, investor attention, and market capitalization. The results demonstrate that LGBM models effectively capture the nonlinear and high-variance characteristics of cryptocurrency markets while providing interpretable insights into the underlying volatility dynamics.
This research investigates the dynamics of connectedness among cryptocurrency and various risk factors, including oil price demand and supply shocks, EPU, GPR, and the ADS business conditions index using the quantile time-frequency connectedness approach. The findings reveal that cryptocurrency behaves as a net receiver of shocks in the short term but transitions to a net transmitter over the long term. Critical sources of both short- and long-term shocks are attributed to oil price demand, supply fluctuations, and GPR. However, during extreme events like the COVIDâ19 pandemic and the Russia-Ukraine war, cryptocurrency, oil shocks, and other indices alternately become net transmitters and receivers of shocks depending on time frames and quantile ranges. During periods of heightened market uncertainty, monitoring the interconnected behavior of these variables is critical for investors and policymakers aiming to predict market shifts and manage risks effectively.
This study proposes a hybrid model that integrates Wavelet frequency decomposition, convolutional neural networks (CNNs), and Transformers to predict correlation structures among eight major cryptocurrencies. The Wavelet module decomposes asset time series into short-, medium-, and long-term components, enabling multi-scale trend analysis. CNNs capture localized correlation patterns across frequency bands, while the Transformer models long-term temporal dependencies and global relationships. Ablation studies with three baselines (WaveletâCNN, WaveletâTransformer, and CNNâTransformer) confirm that the proposed WaveletâCNNâTransformer (WCT) consistently outperforms all alternatives across regression metrics (MSE, MAE, RMSE) and matrix similarity measures (Cosine Similarity and Frobenius Norm). The performance gap with the WaveletâTransformer highlights CNNâs critical role in processing frequency-decomposed features, and WCT demonstrates stable accuracy even during periods of high market volatility. By improving correlation forecasts, the model enhances portfolio diversification and enables more effective risk-hedging strategies than volatility-based approaches. Moreover, it is capable of capturing the impact of major events such as policy announcements, geopolitical conflicts, and corporate earnings releases on market networks. This capability provides a powerful framework for monitoring structural transformations that are often overlooked by traditional price prediction models.
StanisĹaw DroĹźdĹź, Robert KluszczyĹski, JarosĹaw KwapieĹ, Marcin WÄ torek
Multifractality in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital currency markets, multifractal properties arise due to the interplay of long-range temporal correlations and heavy-tailed distributions of returns, reflecting intricate market microstructure and trader interactions. Incorporating multifractal analysis into the modeling of cryptocurrency price dynamics enhances the understanding of market inefficiencies, may improve volatility forecasting and facilitate the detection of critical transitions or regime shifts. Based on the multifractal cross-correlation analysis (MFCCA) whose spacial case is the multifractal detrended fluctuation analysis (MFDFA), as the most commonly used practical tools for quantifying multifractality, in the present contribution a recently proposed method of disentangling sources of multifractality in time series was applied to the most representative instruments from the digital market. They include Bitcoin (BTC), Ethereum (ETH), decentralized exchanges (DEX) and non-fungible tokens (NFT). The results indicate the significant role of heavy tails in generating a broad multifractal spectrum. However, they also clearly demonstrate that the primary source of multifractality are temporal correlations in the series, and without them, multifractality fades out. It appears characteristic that these temporal correlations, to a large extent, do not depend on the thickness of the tails of the fluctuation distribution. These observations, made here in the context of the digital currency market, provide a further strong argument for the validity of the proposed methodology of disentangling sources of multifractality in time series.
The Generalized Tempered Stable (GTS) distribution extends classical stable laws through exponential tempering, preserving the power-law behavior while ensuring finite moments. This makes it especially suitable for modeling heavy-tailed financial data. However, the lack of closed-form densities poses significant challenges for simulation. This study provides a comprehensive and systematic comparison of GTS simulation methods, including rejection-based algorithms, series representations, and an enhanced Fast Fractional Fourier Transform (FRFT)-based inversion method. Through extensive numerical experiments on major financial assets (Bitcoin, Ethereum, the S&P 500, and the SPY ETF), this study demonstrates that the FRFT method outperforms others in terms of accuracy and ability to capture tail behavior, as validated by goodness-of-fit tests. Our results provide practitioners with robust and efficient simulation tools for applications in risk management, derivative pricing, and statistical modeling.
This study provides an in-depth analysis of the dynamic connectedness between G7 stock market indices, traditional cryptocurrencies (Bitcoin, Ethereum), gold, digital gold (PAXG, XAUT), and companies specializing in artificial intelligence (AI). Covering the period from 2020 to 2024, the analysis focuses on four distinct periods: the COVID-19 pandemic, the Russia-Ukraine conflict, the banking crisis triggered by the collapse of Silicon Valley Bank in March 2023 and the speculative rise in the gold markets in 2024. The methodology employs a Quantile Vector Autoregressive (QVAR) connectivity approach, starting with the median quantile and systematically extending to various quantiles to capture the entire distribution of connectedness under different market conditions. Our results reveal significant fluctuations in the Total Connectivity Index (TCI) during the studied crises and demonstrate how the roles of key assetsâBitcoin, Ethereum, gold, PAXG, XAUT, and AI firmsâshift between being net emitters and receivers of shocks. These shifts underscore the importance of asset selection in crafting effective hedging strategies. Specifically, we observe that G7 investors adopt varying diversification strategies depending on their domestic market conditions and the specific crisis period. The study highlights that assets for diversification and risk reduction vary by country and crisis. Traditional cryptocurrencies and AI companies in general emerge as promising diversification tools, especially in times of technological disruption and economic uncertainty. Several financial implications for investors and policymakers are proposed, providing insights for optimizing portfolio resilience in the face of global market volatility.
Arthur Rodrigues Pereira de Carvalho, Felipe Quintino, Helton Saulo, Luan Carlos de Sena Monteiro Ozelim ¡ 6 authors
This study introduces and evaluates stochastic models to describe Bitcoin price dynamics at different time scales, using daily data from January 2019 to December 2024 and intraday data from 20 January 2025. In the daily analysis, models based on are introduced to capture long memory, paired with both constant-volatility (CONST) and stochastic-volatility specifications via the CoxâIngersollâRoss (CIR) process. The novel family of models is based on Generalized OrnsteinâUhlenbeck processes with a fluctuating exponential trend (GOU-FE), which are modified to account for multiplicative fBm noise. Traditional Geometric Brownian Motion processes (GFBM) with either constant or stochastic volatilities are employed as benchmarks for comparative analysis, bringing the total number of evaluated models to four: GFBM-CONST, GFBM-CIR, GOUFE-CONST, and GOUFE-CIR models. Estimation by numerical optimization and evaluation through error metrics, information criteria (AIC, BIC, and EDC), and 95% Expected Shortfall (ES95) indicated better fit for the stochastic-volatility models (GOUFE-CIR and GFBM-CIR) and the lowest tail-risk for GOUFE-CIR, although residual analysis revealed heteroscedasticity and non-normality. For intraday data, Exponential, Weibull, and Generalized Gamma Autoregressive Conditional Duration (ACD) models, with adjustments for intraday patterns, were applied to model the time between transactions. Results showed that the ACD models effectively capture duration clustering, with the Generalized Gamma version exhibiting superior fit according to the CoxâSnell residual-based analysis and other metrics (AIC, BIC, and mean-squared error). Overall, this work advances the modeling of Bitcoin prices by rigorously applying and comparing stochastic frameworks across temporal scales, highlighting the critical roles of long memory, stochastic volatility, and intraday dynamics in understanding the behavior of this digital asset.
Traditional portfolio optimization models, rooted in the meanâvariance framework of Markowitz, rely heavily on variance as a risk measure. Although theoretically elegant, this approach becomes fragile in volatile and structurally unstable markets such as cryptocurrencies, where return distributions deviate significantly from normality, cor-relations are unstable, and concentration risk emerges. These limitations have motivated the search for alternative frameworks capable of capturing uncertainty in a more flexible and distribution-free manner. Entropy, originally introduced by Shannon as a measure of information, has gradually been recognized in the financial literature as a suitable proxy for diversification and systemic uncertainty. To address the shortcomings of variance-based models, this paper introduces the Weighted Shannon Entropy (WSE) model as a diversification-oriented alternative. By extending the classical Shannon entropy with asset-specific informational weights, the WSE framework provides additional flexibility for modeling heterogeneous asset char-acteristics, such as liquidity, informational value, or perceived reliability. Using the principle of maximum entropy and the method of Lagrange multipliers, we derive ex-ponential-form solutions for portfolio weights that naturally discourage concentration, ensure balanced allocations, and remain analytically tractable. The methodology is validated empirically on a portfolio of four leading cryptocurren-ciesâBitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)âusing market data from January to March 2025. The results demonstrate that the entropy-based optimization framework produces well-diversified portfolios, robust to volatility and structural instability, and provides a distribution-free alternative to the classical meanâvariance model. Beyond its empirical performance, the WSE formulation highlights the conceptual advantage of entropy in integrating return, risk, and diversification into a single unified framework. The paper contributes both theoretically and practically: it strengthens the mathematical foundation of entropy-based portfolio selection, extends its applicability to digital asset markets, and illustrates how weighting schemes can enrich the classical Shannon measure. Future research may extend this approach to multi-period optimization, gen-eralized entropies such as Tsallis and Kaniadakis, or integration with machine learning models for dynamic portfolio management.
This study is the first to integrate recurrence plots, recurrence quantification analysis (RQA) and short-time Fourier Transform (STFT) to predict cryptocurrency market behaviour. Recurrence plots, RQA statistics and STFT spectrograms were calculated from return data and used as input in random forest algorithms as they are optimal tools for identifying non-linear dynamics in market data and analyse their frequency. Our optimised XGBoost algorithm provided a forecasting AUC above 76.7% and accuracy of 70% in predicting increasing or decreasing returns. This highlights the modelâs ability to support cryptocurrency investment decision-making within an interpretable machine learning framework.
In the scholarly literature on financial services, the prevailing paradigm over the past century was the supply of lending, borrowing, trading, and investment by regulated intermediaries, i.e. mainly banks, brokers and exchanges. These are institutions, which operate under a known regulatory structure that assumes homogeneity in their operations. Most recently, the fusion of an entirely new set of technologies such as Decentralized Finance (DeFi) has been changing the sector in a very fundamental way. Blockchain technology currently provides a framework, with the help of which financial applications can perform the transaction process automatically without the existence of central power and, thus, create an environment that is transparent and available.
Cryptocurrency markets are characterized by ex-treme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, underscoring the importance of probabilistic approaches. To address this limitation, this paper introduces probabilistic fore-casting methods that leverage point forecasts from a wide range of base models, including statistical (HAR, GARCH, ARFIMA) and machine learning (e.g. LASSO, SVR, MLP, Random Forest, LSTM) algorithms, to estimate conditional quantiles of cryp-tocurrency realized variance. To the best of our knowledge, this is the first study in the literature to propose and systematically evaluate probabilistic forecasts of variance in cryptocurrency markets based on predictions derived from multiple base models. Our empirical results for Bitcoin demonstrate that the Quantile Estimation through Residual Simulation (QRS) method, partic-ularly when applied to linear base models operating on log-transformed realized volatility data, consistently outperforms more sophisticated alternatives. Additionally, we highlight the robustness of the probabilistic stacking framework, providing comprehensive insights into uncertainty and risk inherent in cryptocurrency volatility forecasting. This research fills a sig-nificant gap in the literature, contributing practical probabilistic forecasting methodologies tailored specifically to cryptocurrency markets.
This study analyzes the volatility of Bitcoin using stochastic volatility models fitted to one-minute transaction data for the BTC/USDT pair between 1 April 2023, and 31 March 2024. Bernstein polynomial terms were introduced to accommodate intraday and intraweek seasonality, and flexible return distributions were used to capture distributional characteristics. Seven return distributionsânormal, Student-t, skew-t, Laplace, asymmetric Laplace (AL), variance gamma, and skew variance gammaâwere considered. We further incorporated explanatory variables derived from the trading volume and price changes to assess the effects of order flow. Our results reveal structural market changes, including a clear regime shift around October 2023, when the asymmetric Laplace distribution became the dominant model. Regression coefficients suggest a weakening of the volumeâvolatility relationship after September and the presence of non-persistent leverage effects. These findings highlight the need for flexible, distribution-aware modeling in 24/7 digital asset markets, with implications for market monitoring, volatility forecasting, and crypto risk management.
This study utilizes version 6 of the regression analysis of time series (RATS) software package to implement the estimation of the bivariate diagonal generalized autoregressive conditional heteroscedasticity (GARCH) model combined with a composite asset selection approach including two hybrid performance measures to solve âthe trade-off problem between return and riskâ and âthe inconsistent results from different performance measuresâ in the problem of asset allocation within a group of minimum variance portfolios during the pre-COVID-19 and COVID-19 periods. Empirical results show that the optimal portfolios obtained from this approach and the assets added to a portfolio to achieve better performance differ between the pre-COVID-19 and COVID-19 periods. For instance, the optimal portfolios are the Chinese yuan-Ethereum and Bitcoin-Ethereum for the pre-COVID-19 period, but the WTI-Ethereum for the COVID-19 period. To achieve better performance, we added Ethereum to our portfolio during the pre-COVID-19 period, while WTI and Bitcoin were added during the COVID-19 period. Thus, the COVID-19 pandemic had a significant impact on the performance of asset allocation in the three markets. The proposed approaches in this study can be embedded in a computer as an asset allocation algorithm of Robo-advisers.
Cryptocurrency markets are highly volatile, creating challenges for accurate risk management and forecasting. As digital assets become more integrated into financial systems, understanding their volatility dynamics is essential for investors and policymakers. Previous research has primarily applied standard GARCH models to cryptocurrencies, often neglecting advanced specifications that capture asymmetry, regime-switching, and long-memory effects. This limits the accuracy of volatility forecasts and fails to reflect the unique behaviour of digital assets. This study aims to identify the most effective GARCH-class models for forecasting volatility in Bitcoin, Ethereum, Binance Coin, and Ripple. We analyse daily returns from August 2017 to December 2024, applying eight advanced GARCH specifications: EGARCH, GJR-GARCH, FIGARCH, HYGARCH, MSGARCH, CS-GARCH, and Log-GARCH. Hyperparameter tuning is conducted via grid search across lag orders (p, q â [1, 5]), mean equations, and error distributions. Model performance is evaluated using AIC, BIC, RMSE, and MAE. Results show that MSGARCH and EGARCH outperform symmetric and short-memory models, highlighting the importance of regime-switching and leverage effects. FIGARCH provides the best fit for Bitcoin and Ethereum, confirming long-memory persistence. Skewed Studentâs t and GED distributions improve accuracy by capturing heavy tails and asymmetry. These findings demonstrate the limitations of standard GARCH models and underscore the value of advanced specifications in modelling cryptocurrency volatility. The study offers practical insights for traders and risk managers, contributing to more robust forecasting in non-stationary markets. Advanced GARCH models significantly enhance volatility prediction for digital assets. Future research could extend this framework to other speculative instruments or integrate machine learning techniques to further improve performance.
Introduction This article presents a method for short-term cryptocurrency price forecasting utilizing news headlines. Methods The study analyzes the impact of news on asset prices within one hour of publication, employing machine learning-based classification with BERT and GPT models, as well as GloVe vector representations. Results The proposed cascade classifier model enhances prediction accuracy by initially assessing the strength of a news item and subsequently forecasting the direction of price movement. Experimental results demonstrate the effectiveness of the developed classification model. Discussion The model achieves an accuracy of 79% in predicting price movements, confirming the potential of leveraging news headlines to improve short-term forecasts in cryptocurrency markets.
This paper develops a novel modeling framework that integrates time-varying quantile-based spillover effects into a regime-switching realized volatility model. A dynamic spillover factor is constructed by identifying the most influential contributors to Bitcoinâs realized volatility across different quantile levels. This quantile-layered structure enables the model to capture heterogeneous spillover paths under varying market conditions at a macro level while also enhancing the sensitivity of volatility regime identification via its incorporation into a time-varying transition probability (TVTP) Markov-switching mechanism at a micro level. Empirical results based on the cryptocurrency market demonstrate the superior forecasting performance of the proposed TVTP-MS-HAR model relative to standard benchmark models. The model exhibits strong capability in identifying state-dependent spillovers and capturing nonlinear market dynamics. The findings further reveal an asymmetric dual-tail amplification and time-varying interconnectedness in the spillover effects, along with a pronounced asymmetry between market capitalization and systemic importance. Compared to decomposition-based approaches, the X-RV type of modelsâespecially when combined with the proposed quantile-driven factorâoffers improved robustness and predictive accuracy in the presence of extreme market behavior. This paper offers a coherent approach that bridges phenomenon identification, source localization, and predictive mechanism construction, contributing to both the academic understanding and practical risk assessment of cryptocurrency markets.
Abstract ValueâatâRisk (VaR), the primary measure of downside risk in market risk management, relies heavily on the accuracy of volatility forecasts produced by risk models. This paper shows that, for forecasting the VaR of cryptocurrencies, the timeâheterogeneous Student's t autoregressive model outperforms standard models commonly used by practitioners.
Abstract Cryptocurrency markets have evolved into a vital segment of the global financial ecosystem, drawing considerable interest from both investors and regulatory bodies. Yet, their extreme price instability demands innovative strategies for risk mitigation and investment that diverge from conventional financial practices. This research focuses on analyzing the volatility patterns of leading cryptocurrenciesâBitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB)âby employing GARCH-family models such as GARCH, EGARCH, TGARCH, and CGARCH. Through a comparative evaluation of these models, the study identifies the optimal framework for characterizing cryptocurrency market volatility. Utilizing daily closing prices from Yahoo Finance (January 1, 2019, to January 8, 2025), the analysis reveals that TGARCH outperforms others for BTC, EGARCH for ETH, and CGARCH for BNB, underscoring the critical role of asymmetric volatility in these markets. This work advances existing research by offering a detailed comparison of GARCH-based approaches and practical insights for risk evaluation and portfolio optimization.
Abstract The approval of Bitcoin ETFs by the Securities and Exchange Commission (SEC) on 01/11/2024 was an essential event for both the cryptocurrency market and the traditional financial system. Bitcoin ETFs work as a bridge between digital assets and traditional financial instruments, contributing to increased liquidity and attracting new institutional investors who were reluctant before due to regulatory and security concerns. This study assesses the impact of the approval of Bitcoin ETFs on the stability of the financial system, focusing on the correlations and the volatility spillover effects of Bitcoin and three major financial indices (S&P 500, Dow Jones Industrial Average, and Nasdaq-100). Using Pearson Correlation, Time-Varying Parameter Vector Autoregression (TVP-VAR) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, this research offers a comprehensive analysis of the influence of Bitcoin on the dynamics of market. The results show that, although the correlations between Bitcoin and stock market indices reached a peak in 2021, they dropped later, suggesting a gradual decoupling from traditional financial markets. However, after the launch of Bitcoin ETFs in 2024, the correlations with financial indices â especially with S&P 500 â started to rise again, suggesting a reintegration of Bitcoin into the traditional financial system. Contrary to initial expectations, the results obtained from data covering 90 days before and after the launch of Bitcoin ETFs donât show a significant increase in short-term correlations, which suggest a smooth adaptation of the market to these new financial instruments. In addition, although Bitcoin ETFs contribute to the stabilization of cryptocurrency volatility, they introduced new types of intra-day fluctuations, highlighting the need for an advanced strategy of risk management. The study concludes that, while Bitcoin ETFs contribute to the stability of financial markets, they introduce systemic risks which require continuous surveillance from the regulatory authorities. Long-term implications of the approval of Bitcoin ETFs remain uncertain, hence more research is needed in order to comprehensively assess the impact of these new financial instruments on the global financial stability.
This study compares two approaches for measuring Conditional Value-atRisk (CoVaR), emphasizing the role of high-frequency intraday data in assessing systemic risk within financial systems. The first approach, AB CoVaR, estimates the risk of an asset Y conditional on another asset X being exactly at its Value-at-Risk (VaR) threshold. In contrast, the GE CoVaR refines this measure by capturing the risk of Y when X exceeds its VaR threshold, thereby accounting for more extreme scenarios and larger potential losses. To estimate these CoVaR measures, we employ high-frequency data sampled at five-minute intervals from major cryptocurrencies, including Bitcoin, Ethereum, Ripple, Solana, and Binance Coin. The results indicate that the GE CoVaR approach systematically yields higher risk estimates and exhibits superior predictive performance when applied to intraday data. Moreover, the analysis reveals strong interconnectedness among cryptocurrency returns. Bitcoin and Ethereum emerge as the primary sources of systemic risk, whereas Solana and Binance Coin are the most heavily affected assets. These findings underscore the granular risk dynamics captured through intraday analysis.
Bitcoin and other cryptocurrency returns show higher volatility than equity, bond, and other asset classes. Increasingly, researchers rely on machine learning techniques to forecast returns, where different machine learning algorithms reduce the forecasting errors in a high-volatility regime. We show that conventional time series modeling using ARMA and ARMA GARCH run on a rolling basis produces better or comparable forecasting errors than those that machine learning techniques produce. The key to achieving a good forecast is to fit the correct AR and MA orders for each window. When we optimize the correct AR and MA orders for each window using ARMA, we achieve an MAE of 0.024 and an RMSE of 0.037. The RMSE is approximately 11.27% better, and the MAE is 10.7% better compared to those in the literature and is similar to or better than those of the machine learning techniques. The ARMA-GARCH model also has an MAE and an RMSE which are similar to those of ARMA.
Portfolio optimization is a fundamental problem in financial theory, aiming to balance risk and return in asset allocation. Traditional models, such as MeanâVariance optimization, are effective, but often fail to account for diversification adequately. This study introduces the MeanâVarianceâEntropy (MVE) model, which integrates Tsallis entropy into the classic MeanâVariance framework to enhance portfolio diversification and risk management. Entropy, specifically second-order entropy, penalizes excessive concentration in the portfolio, encouraging a more balanced and diversified allocation of assets. The model is applied to a portfolio of five major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Solana (SOL), Cardano (ADA), and Binance Coin (BNB). The performance of the MVE model is compared with that of the traditional MeanâVariance model, and results demonstrate that the entropy-enhanced model provides better diversification, although with a slightly lower Sharpe ratio. The findings suggest that while the entropy-adjusted model results in a slightly lower Sharpe ratio, it offers better diversification and a more resilient portfolio, especially in volatile markets. This study demonstrates the potential of incorporating entropy into portfolio optimization as a means to mitigate concentration risk and improve portfolio performance. The approach is particularly beneficial for markets such as cryptocurrency, where volatility and asset correlations fluctuate rapidly. This paper contributes to the growing body of literature on portfolio optimization by offering a more diversified, robust, and risk-adjusted approach to asset allocation
This study examines and compares the effectiveness of GARCH (Generalized Autoregressive Conditional Heteroskedasticity) and EGARCH (Exponential GARCH) models in forecasting volatility across three distinct financial markets: cryptocurrencies, Indonesian stocks, and U.S. stocks. The research analyzes daily closing price data from April 2018 to September 2024, focusing on five major cryptocurrencies (Bitcoin, Ethereum, Tether, Binance Coin, and Ripple), five Indonesian blue-chip stocks (BBCA, BBRI, BYAN, BMRI, and TPIA), and five major U.S. stocks (Apple, Nvidia, Microsoft, Google, and Amazon). Using comparative analysis of ARCH(1), GARCH(1,1), and EGARCH(1,1,1) models, the study evaluates their predictive accuracy through multiple metrics including AIC, MAE, RMSE, and SMAPE. Results indicate that EGARCH(1,1,1) generally performs better for cryptocurrencies and U.S. stocks, while GARCH(1,1) shows superior performance for Indonesian stocks, suggesting that volatility patterns and optimal forecasting models vary across different market contexts.
This paper investigates the volatility dynamics and underlying long memory features of four major cryptocurrencies-Bitcoin, Ethereum, Litecoin, and Ripple-which were selected due to their high liquidity, large trading volumes, and historical significance in the digital asset market. The long-range dependence exhibited in cryptocurrency markets is often overlooked. However, based on the strong evidence of persistent dependence in the return series, we adopt advanced volatility models that are capable of accommodating high volatility and heavy-tails, as well as the long memory properties of cryptocurrencies. Specifically, we employ long-memory extensions of the GAS (Long memory GAS) and GARCH (Fractionally Integrated Asymmetric Power ARCH) models, integrating heavy-tailed innovation distributions: the Generalized Hyperbolic Distribution (GHD) and Generalized Lambda Distribution (GLD). Standard GARCH and GAS models are included as benchmarks. The performance of the models are assessed using Value-at-Risk (VaR) estimation, backtesting (in-sample and out-of-sample) and volatility forecasting metrics. The results indicate that long memory models, particularly the FIAPARCH model, consistently outperforms the standard GAS and GARCH models in capturing tail risk and the volatility persistence. These findings emphasize the critical role of long memory in modeling the risk of cryptocurrencies, indicating that accounting for volatility persistence can significantly enhance the accuracy of risk estimates and strengthen risk management practices.