The rapid growth of cryptocurrency markets has created new challenges in understanding and predicting the structural dynamics of digital asset prices. Bitcoin, as the most traded blockchain-based currency, exhibits extreme volatility, nonlinear patterns, and complex regime shifts that traditional financial models cannot adequately capture. This study proposes a hybrid analytical framework that integrates K Means clustering with the Hidden Markov Model to identify and model multiple market regimes in Bitcoin time series data. The Bitcoin dataset used in this research contains minute-level records that were preprocessed to extract key indicators, namely logarithmic returns and rolling volatility, which represent the short-term dynamics of market behavior. The K Means algorithm was first employed to segment the data into three distinct clusters that correspond to bullish, bearish, and sideways regimes, followed by the application of the Hidden Markov Model to estimate probabilistic transitions between these regimes over time. The results reveal that the hybrid K Means and Hidden Markov Model approach achieves superior performance compared to a standalone model, as indicated by a higher log likelihood and a lower Bayesian Information Criterion value. The transition probability matrix shows that bullish and bearish regimes are highly persistent, while the sideways regime acts as a transitional buffer that connects both market extremes. The empirical findings confirm that Bitcoin prices evolve through persistent and probabilistically determined regimes rather than random fluctuations. The proposed framework provides a more comprehensive understanding of cryptocurrency market dynamics and offers practical value for investors, risk analysts, and policymakers in designing adaptive trading and risk management strategies within blockchain-based financial ecosystems.
Abstract Bitcoin's price history follows an approximate power law in time, with \((R^2 = 0.947)\) over 2011--2026. We show that replacing uniform calendar time with activity-warped time ---where time advances faster during high-activity periods---improves both in-sample fit and out-of-sample prediction. Two warping signals are evaluated: price volatility (absolute daily log-returns) and on-chain transaction volume (daily USD value transacted). Both benefit from a power transform \((w_t^\gamma)\) that reshapes the weight distribution: \((\gamma = 2.41)\) for volatility (amplifying large-move days) and \((\gamma = 0.56)\) for transaction volume (compressing extreme spikes). Transaction volume emerges as the stronger signal, achieving \((R^2 = 0.958)\) in-sample and winning 8 of 9 walk-forward splits (mean \((\Delta R^2 = +0.414)\)). Volatility wins 5 of 9 splits but requires no external data. Transaction volume selects \((\alpha = 0)\) (pure warped time), while volatility retains a calendar component (\((\alpha \approx 0.4)\)). Neither signal benefits from smoothing. Despite being nearly uncorrelated (\((r = -0.007)\)), combining the two signals does not improve out-of-sample performance---each captures complementary but individually sufficient information about Bitcoin's growth dynamics.
Recent developments in distributed ledger technology, artificial intelligence, and decision-making agents hold the promise of radically transforming market infrastructures. Indeed, the emergence of Autonomous Market Infrastructure (AMI)âan open, fully automated, and decentralized set of market-related functionalitiesâis widely anticipated. Such infrastructures, serving agents capable of fully autonomous behavior, would enable fully automated trading strategies. Moreover, as AMI-based solutions require minimal human intervention, they could be implemented at a fraction of existing costs. This should bolster competition and democratization, as AMI is accessible to everyone and establishes a level playing field.
Cryptocurrencies have started gaining ground as investment vehicles. Cryptocurrencies exhibit characteristics that differentiate them from traditional financial assets. In 2009, Bitcoin (BTC), the first digital currency, was launched. In 2021, the Securities and Exchange Commission (SEC) approved ProShares Bitcoin Strategy (BITO), the first U.S. Bitcoin futures exchange-traded fund (ETF). In 2024, SEC gave final approval for spot Ether (ETH) ETFs to start trading, further legitimizing the asset class. Although cryptocurrencies share many features of alternative assets, they are hindered by high volatility and regulatory uncertainties. Extant literature studies cryptocurrencies as alternative investments from various perspectives. Using market data, this empirical paper aims to contribute to the literature by studying the extent to which cryptocurrencies improve the risk-return profile of a diversified portfolio. Specifically, we do so by examining the economic impact of including Bitcoin for a passive investor investing in the U.S. Stock market index (S&P 500 index).
This paper proposes an AI-based trading framework that integrates supervised price forecasting with reinforcement learning (RL)-based decision-making. The objective is to enhance both profitability and risk management in cryptocurrency trading by equipping RL agents with forward-looking market information and risk-aware incentives. The proposed methodology follows a two-stage design. First, a univariate long short-term memory (LSTM) model generates 72 bitcoin price forecasts. These predictions are used to compute future technical indicators, which are combined with current market indicators to construct an enriched, forward-looking state representation. Second, an RL agent is trained in this environment using a novel long-term reward function that incorporates transaction costs, drawdown penalties, volatility penalties, and delayed rewards to promote stable and sustainable trading behavior. Four state-of-the-art RL algorithms (PPO, SAC, TD3, and A2C) are systematically evaluated over randomized 180-day episodes using hourly bitcoin data. The results demonstrate that the proposed agent consistently outperforms conventional buy-and-hold and moving average crossover strategies, achieving an average profit ratio of 32% and a Sharpe ratio of 1.34. These findings highlight the novelty and effectiveness of combining mid-term price forecasts, enriched technical states, and risk-aware RL training for robust cryptocurrency trading.
A Long Short-Term Memory (LSTM) neural network trained on hourly ETH/USDT market data from the Binance exchange is used in this study to examine short-term Ethereum price behavior. The proposed model emphasizes learning temporal dependencies and momentum-driven structures rather than relying on conventional linear forecasting assumptions, acknowledging the highly nonlinear and noise-dominated nature of cryptocurrency markets. The daily high price of Ethereum is selected as the target variable in the forecasting task, which is defined as a univariate regression problem. To ensure realistic predictive assessment, model performance is evaluated using a strictly out-of-sample testing methodology. Empirical findings demonstrate that the LSTM model achieves a strong statistical fit despite significant market volatility. The obtained resultsâRMSE of 127.33, MAE of 98.76, MSE of 16,213.76, MAPE of 2.73%, and an R² of 0.96âindicate that a substantial portion of short-term price volatility is effectively captured by the nonlinear architecture. Even in a noise-dominated market, the low MAPE and high coefficient of determination suggest robust predictive alignment. Forecasts over the next five days reveal a recurring short-term directional pattern accompanied by widening prediction intervals, which reflect increasing uncertainty as the forecast horizon extends. This pattern underscores the intrinsic difficulty of achieving accurate price-level forecasts in highly volatile cryptocurrency markets. Overall, when applied to short-term cryptocurrency price dynamics, the results indicate that LSTM models are well-suited for capturing trend persistence and regime-related signals, affirming their usefulness as risk-aware decision-support tools rather than deterministic forecasting systems.
Manaf Ahmed, Mohammed Adnan, Ali Matar, Faez Hlail Srayyih ¡ 7 authors
Predicting cryptocurrency price is challenging owing to high volatility, less historical data, and the impact of external parameters like news, public sentiment, and regulatory announcements. This challenge is tackled in this research by employing models of deep learning like Recurrent Neural Network (RNN), Bidirectional Long Short-Term Memory (BiLSTM) and Gated Recurrent Unit (GRU)âto predict Bitcoin's OHLC prices daily. Based on historical time-series data of Coin Codex, the research uses an autoencoder-based feature extraction method with five-day sliding window method for sequence generation. Hyperband optimization is used to tune hyperparameter of each model. The result shows that BiLSTM performs better than all the other models with minimum Mean Squared Error (MSE = 0.001183), Mean Absolute Error (MAE = 0.026090), and maximum R² score (0.980596) after optimization. The results emphasize the significance of deep learning in capturing nonlinear dynamics in time series of financial applications and bear testimony to the effectiveness of hyperparameter tuning in enhancing model accuracy. The study enhances the development of prediction tools for digital asset markets and enables more informed investment decisions.
Hoseung Kang, Yeonchan Kang, Doojin Ryu, Robert I. Webb
This study evaluates machine learning models for forecasting daily Bitcoin returns using on-chain, macroeconomic, and market variables from January 2017 to December 2023. We implement a rolling-window framework with window lengths ranging from 365 to 730 days and compare several machine learning models against an autoregressive benchmark. Random Forest and Support Vector Machine achieve the lowest forecasting errors consistently across volatility regimes. Feature importance analysis using permutation importance and SHAP decomposition reveals that on-chain variables account for approximately 50 per cent of total forecasting contribution, with transaction fees and mining-related metrics ranking among the top important variables. Traditional market indicators such as VIX show limited relevance for Bitcoin return forecasting. These findings highlight the distinct informational value of blockchain-native variables for cryptocurrency forecasting.
This article examines the revolutionary impact of Artificial Intelligence (AI) on transforming cryptocurrency trading, a sector characterised by extreme volatility, dynamism, and nonlinear data. Through a rigorous bibliometric analysis based on the Web of Science database, this study examines a sample of 555 scientific papers published between 2016 and 2025, utilising the PRISMA protocol for systematic selection, and tools such as VOSviewer and MS Excel. The analysis identifies five major thematic clusters: (1) blockchain infrastructure and AI integration in decentralised ecosystems, (2) data analysis and practical applicability in crypto markets, (3) financial and social data analysisâmachine learning algorithms, (4) algorithmic trading and automation, and (5) prediction and modelling of crypto market developments. The originality of this study lies in providing an overview of the implementation stage of these technologies by integrating the results into a map of Technology Readiness Levels (TRLs). The findings highlight a clear transition from traditional statistical methods to autonomous decision-making systems capable of processing massive volumes of data for portfolio optimisation. This studyâs limitation is that it may require periodic updates, as the AI and cryptocurrency landscape are constantly evolving.
Lihki Rubio, Keyla Alba, Carlos E VelĂĄsquez, Filipe R. Ramos
Accurately forecasting Bitcoinâs conditional variance is essential for reliable Value-at-Risk (VaR) estimation yet remains challenging due to nonlinear dynamics, volatility clustering, and heavy-tailed return distributions. This study developed a novel stacking ensemble that integrates econometric and machine-learning models through XGBoost meta-learning to produce improved variance forecasts. Hybrid MLâGARCH specifications are incorporated separately to enrich the comparative analysis. All estimators are trained with time-aware cross-validation to ensure temporal coherence and prevent look-ahead bias. Using Bitcoin data from 2014 to 2020, the empirical results show that the stacking ensemble consistently outperforms both standalone and hybrid alternatives in conditional variance forecasting and VaR accuracy, including during periods of severe market stress such as the COVID-19 episode. Residual diagnostics confirm that the ensemble effectively captures persistent temporal dependencies in volatility dynamics. Overall, the proposed methodology offers an innovative and interpretable risk-management tool for financial institutions, combining statistical rigor with the adaptability of machine-learning techniques in digital asset markets.
Tan Khai Lian, Ismail Ahmad Al-Qasem Al-Hadi, Mohammad Ahmed Alomari, Mohammed Nasser Al-Andoli ¡ 6 authors
Bitcoin has recently emerged as a leading asset in the cryptocurrency market. However, its significant price volatility presents challenges for accurate prediction. Due to this volatility, forecasting Bitcoin prices accurately is difficult and complicates decision-making for investors and traders in the cryptocurrency space. This research compares the accuracy of three prediction models: Long Short-Term Memory (LSTM), Recurrent Neural Network (RNN), and Facebook's NeuralProphet, introduced in 2021, focusing on improving Bitcoin price forecasting accuracy. The study uses daily Bitcoin prices from the past five years to assess model performance. Results indicate that the LSTM model outperforms both NeuralProphet and RNN in prediction accuracy. This comparison holds substantial economic significance, as accurate predictions can assist investors and traders in making informed decisions within the cryptocurrency market.
Petr Hajek, Josef Novotny, Michal Munk, DaĹĄa MunkovĂĄ
The rapid expansion of cryptocurrency markets has coincided with the growing prominence of social media platforms as influential channels for shaping investor sentiment. Among these platforms, YouTube has become a medium for disseminating investment opinions and behavioral signals. This study investigates the extent to which YouTube-derived featuresâsuch as video influence scores, sentiment embedded in video titles, and user engagement indicatorsâcan enhance the prediction of Bitcoin price fluctuations. A novel dataset is compiled, covering the period from January 2015 to September 2025. Sentiment is assessed using a combination of transformer-based language models, while influence metrics are computed through engagement statistics adjusted for temporal decay and relevance. These features are combined with historical Bitcoin price data and applied within an XGBoost forecasting framework. The empirical findings suggest that augmenting price-based models with YouTube-related sentiment and engagement features yields a notable improvement in directional forecasting accuracy, outperforming price-only benchmarks by approximately 4 %. Moreover, the study highlights that YouTube-derived behavioral signals offer predictive insights that are not fully captured by conventional indicators such as Google Trends or the Crypto Fear and Greed Index.
This study explores the diversification potential of Bitcoin in a French investment portfolio comprising oil, currency, and gold across three distinct market regimes: a pre-crisis stable period, the COVID-19 pandemic, and the RussiaâUkraine conflict. The purpose is to assess whether Bitcoin can enhance portfolio efficiency and provide hedging opportunities under varying market conditions. The analysis is conducted using daily data for Bitcoin, gold, oil, currency, and the CAC40 index from January 1, 2019, to April 22, 2022. Portfolio performance is evaluated through the MeanâVariance (MV) framework and Stochastic Dominance (SD) analysis, allowing for a robust comparison of riskâreturn trade-offs and investor preferences. The MV results show that including Bitcoin consistently improves the portfolioâs riskâreturn profile, evidenced by an upward shift in the efficient frontier across all sub-periods. However, the SD analysis yields more nuanced insights. Before and during the COVID-19 crisis, the portfolio excluding Bitcoin dominates the Bitcoin-inclusive portfolio under second- and third-order stochastic dominance criteria, suggesting that risk-averse investors would prefer the traditional asset mix. In contrast, during the RussiaâUkraine war, no clear stochastic dominance is detected between Bitcoin-inclusive and Bitcoin-exclusive portfolios. These findings emphasize that Bitcoinâs diversification role is highly context- and framework-dependent.
⢠We examine the profitability of a cryptocurrency momentum strategy using 9 âsurvivor coinsâ. ⢠The survivor cryptocurrency momentum portfolio (SCMP) does not generate significant payoffs. ⢠SCMP does not leverage a plain momentum strategy based on a broader set of coins. ⢠Significant payoffs documented for momentum strategies are an artefact of coins that are only temporarily accessible for trading. Motivated by the significant illiquidity observed in the cryptocurrency marketâexemplified by phenomena such as "defaulted coins"âthis study is the first to investigate a cryptocurrency-specific analog of currency momentum, as implemented among G10 currencies. We analyze nine free-floating cryptocurrencies that remained within the top 100 altcoins by market capitalization during the sample period, spanning January 2017 to August 2024. Using weekly data, we evaluate two cryptocurrency momentum strategies: one focused solely on survivor coins and another utilizing the largest 30 coins for a given year (referred to as "plain cryptocurrency momentum"). Our main findings are as follows: (a) Cryptocurrency momentum is not evident when applied to survivor coins; (b) plain cryptocurrency momentum is profitable only after the dataset is trimmed; (c) the profitability of trimmed plain cryptocurrency momentum does not result from leveraging survivor coin-based cryptocurrency momentum; (d) even after trimming, the profitability of plain cryptocurrency momentum is highly sample-dependent.
This research aims to develop a predictive model for estimating the daily closing price of Ethereum (ETH) against the Indonesian Rupiah (IDR) using the Random Forest Regression algorithm. Ethereum is one of the most widely traded cryptocurrencies and is known for its high volatility, which makes accurate price prediction essential for supporting data-driven investment decisions. Historical price data were collected from the CoinGecko API for a period of 365 days, followed by preprocessing, feature engineering, and the computation of several technical indicators including Exponential Moving Average (EMA-14), Relative Strength Index (RSI-14), Daily Return, Bollinger Bands Upper, Average True Range (ATR-14), and Close Lag-1.The research starting from data selection and preprocessing to modeling, evaluation and visualization. Random Forest Regression was chosen due to its robustness in handling nonlinear relationships and noisy time-series data. The dataset was split using a 90:10 time-based hold-out method, and model performance was evaluated using four regression metrics: MAE, RMSE, MAPE, and R-squared. The best configuration of the model achieved a MAPE of 2.88%, indicating a high level of predictive accuracy. Feature importance analysis shows that Daily Return and ATR-14 contributed most significantly to the prediction. The findings demonstrate that Random Forest Regression can effectively capture the nonlinear patterns in cryptocurrency price movements, providing an accurate and reliable model for short-term forecasting. This model may serve as a valuable reference for investors, financial analysts, and developers of automated trading systems.
The decentralized finance market exhibits extreme volatility and complex nonlinear dynamics that pose significant challenges for accurate price prediction and risk management. Traditional time series models, including Long Short-Term Memory networks and Transformer architectures, struggle with either computational inefficiency in capturing long-rangedependencies or inadequate context retention across extended sequences. This research investigates the application of Structured State Space Models, particularly the Mamba architecture with selective state spaces, for modeling temporal dependencies in DeFi markets. The proposed framework addresses the limitations of conventional approaches by leveraging SSMs' linear-time complexity while maintaining superior long-sequence modeling capabilities through context-aware selective mechanisms. Our methodology integrates SSM architectures with DeFispecific features including on-chain transaction volumes, liquidity metrics, and market microstructure indicators. Experimental validation across multiple cryptocurrency pairs demonstrates that SSM-based models achieve competitive performance compared to attentionbaseTransformers while offering substantial computational advantages. The results indicate that selective state space mechanisms enable effective capture of both short-term volatility patterns and long-horizon price trends in decentralized markets. This work contributes to the emerginintersection of advanced sequence modeling techniques and blockchain-based financial systems, providing insights for algorithmic trading strategies and risk assessment frameworks in the rapidly evolving DeFi ecosystem.
The integration of distributed ledger technology with financial markets has precipitated a paradigm shift in how algorithmic trading strategies are conceived, executed, and settled. This paper presents a comprehensive analysis of blockchain-based algorithmic trading systems, focusing specifically on the dual challenges of execution efficiency and cryptographic security. While traditional high-frequency trading relies on centralized exchanges and proprietary networks to minimize latency, decentralized trading protocols introduce novel constraints related to block generation intervals, consensus mechanisms, and network propagation delays. We examine the implementation of algorithmic strategies via smart contracts, evaluating the trade offs between on-chain transparency and the privacy requirements of institutional investors. Furthermore, the study investigates critical vulnerabilities inherent to decentralized exchanges, such as Miner Extractable Value and front-running attacks, and proposes mitigation strategies utilizing commit-reveal schemes and zero-knowledge proofs. By analyzing the performance metrics of automated market makers against order book models, we provide empirical evidence regarding the current limitations and potential scalability of blockchain-based trading environments. The findings suggest that while blockchain architectures offer superior settlement finality and auditability, significant advancements in layer-two scaling solutions and privacy preserving cryptographic protocols are requisite for these systems to compete with traditional financial infrastructure in terms of throughput and latency.
Statistical arbitrage strategies, including pairs trading, rely on identifying co-movements and static long-term equilibrium relationships between assets, where conventional methods fail to capture non-stationary dynamics, hence reducing trading effectiveness. This study, therefore, addresses this challenge by employing a dynamic co-integration approach combined with deep learning techniques to select suitable cryptocurrency pairs and forecast spread dynamics. The study examines multiple cryptocurrencies, namely: BNB, Ethereum, Litecoin, Ripple, and USDT, using dynamic Johansen co-integration tests to identify pairs with time-varying equilibrium relationships, and model the spread through a Dynamic Weighted Ensemble of Deep Neural Network and Long Short-Term Memory. Forecasting accuracy, trading performance, and predictive uncertainty are evaluated using error metrics, trading outcomes, and 99% prediction intervals. The results indicate that only those cryptocurrencies with dynamically coherent relationships are suitable for mean-reversion strategies. Furthermore, the study found that the Dynamic Weighted Ensemble achieves the best predictive accuracy. At the same time, LSTM captures proportional temporal dynamics effectively, and the ensemble-driven trading signals generate timely buy and sell decisions with low-lag execution and robust management of market volatility. These findings, therefore, highlight the advantages of combining dynamic co-integration and adaptive deep learning for statistical arbitrage.
We investigate whether sophisticated deep learning architectures justify their computational cost for short-term cryptocurrency price forecasting. Our study evaluates a 2.1M-parameter (M represents millions (e.g., 2.1M = 2,100,000 parameters), with all RMSE values reported in USD) wavelet-enhanced transformer that decomposes the Fear and Greed Index (FGI) into multiple timescales before integrating these signals with technical indicators. Using DieboldâMariano tests with HAC-corrected variance, we find that all modelsâincluding our waveletâtransformer, ARIMA, XGBoost, LSTM, and vanilla Transformerâfail to significantly outperform the O(1) naive persistence baseline at the 1-day horizon (DM statistic = +19.13, p<0.001, naive preferred). Our model achieves an RMSE of USD 2005 versus USD 1986 for naive (ratio 1.010), requiring 3909Ă more inference time (2.43 ms vs. 0.0006 ms) for a statistically worse performance. These results provide strong empirical support for the Efficient Market Hypothesis in cryptocurrency markets: even sophisticated multi-scale architectures combining wavelet decomposition, cross-attention, and auxiliary technical indicators cannot extract profitable short-term signals. Through systematic ablation, we identify positional encoding as the only critical architectural componentâits removal causes 30% RMSE degradation. Our findings carry important implications, as follows: (1) short-term crypto forecasting faces fundamental predictability limits, (2) architectural complexity provides negative ROI in efficient markets, and (3) rigorous statistical validation reveals that apparent improvements often represent noise rather than signal.
Abstract This study empirically assesses the viability of Bitcoin as an alternative investment asset within the Egyptian context from 2011 to 2023. We conduct a comparative analysis of Bitcoinâs risk-return characteristics against traditional Egyptian investment vehicles: the EGX30 stock index, physical Gold, and the USD/EGP exchange rate. Utilizing historical daily data sourced from Coinbase, Bloomberg, Yahoo Finance, and the Central Bank of Egypt, we employ standard financial metrics including annualized returns, volatility (standard deviation), and Sharpe ratios. Correlation analysis is performed to evaluate Bitcoinâs diversification potential. Furthermore, we examine asset performance during significant periods of socio-economic stress: the 2011 Egyptian Revolution, the COVID-19 pandemic (2019-2020), and the EGP devaluation period (2022-2023). Our findings reveal Bitcoinâs exceptionally high volatility ( $$\sigma \approx 3.6\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ď</mml:mi> <mml:mo>â</mml:mo> <mml:mn>3.6</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> daily) and potential for substantial returns, yet yielding a surprisingly negative cumulative return over the entire sample period. Gold demonstrated characteristic stability ( $$\sigma \approx 1.0\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ď</mml:mi> <mml:mo>â</mml:mo> <mml:mn>1.0</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> daily), while the EGX30 offered moderate growth amidst volatility ( $$\sigma \approx 1.6\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ď</mml:mi> <mml:mo>â</mml:mo> <mml:mn>1.6</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> daily). Correlation analysis suggests limited diversification benefits between Bitcoin and traditional assets during certain periods. Event analysis highlights varying asset reactions, with Gold often acting as a safe haven, while Bitcoin exhibited mixed behavior. While Bitcoin presents diversification potential, its extreme volatility, negative long-term cumulative return within this sample period, and the prevailing regulatory uncertainty in Egypt necessitate careful consideration for investors seeking alternative assets in a challenging macroeconomic environment characterized by inflation and currency depreciation.
Kwestan Ahmed Ismael, Heshu Othman Faqe, Mohammed Hussein Abdalla, Hindreen A. Taher
In this work we use historical market data from Bitget to predict weekly open prices of Ethereum (ETH) for a 96-week period with the Prophet forecast model trained by using Particle Swarm Optimization (PSO) algorithm. Because of this, the research delves into automated hyperparameter tuning for Prophet in order to improve forecast performance on cryptocurrency markets where volatility, structural breaks and irregular trading patterns pose a significant challenge to time series prediction. The PSO algorithm is a good method to explore the high dimensional parameter space in which it can strike between the global analysis and local exploitation for detecting minimal forecast errors. Based on evaluating model performance for which we used accuracy metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in training, test holdout & full-fit situations. PSO-optimized Prophet: The results show a great in-sample fitting and fast convergence behaviour, as the best CV RMSE is slightly higher than the lowest one should have obtained if used only 10 iterations. Although forecasts exhibit stability and track long-term trends well, the model does not predict short-term fluctuations in the holdout set with high accuracy (wider forecast uncertainty intervals). Our results shed light on the utility of PSO to improve Prophet-based price prediction in cryptocurrencies, reinforce the relevance of uncertainty quantification in asset markets and inform risk-aware decisions of financial agents dealing with unstable assets.