Background. Market-cycle forecasts are vulnerable to hindsight because a low becomes identifiable only after subsequent price confirmation. Objective. This study evaluated whether an adaptive, confirmation-aware interval could attain at least 80% chronological forecast precision for daily cycle lows (DCLs) and weekly cycle lows (WCLs) in Bitcoin, S&P 500 futures, and gold. Methods. The Adaptive Quantile-Calibrated Cycle Window used only the latest 20 completed cycles. Its lower endpoint was the empirical 10th percentile of prior low-to-low durations, and its upper endpoint was the 90th percentile of prior-low-to-next-confirmation durations. Forecasts originating from 1 January 2021 through 14 July 2026 were evaluated sequentially, and the retrospective protocol was externally preregistered. Results. Fixed clocks achieved 70.9% DCL precision and 55.6% WCL precision. The adaptive interval achieved 109/127 DCL hits (85.8%; 95% CI 78.7%–90.8%) and 27/27 WCL hits (100.0%; 95% CI 87.5%–100.0%). Mean window width increased from 14.7 to 32.8 days for DCL and from 4.0 to 11.7 weeks for WCL. A wider 5th–95th percentile band produced 93.7% DCL precision with a 95% lower confidence bound of 88.1%. Conclusion. Adaptive interval calibration exceeded the 80% point target, but the gain depended on materially wider windows and a small WCL sample; prospective replication remains necessary.
This paper introduces the Dynamic External Memory LSTM (DEM-LSTM), a novel deep neural architecture designed to address the hidden state information bottleneck and temporal context decay inherent to standard LSTMs in financial time-series forecasting. By decoupling sequence processing from persistent state storage via an addressable external memory matrix ($M_t$), DEM-LSTM dynamically reads, erases, and updates market context across long sequences without corrupting internal hidden representations. Evaluated across four distinct asset classes—Foreign Exchange (EUR/USD), Commodities (XAU/USD and USOIL), and Cryptocurrencies (BTC/USD)—DEM-LSTM consistently outperforms standard LSTM baselines across all metrics, achieving up to a 41.4% reduction in RMSE on Gold spot prices while maintaining superior stability across high-volatility market regimes.
Consumers facing home-renovation quotes operate in a classic credence-goods market: they cannot readily verify whether a quoted price is fair, and general-purpose large language models (LLMs) are now a zero-cost place to ask. Whether LLM answers are actionable for this purpose is untested. Demand-side benchmarks exist for medical, legal, and financial advice, but not for construction costs. We present, to our knowledge, the first consumer-question benchmark for construction costs. Forty Japanese renovation-price questions were posed to frontier LLMs, with repeated-trial sets measuring output stability. A matched re-run at bare provider defaults with a current frontier model (gpt-5.5) was added to remove a settings confound present in the original configuration. Two findings are robust across models, generations, and settings: no LLM answer contained an explicit over-charge decision threshold, and repeated runs of the same question returned materially different price figures. Within-answer price spans are also wide, with a median of 10x under bare defaults. A deterministic structured engine over an open cost database is included as an existence proof that a citable reference layer is constructible. Its consistency is a design property and its accuracy is not validated here; validating it against completed real-world quotations is the next study. All questions, raw outputs, harness, and scoring code are public.
This paper empirically compares four architectures for financial time-series forecasting: LSTM, CNN, the original Regularized Self Attention Regression (RSAR) model, and a multiobjective optimized RSAR variant, denoted MO-RSAR, obtained using the Non dominated Sorting Genetic Algorithm II (NSGA-II). The models are evaluated on six datasets covering Forex, equity index and cryptocurrency markets, for short and long horizons. All models share a common preprocessing pipeline and evaluation framework and are assessed using standard error metrics, with emphasis on Mean Absolute Percentage Error (MAPE). MORSAR yields the lowest average prediction error across all datasets and provides significant gains for longer, more volatile horizons, while simpler architectures remain competitive for short-term forecasts. The key methodological contribution is the first empirical integration of the RSAR architecture with NSGA-IIbased multi-objective hyperparameter optimization for financial time-series forecasting. The proposed framework treats RSAR configuration as a bi-objective search over accuracy and generalization (via the train-validation gap), and evaluates the resulting model under a unified protocol across heterogeneous markets and horizons.
Akhter Javed, Huma Gul, Ali Husnain, Rahmat Said · 5 authors
Background: In this study, the increased complexity of today supply chains and explain why conventional forecasting and inventory management techniques are inadequate in today's dynamic and uncertain market conditions. As globalization and data increase, AI has become a gamechanger in delivering better demand forecasting and inventory management, in turn driving a better operation and cost savings. Objectives: This study seeks to assess the performance of AI-based demand forecasting models combined with inventory optimization methods on improving the overall performance of the supply chain. Methods: A quantitative, data-driven methodology was employed, and secondary data were used, including historical demand, inventory levels, and other external data that included seasonality and economic indicators. Demand forecasting models: Advanced machine learning and deep learning models such as Long Short-Term Memory (LSTM), Random Forest and Gradient Boosting were used for demand forecasting. The results of the forecasts were fed into an inventory optimization system using reinforcement learning for dynamic decision-making. Standard deviations like Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) were used to measure the model's performance along with cost-performance analysis. Results: The accuracy of the prediction is significantly higher in AI-based models, especially the LSTM model, than the traditional models, which decreases the errors of the prediction and enhances its responsiveness. AI-powered inventory optimization resulted in significant savings on inventory holding and shortage/cost of order, and improved service levels and inventory stockout rates. The use of external data had yet further improved predictive performance. Conclusion: AI-powered demand forecasting and inventory optimization offer a solid solution to improve the efficiency of the supply chain, make intelligent decisions and minimize operational costs. References Ahn, H. I., Song, Y. C., Olivar, S., Mehta, H., & Tewari, N. (2024). GNN-based probabilistic supply and inventory predictions in supply chain networks. arXiv. Albayrak Ünal, Ö., Erkayman, B., & Usanmaz, B. (2023). Applications of artificial intelligence in inventory management: A systematic review of the literature. Archives of Computational Methods in Engineering. Advance online publication. https://doi.org/10.1007/s11831-023-09977-2 Ayub, M. I., Gharami, A. K., Nitu, F. N., Uddin, M. N., Islam, M. I., Nijhum, A. M., … Yezdani, S. (2025). AI-driven demand forecasting for multi-echelon supply chains: Enhancing forecasting accuracy and operational efficiency through machine learning and deep learning techniques. 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This study compares the forecasting performance of four deep learning architectures—GRU, LSTM, RNN, and CNN—for one-step-ahead Bitcoin price prediction. A grid search determined the optimal configuration, which was applied uniformly across models to ensure fair evaluation. Using daily BTC closing prices from January 2018 to July 2025, it is found that the GRU model achieved the lowest forecasting errors (MSE, RMSE, MAE, MAPE) and the highest R², with LSTM performing closely behind. Visual analyses confirmed that GRU and LSTM maintained stronger alignment with actual prices during volatile periods. To assess economic value, model forecasts were integrated into a rule-based trading strategy under realistic market frictions, including a 0.10% transaction cost and a 0.10% trading threshold, with both short-selling-enabled and long-only variants tested. The GRU strategy with short-selling generated the highest terminal wealth (approximately 24% higher than the Buy-and-Hold benchmark) and superior risk-adjusted returns, measured by CAGR, Maximum Drawdown, and Sharpe Ratio. The findings demonstrate that careful hyperparameter optimization, coupled with an architecture capable of capturing complex temporal dependencies, can significantly improve both predictive accuracy and trading profitability in cryptocurrency markets. These results provide practical implications for designing AI-driven trading systems.
# Proof-of-Information (PoI) Consensus Protocol## Complete Specification: MVP + Production > **Version:** 1(PIntegration) > **Status:** Specification Complete • MVP Ready for Testing > **License:** CC BY‑SA 4.0 > **Core Thesis:** *Consensus driven by predictive information quality, not resource expenditure.* --- > *"This proposal deserves serious study, refinement, and testing — not only for its technical merits, but for its potential to reframe our understanding of the relationship between truth, forecasting, and legitimate power in distributed systems."*>> — *Design Principle & Call to Validation* --- ## 📋 Executive Summary | Aspect | Description ||--------|-------------|| **Problem** | PoW wastes energy; PoS concentrates capital. Neither rewards *informational value*. || **Solution** | PoI secures the network through **verifiable forecasting accuracy** — validators earn influence via epistemic performance. || **Two-Track Design** | **MVP**: Minimal testable core (binary events, Brier scoring). **Full Spec**: Production-ready with ZK proofs, uncertainty layers, adaptive mechanisms. || **Output** | A blockchain that finalizes blocks *and* produces a public good: continuously updated, uncertainty-quantified global forecasts. || **Evaluation Ready** | Clear validation thresholds, implementation checklist, and progression roadmap from MVP → Production. | --- ## 🎯 Core Thesis > **Proof-of-Information** redefines blockchain security: instead of rewarding those who burn electricity or lock capital, PoI rewards those whose predictions about the external world are historically the most accurate, well-calibrated, and information-rich. By integrating strictly proper scoring rules (Brier, CRPS), zero-knowledge proofs of inference, and adaptive reputation systems directly into consensus, PoI transforms the blockchain from a transactional ledger into a **decentralized truth-seeking engine** — where the right to produce blocks is earned through epistemic merit. --- ## 📜 Epistemic Mandate > **Purpose Beyond Protocol** > Proof-of-Information is designed with a trans-temporal objective: to create a verifiable epistemic substrate that future superintelligent systems can use to anchor their understanding of reality. > > **Core Premise**: An ASI trained on data where every claim is cryptographically linked to an outcome, and every error is scored by a strictly proper rule, develops not just competence — but *calibrated humility*. > > **Design Implication**: Every technical choice in PoI (scoring rules, delay mechanisms, Cassandra bonuses) serves two masters: > 1. Immediate network security through epistemic merit > 2. Long-term value as a training environment for truth-aligned intelligence > > *This is not an aspiration. It is a constraint: if a feature does not serve at least one of these goals, it is out of scope.*
Piotr Fiszeder, Witold Orzeszko, Radosław Pietrzyk
Abstract This study investigates the use of ChatGPT as an automated tool for extracting and labeling Bitcoin-related news sentiment and examines how the resulting sentiment indicators affect Bitcoin returns and volatility. A large dataset of news headlines is processed via an API-based workflow, and the ChatGPT-derived sentiment indicators are subsequently incorporated as explanatory variables into selected statistical and machine learning models, including autoregressive (AR), heterogeneous autoregressive (HAR), Bayesian model averaging (BMA), least absolute shrinkage and selection operator (LASSO), and support vector regression (SVR). We find that while the sentiment indicators significantly improve in-sample estimation accuracy for returns and volatility, they do not lead to statistically significant gains in out-of-sample forecasting performance. This result suggests that ChatGPT-based sentiment measures primarily capture contemporaneous market-relevant information rather than persistent predictive signals, consistent with semi-strong market efficiency.
The retail and consumer packaged goods industries are at an inflection point; the autonomous, goal-oriented software agents are substituting the inflexible, analyst-reliant business decision cycles with closed-loop intelligence systems, which can perceive, reason, and act in real-time. The autonomy, proactivity, and constant learning of agentic AI redesign the pricing, trade promotion optimization, and supply chain coordination processes within complicated, multi-account business settings. Based on proven sources of empirical evidence in the literature on machine learning, multi-agent reinforcement learning, and supply chain optimization, the technical architecture of an agentic commercial system is discussed along five related dimensions: autonomous trade performance monitoring through perception-reasoning-action pipelines; cooperative multi-agent system design under the models of centralized training and decentralized execution; scenario simulation engine based on digital twin models; multi-objective trade promotion optimization with Pareto-front metaheuristic algorithms; and practical barriers of data infrastructure, model drift, organizational change management, and algorithmic governance. Bringing these capabilities together into a single agentic decision stack is a paradigm shift in the concept of commercial intelligence in retail and CPG, moving the operational center of gravity off retrospective dashboards and onto adaptive, constantly learning systems that coordinate the decisions on pricing, promotion, and supply.
In this study, it is aimed to compare quantitative forecasting methods (traditional and learning based) in cryptocurrency market. For his purpose the daily prices between 16 September 2017 – 15 September 2022 of Bitcoin, Ethereum, Binance Coin and Monero were analyzed with five different methods: ARIMA, exponential smoothing, artificial neural networks, RNN and LSTM.In the results it is indicated that exponential smoothing method is the most successful method at forecasting daily prices. The method has high performance in forecasting BTC, ETH and BNB daily prices. But at forecasting daily XMR prices, artificial neural networks method was the most successful one.The other point which was detected in this study is deep learning based methods made some unsuccessful forecasts. This is thought to be due to the fact that deep learning methods require more data. In future studies, using other quantitative methods (e.g. GRU, XGBoost, transformer models) on other cryptocurrencies will contribute to the literature.
For many decades, time-series forecasting has been applied to different problems by scientists and industries. Many models have been introduced for the purpose of forecasting. These advancements have significantly improved the accuracy and reliability of predictions, especially in complex scenarios where traditional methods struggled. As data availability continues to expand, the integration of machine learning techniques is likely to further enhance forecasting capabilities across various fields. Today, hybrid techniques are gaining popularity, as they combine the advantages of different approaches to deliver improved predictive performance and more advanced visualization analytics for decision support. These hybrid approaches can provide better prediction, and at the same time, they can develop a more sophisticated set of visualization analytics for decision support. Recently, the integration of cross-entropy, fuzzy logic, and attention mechanisms in hybrid forecasting models has enhanced their ability to capture complex and uncertain patterns in financial and energy markets. In this study, we propose a hybrid ANN–LSTM deep learning model optimized with cross-entropy, fuzzy logic, and an attention mechanism to enhance the forecasting of financial and energy time series, specifically Ethereum and natural gas prices. Our models combine the feature extraction strength of ANN with the temporal learning of LSTM, while cross-entropy improves convergence, fuzzy logic handles uncertainty, and attention refines feature weighting. Since inaccurate forecasts can lead to greater estimation uncertainty and increased financial and operational risk, improving predictive reliability is essential for effective risk mitigation. These techniques prove effective not only in improving estimation accuracy but also in minimizing financial risks and supporting more informed investment decisions.
Puguh Hiskiawan, Jovan William, Louis Feliepe Tio Jansel
Bitcoin, a highly volatile and decentralized digital asset, presents considerable challenges for accurate price forecasting. This study proposes an applied data science framework that compares traditional statistical approaches with modern Artificial Intelligence (AI)-based models to predict Bitcoin’s daily closing price. Using BTC-USD historical data from January 2020 to December 2024, we converted prices into Indonesian Rupiah (IDR) to increase local relevance. Our forecasting horizon is 30 days, based on a 60-day lookback window. We evaluate six models: Linear Regression, ARIMA, and Prophet as traditional techniques, alongside Random Forest, XGBoost, and Long Short-Term Memory (LSTM) networks as AI approaches. All models were trained using lag-based or sequence-based time series features and evaluated using MAE, RMSE, R², MAPE, and SMAPE. Results show that AI models, particularly LSTM and XGBoost, offer better performance in capturing short-term non-linear dynamics compared to traditional models. LSTM provides high accuracy, though with greater computational demand, while XGBoost strikes a balance between speed and precision. Prophet and ARIMA remain effective for quick and interpretable forecasts but struggle with abrupt trend shift common in cryptocurrency markets. In addition to performance metrics, we include a robustness analysis based on median absolute error and outlier detection to assess model stability under extreme variations. Visual analytics—including forecast curves, error distributions, and uncertainty bounds—help interpret and communicate model behavior. This comprehensive evaluation offers practical insights for investors, analysts, and fintech practitioners, and the pipeline can be extended to other volatile assets.
Cryptocurrency is an alternative payment method developed with encryption techniques. To predict Bitcoin values using both weekly and monthly datasets, this study compares four machine learning models: GRU, Weighted LSTM, LSTM, and LSTM with Attention. The models' accuracy and dependability in capturing the dynamics of cryptocurrency prices were assessed using Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R-Squared (RSCORE). While LSTM with Attention did well with an RSCORE of 0.7173, LSTM with Attention had the highest RSCORE of 0.9173 in the weekly dataset, indicating higher ability in modelling short-term sequential patterns. Additionally, weighted LSTM performed well (RSCORE of 0.8002), surpassing GRU (RSCORE of 0.5728), which had trouble keeping up with the volatility of Bitcoin prices. Both LSTM and LSTM with Attention performed best in the monthly dataset, each with the lowest MSE (0.0304) and an RSCORE of 0.8173. With an RSCORE of 0.7002, weighted LSTM came next, using temporal weighting to enhance predictions. Because of its limited capacity to grasp intricate temporal connections, GRU continuously fared poorly in both datasets. According to the analysis, LSTM is the most dependable model for both short-term and long-term forecasts, and for weekly forecasts, LSTM with Attention provides improved interpretability. These results provide a framework for applying machine learning approaches to financial time series forecasting, highlighting the significance of choosing suitable models based on data frequency, volatility, and prediction aims.
I WAYAN SUMARJAYA, RENOVAR JOJOR DELIMA SIMANULLANG, RATNA SARI WIDIASTUTI
Forecasting is the process of estimating future events using past data. Financial time series forecasting often prioritizes stock price variables. Apart from the stock price variable, inter-transaction time or duration is also an important variable to predict, because the timing of changes in financial prices cannot be predicted. Duration modeling and forecasting can be done using the autoregressive conditional duration (ACD) model. In this research, modeling and forecasting using the ACD model was carried out on Ethereum. This research aims to predict the duration of Ethereum in order to help traders know the time needed to reach the next price change. Several ACD models with four distributions, i.e., exponential, Weibull, Burr, and generalized gamma were fit to the Ethereum duration. The research results suggest that the Burr-ACD model produces the smallest AIC value compared to other distributed ACD models. However, the forecast results using the Burr-ACD models show increasing duration and hence are less accurate. The generalized gamma-ACD (2,2) model was then chosen as an alternative for forecasting Ethereum duration, showing that Ethereum duration forecast results are less than one second, which indicates the high frequency of transactions that occur on Ethereum.
Deep learning and hybrid deep learning models are widely regarded as some of the most effective predictive modeling techniques to date. Their hierarchical architecture enables them to capture complex, non-linear relationships among features and uncover hidden patterns within data, making them particularly powerful for tasks involving high-dimensional and unstructured inputs. But, these models are computationally intensive and require substantial processing time. Moreover, their predictive efficiency is highly dependent on the availability of large-scale datasets. In this study, meta learning model is employed for the prediction of two financial markets: equity market and crypto market. NASDAQ and S&P 500 index has been taken for equity market prediction. On the other hand, Bitcoin & Ethereum are considered for crypto market. Three deep learning models: LSTM, GRU and CNN are trained for the prediction of these four indices and a hybrid deep learning model of GRU and CNN is also developed. Based on RMSE, MAE and R 2 values, it is observed that meta learning yields best results among all trained models with minimum time and using scarce computation resources based on small dataset.
Romario Desouza Daniel Mangiwa, Revina Siregar, Sri Anum Sari, Neli Agustina
Ethereum is one of the leading cryptocurrencies utilizing blockchain technology for peer-to-peer financial transactions. This study aims to forecast Ethereum's price using the Autoregressive Integrated Moving Average (ARIMA)model. Historical price data from January 1, 2023, to January 15, 2025, covering 534 periods, was analyzed. The ARIMA (0,1,9) model was selected based on AIC, SC, and Adjusted R-squared criteria, with forecast evaluation showing a Mean Absolute PercentageError (MAPE) of 15.01% and a Root Mean Squared Error (RMSE) of 649.702. Forecast results indicate an upward trend in Ethereum's price over the next 30 periods, with fluctuations being less pronounced compared to historical data. The study concludes that ARIMA provides reasonably accurate short-term predictions, although forecasting errors increase with longer prediction periods. These findings can serve as a reference for investors in developing short-term investment strategies for Ethereum.
The emergence of Bitcoin as a pioneering cryptocurrency has transformed financial markets, garnering widespread interest from academicians, policymakers, and investors. The market's inherent volatility and the rapid integration of public information into price movements continue to present a formidable challenge in accurately forecasting Bitcoin prices despite its potential. The limitations of conventional financial models, which frequently need to consider the distinctive attributes of cryptocurrencies, further exacerbate this challenge. Despite the proliferation of ML in various fields, existing models have not fully harnessed these techniques, performing only marginally better than random guesses due to the unique challenges posed by the high volatility and complex dynamics of cryptocurrency markets. This study introduces a systematic review of ML methods specifically tailored for Bitcoin price prediction, with a focus on evaluating the robustness, accuracy, and appropriateness of advanced ML techniques like Long Short-Term Memory (LSTM) networks. The novelty lies in its comprehensive assessment of these methods in the context of data-driven marketing, aiming to enhance both academic understanding and practical applications in financial technology. The previous studies haven't Machine Learning (ML) has become a formidable instrument that has the potential to improve the accuracy of forecasting; however, there still needs to be more comprehension regarding the most effective ML models in this field. The study's importance is derived from its systematic examination of various machine learning (ML) techniques employed to predict the price of Bitcoin, with a particular emphasis on their integration into data-driven marketing strategies. The results will substantially contribute to both academic research and practical applications, providing valuable insights that can be used to develop more dependable forecasting tools, thereby benefiting investors, marketers, and policymakers.
The inherent challenges of financial time series forecasting demand advanced modeling techniques for reliable predictions. Effective financial time series forecasting is crucial for financial risk management and the formulation of investment decisions. The accurate prediction of stock prices is a subject of study in the domains of investing and national policy. This problem appears to be challenging due to the presence of multi-noise, nonlinearity, volatility, and the chaotic nature of stocks. This paper proposes a novel financial time series forecasting model based on the deep learning ensemble model LSTM-mTrans-MLP, which integrates the long short-term memory (LSTM) network, a modified Transformer network, and a multilayered perception (MLP). By integrating LSTM, the modified Transformer, and the MLP, the suggested model demonstrates exceptional performance in terms of forecasting capabilities, robustness, and enhanced sensitivity. Extensive experiments are conducted on multiple financial datasets, such as Bitcoin, the Shanghai Composite Index, China Unicom, CSI 300, Google, and the Amazon Stock Market. The experimental results verify the effectiveness and robustness of the proposed LSTM-mTrans-MLP network model compared with the benchmark and SOTA models, providing important inferences for investors and decision-makers.
R. Aarthi, P. Vanitha, S Reshma, C Mounisha · 5 authors
Bitcoin (BTC) and Ethereum (ETH) price and trends prediction is performed by long short-term memory (LSTM) networks, gated recurrent unit (GRU) and Random Forest machine learning algorithm, the authors explain. Feature selection techniques were effectively and widely adopted to preprocess and feed real cryptocurrency market data as input data. LSTM performs have an accuracy of 96%, GRU performs have accuracy of 97%, and Random forest 98%, meaning they are satisfactory in predicting cryptocurrency trends theme. These models were used to construct two real worlds advert based knowledge driven investment strategies which were simulated through the period under study and show the potential of this class of models. Results of which showed across different times period cases how well your prediction works [7], and all pointed out on the huge probably availability of the presence of profit making opportunity and hence the way in which your predictive way of prediction the unpredictable market crypto currency.
Ali Yeganeh, Xuelong Hu, Sandile Charles Shongwe, Frans F. Koning
In the area of multivariate process quality control, it is sometimes important to monitor the ratio of two normal random variables denoted by RZ over time. The concept of control charts has often been harnessed in this field, leading to the application of various types of statistical models, including Shewhart, Exponentially Weighted Moving Average (EWMA), and so forth. However, there is little attention to implementation of machine learning-based control charts. To bridge this gap, a novel machine learning based model incorporating the attention mechanism approach, as an implemented Artificial Intelligence (AI) model, is proposed to monitor the RZ in Phase II applications. The proposed RZ method not only provides quicker Out-of-Control (OC) shift detection than conventional RZ control charts but also does not require the quality controller to have any prior information about the upward or downward shift patterns, which is a major assumption in most of the previous RZ models. We provide extensive performance comparison results to discuss the statistical performance of our proposed method through Monte Carlo simulations. Moreover, a comprehensive real example about surveillance of the cryptocurrency market is provided to illustrate the practical application of our proposed method. Through simulation and back-testing results, it is shown how the proposed method can lead to an automated trading strategy.
The paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes the maximum likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the function characteristic and the fractional Fourier transform (FRFT), we provide a comprehensive approach to circumvent the problem and yield a good parameter estimation of the GTS probability. The methodology was applied to fit two heavily tailed data (Bitcoin and Ethereum returns) and two peaked data (S\&P 500 and SPY ETF returns). For each index, the estimation results show that the six-parameter estimations are statistically significant except for the local parameter, $μ$. The goodness-of-fit was assessed through Kolmogorov-Smirnov, Anderson-Darling, and Pearson's chi-squared statistics. While the two-parameter geometric Brownian motion (GBM) hypothesis is always rejected, the GTS distribution fits significantly with a very high p-value; and outperforms the Kobol, Carr-Geman-Madan-Yor, and Bilateral Gamma distributions.
Олександр Кузнецов, Anton Yezhov, Kateryna Kuznetsova, Oleksandr Domin
This study presents a comprehensive theoretical and empirical analysis of Patricia tries, the fundamental data structure underlying Ethereum's state management system. We develop a probabilistic model characterizing the distribution of path lengths in Patricia tries containing random Ethereum addresses and validate this model through extensive computational experiments. Our findings reveal the logarithmic scaling of average path lengths with respect to the number of addresses, confirming a crucial property for Ethereum's scalability. The study demonstrates high precision in predicting average path lengths, with discrepancies between theoretical and experimental results not exceeding 0.01 across tested scales from 100 to 100,000 addresses. We identify and verify the right-skewed nature of path length distributions, providing insights into worst-case scenarios and informing optimization strategies. Statistical analysis, including chi-square goodness-of-fit tests, strongly supports the model's accuracy. The research offers structural insights into node concentration at specific trie levels, suggesting avenues for optimizing storage and retrieval mechanisms. These findings contribute to a deeper understanding of Ethereum's fundamental data structures and provide a solid foundation for future optimizations. The study concludes by outlining potential directions for future research, including investigations into extreme-scale behavior, dynamic trie performance, and the applicability of the model to non-uniform address distributions and other blockchain systems.
Cryptocurrency is a form of decentralized digital currency. Ethereum is the second-largest cryptocurrency by market capitalization and the largest altcoin. Cryptocurrencies including Ethereum are highly volatile. Hence, shortterm directional forecasts in the cryptocurrency market have become a widely discussing topic. Candlestick charts are useful visualizations of the open, high, low and close prices which can identify patterns and gauge the near-term direction of prices. This research explores the effectiveness of forecasting hourly Ethereum closing price direction based on candlestick charts within a short time horizon. The proposed forecasting algorithm incorporates clustering methods such as fuzzy K-means, K-means and partition around medoids clustering to cluster candlestick chart properties namely upper shadow length, body length and lower shadow length. Classification methods such as random forest, support vector machine and K-nearest neighbour were used to forecast closing price direction using 16 different predictor variable sets including open, high, low and close prices, candlestick chart price direction, USL, BL and LSL. The accuracy for all considered cases was around 50%. Clustering improved the accuracy slightly and including the CPD with the predictor variable sets under consideration can increase the accuracy slightly. However, this approach is performing better in predicting the Down cases to the total number of actual Down cases because there is a higher sensitivity of 81.20% based on the SVM with Open, High, Low and Close at t in the clustering ignored method.