Maria Inês Silva, Johnnatan Messias, Benjamin Livshits
Despite blockchain data being publicly available, practical challenges and high costs often hinder its effective use by researchers, thus limiting data-driven research and exploration in the blockchain space. This is especially true when it comes to Layer-2 (L2) ecosystems, and ZKsync, in particular. To address these issues, we have curated a dataset from 1 year of activity extracted from a ZKsync Era archive node and made it freely available to external parties. We provide details on this dataset and how it was created, showcase a few example analyses that can be performed with it, and discuss some future research directions.
Lei Xu, Yulong Chen, Yuntian Chen, Longfeng Nie · 7 authors
Machine learning models offer the capability to forecast future energy production or consumption and infer essential unknown variables from existing data. However, legal and policy constraints within specific energy sectors render the data sensitive, presenting technical hurdles in utilizing data from diverse sources. Therefore, we propose adopting a Swarm Learning (SL) scheme, which replaces the centralized server with a blockchain-based distributed network to address the security and privacy issues inherent in Federated Learning (FL)'s centralized architecture. Within this distributed Collaborative Learning framework, each participating organization governs nodes for inter-organizational communication. Devices from various organizations utilize smart contracts for parameter uploading and retrieval. Consensus mechanism ensures distributed consistency throughout the learning process, guarantees the transparent trustworthiness and immutability of parameters on-chain. The efficacy of the proposed framework is substantiated across three real-world energy series modeling scenarios with superior performance compared to Local Learning approaches, simultaneously emphasizing enhanced data security and privacy over Centralized Learning and FL method. Notably, as the number of data volume and the count of local epochs increases within a threshold, there is an improvement in model performance accompanied by a reduction in the variance of performance errors. Consequently, this leads to an increased stability and reliability in the outcomes produced by the model.
This paper investigates the stochastic behavior of an n-node blockchain which is continuously monitored and faces non-stop cyber attacks from multiple hackers. The blockchain will start being re-set once hacking is detected, forfeiting previous efforts of all hackers. It is assumed the re-setting process takes a random amount of time. Multiple independent hackers will keep attempting to hack into the blockchain until one of them succeeds. For arbitrary distributions of the hacking times, detecting times, and re-setting times, we derive the instantaneous functional probability, the limiting functional probability, and the mean functional time of the blockchain. Moreover, we establish that these quantities are increasing functions of the number of nodes, formalizing the intuition that the more nodes a blockchain has the more secure it is.
This paper investigates the distribution of public school expenditures across U.S. school districts using a bayesian maximum entropy model. Covering the period 2000-2016, I explore how inter-jurisdictional competition and household choice influence spending patterns within the public education sector, providing a novel empirical treatment of the Tiebout hypothesis within a statistical equilibrium framework. The analysis reveals that these expenditures are characterized by sharply peaked and positively skewed distributions, suggesting significant socioeconomic stratification. Employing Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling, I fit these patterns into a statistical equilibrium model to elucidate the roles of competition, as well as household mobility and arbitrage in shaping the distribution of educational spending. The analysis reveals how the scale parameters associated with competition and household choice critically shape the equilibrium outcomes. The model and analysis offer a statistical basis for shaping policy measures intended to affect distributional outcomes in scenarios characterized by the decentralized provision of local public goods.
Marcin Wątorek, Paweł Szydło, Jarosław Kwapień, Stanisław Drożdż
The non-fungible token (NFT) market emerges as a recent trading innovation leveraging blockchain technology, mirroring the dynamics of the cryptocurrency market. The current study is based on the capitalization changes and transaction volumes across a large number of token collections on the Ethereum platform. In order to deepen the understanding of the market dynamics, the collection-collection dependencies are examined by using the multivariate formalism of detrended correlation coefficient and correlation matrix. It appears that correlation strength is lower here than that observed in previously studied markets. Consequently, the eigenvalue spectra of the correlation matrix more closely follow the Marchenko-Pastur distribution, still, some departures indicating the existence of correlations remain. The comparison of results obtained from the correlation matrix built from the Pearson coefficients and, independently, from the detrended cross-correlation coefficients suggests that the global correlations in the NFT market arise from higher frequency fluctuations. Corresponding minimal spanning trees (MSTs) for capitalization variability exhibit a scale-free character while, for the number of transactions, they are somewhat more decentralized.
Sandra Johnson, Kerrie Mengersen, Patrick O'Callaghan, Anders L. Madsen
Immediate settlement, or single-slot finality (SSF), is a long-term goal for Ethereum. The growing active validator set size is placing an increasing computational burden on the network, making SSF more challenging. EIP-7251 aims to reduce the number of validators by giving stakers the option to merge existing validators. Key to the success of this proposal therefore is whether stakers choose to merge their validators once EIP-7251 is implemented. It is natural to assume stakers participate only if they anticipate greater expected utility (risk-adjusted returns) as a single large validator. In this paper, we focus on one of the duties that a validator performs, viz. being the proposer for the next block. This duty can be quite lucrative, but happens infrequently. Based on previous analysis, we may assume that EIP-7251 implies no change to the security of the protocol. We confirm that the probability of a validator being selected as block proposer is equivalent under each consolidation regime. This result ensures that the decision of one staker to merge has no impact on the opportunity of another to propose the next block, in turn ensuring there is no major systemic change to the economics of the protocol with respect to proposer selection.
Anurag Gupta, Vikram Krishnamurthy, Brian M. Sadler
This paper introduces a novel non-parametric change detection algorithm to identify eclipse attacks on a blockchain network; the non-parametric algorithm relies only on the empirical mean and variance of the dataset, making it highly adaptable. An eclipse attack occurs when malicious actors isolate blockchain users, disrupting their ability to reach consensus with the broader network, thereby distorting their local copy of the ledger. To detect an eclipse attack, we monitor changes in the Fréchet mean and variance of the evolving blockchain communication network connecting blockchain users. First, we leverage the Johnson-Lindenstrauss lemma to project large-dimensional networks into a lower-dimensional space, preserving essential statistical properties. Subsequently, we employ a non-parametric change detection procedure, leading to a test statistic that converges weakly to a Brownian bridge process in the absence of an eclipse attack. This enables us to quantify the false alarm rate of the detector. Our detector can be implemented as a smart contract on the blockchain, offering a tamper-proof and reliable solution. Finally, we use numerical examples to compare the proposed eclipse attack detector with a detector based on the random forest model.
Yaoyue Tang, Karina Arias-Calluari, M. N. Najafi, Michael Harré · 5 authors
This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The Bitcoin price returns for both periods can be described by an anomalous diffusion process, transitioning from subdiffusion for short intervals to weak superdiffusion over longer time intervals. The characteristic features related to this anomalous behavior studied in the present paper include heavy tails, which can be described using a $q$-Gaussian distribution and correlations. When we sample the autocorrelation of absolute returns, we observe a power-law relationship, indicating time dependence in both periods initially. The ensemble autocorrelation of the returns decays rapidly. We fitted the autocorrelation with a power law to capture the decay and found that the second period experienced a slightly higher decay rate. The further study involves the analysis of endogenous effects within the Bitcoin time series, which are examined through detrending analysis. We found that both periods are multifractal and present self-similarity in the detrended probability density function (PDF). The Hurst exponent over short time intervals shifts from less than 0.5 ($\sim$ 0.42) in Period 1 to closer to 0.5 in Period 2 ($\sim$ 0.49), indicating that the market has gained efficiency over time.
The growing interest in cryptocurrencies has drawn the attention of the financial world to this innovative medium of exchange. This study aims to explore the impact of cryptocurrencies on portfolio performance. We conduct our analysis retrospectively, assessing the performance achieved within a specific time frame by three distinct portfolios: one consisting solely of equities, bonds, and commodities; another composed exclusively of cryptocurrencies; and a third, which combines both 'traditional' assets and the best-performing cryptocurrency from the second portfolio.To achieve this, we employ the classic variance-covariance approach, utilizing the GARCH-Copula and GARCH-Vine Copula methods to calculate the risk structure. The optimal asset weights within the optimized portfolios are determined through the Markowitz optimization problem. Our analysis predominantly reveals that the portfolio comprising both cryptocurrency and traditional assets exhibits a higher Sharpe ratio from a retrospective viewpoint and demonstrates more stable performances from a prospective perspective. We also provide an explanation for our choice of portfolio optimization based on the Markowitz approach rather than CVaR and ES.
We propose a nonparametric and time-varying directed information graph (TV-DIG) framework to estimate the evolving causal structure in time series networks, thereby addressing the limitations of traditional econometric models in capturing high-dimensional, nonlinear, and time-varying interconnections among series. This framework employs an information-theoretic measure rooted in a generalized version of Granger-causality, which is applicable to both linear and nonlinear dynamics. Our framework offers advancements in measuring systemic risk and establishes meaningful connections with established econometric models, including vector autoregression and switching models. We evaluate the efficacy of our proposed model through simulation experiments and empirical analysis, reporting promising results in recovering simulated time-varying networks with nonlinear and multivariate structures. We apply this framework to identify and monitor the evolution of interconnectedness and systemic risk among major assets and industrial sectors within the financial network. We focus on cryptocurrencies' potential systemic risks to financial stability, including spillover effects on other sectors during crises like the COVID-19 pandemic and the Federal Reserve's 2020 emergency response. Our findings reveals significant, previously underrecognized pre-2020 influences of cryptocurrencies on certain financial sectors, highlighting their potential systemic risks and offering a systematic approach in tracking evolving cross-sector interactions within financial networks.
Nir Chemaya, Lin William Cong, Emma Jorgensen, Dingyue Liu · 5 authors
Decentralized Finance (DeFi) is reshaping traditional finance by enabling direct transactions without intermediaries, creating a rich source of open financial data. Layer 2 (L2) solutions are emerging to enhance the scalability and efficiency of the DeFi ecosystem, surpassing Layer 1 (L1) systems. However, the impact of L2 solutions is still underexplored, mainly due to the lack of comprehensive transaction data indices for economic analysis. This study bridges that gap by analyzing over 50 million transactions from Uniswap, a major decentralized exchange, across both L1 and L2 networks. We created a set of daily indices from blockchain data on Ethereum, Optimism, Arbitrum, and Polygon, offering insights into DeFi adoption, scalability, decentralization, and wealth distribution. Additionally, we developed an open-source Python framework for calculating decentralization indices, making this dataset highly useful for advanced machine learning research. Our work provides valuable resources for data scientists and contributes to the growth of the intelligent Web3 ecosystem.
The issue related to the quantification of the tail risk of cryptocurrencies is considered in this paper. The statistical methods used in the study are those concerning recent developments in Extreme Value Theory (EVT) for weakly dependent data. This research proposes an expectile-based approach for assessing the tail risk of dependent data. Expectile is a summary statistic that generalizes the concept of mean, as the quantile generalizes the concept of the median. We present the empirical findings for a dataset of cryptocurrencies. We propose a method for dynamically evaluating the level of the expectiles by estimating the level of the expectiles of the residuals of a heteroscedastic regression, such as a GARCH model. Finally, we introduce the Marginal Expected Shortfall (MES) as a tool for measuring the marginal impact of single assets on systemic shortfalls. In our case of interest, we are focused on the impact of a single cryptocurrency on the systemic risk of the whole cryptocurrency market. In particular, we present an expectile-based MES for dependent data.
Blockchain technology is leading a revolutionary transformation across diverse industries, with effective governance standing as a critical determinant for the success and sustainability of blockchain projects. Community forums, pivotal in engaging decentralized autonomous organizations (DAOs), wield a substantial impact on blockchain governance decisions. Concurrently, Natural Language Processing (NLP), particularly sentiment analysis, provides powerful insights from textual data. While prior research has explored the potential of NLP tools in social media sentiment analysis, a gap persists in understanding the sentiment landscape of blockchain governance communities. The evolving discourse and sentiment dynamics on the forums of top DAOs remain largely unknown. This paper delves deep into the evolving discourse and sentiment dynamics on the public forums of leading DeFi projects—Aave, Uniswap, Curve Dao, Aragon, Yearn.finance, Merit Circle, and Balancer—placing a primary focus on discussions related to governance issues. Despite differing activity patterns, participants across these decentralized communities consistently express positive sentiments in their Discord discussions, indicating optimism towards governance decisions. Additionally, our research suggests a potential interplay between discussion intensity and sentiment dynamics, indicating that higher discussion volumes may contribute to more stable and positive emotions. The insights gained from this study are valuable for decision-makers in blockchain governance, underscoring the pivotal role of sentiment analysis in interpreting community emotions and its evolving impact on the landscape of blockchain governance. This research significantly contributes to the interdisciplinary exploration of the intersection of blockchain and society, with a specific emphasis on the decentralized blockchain governance ecosystem. We provide our data and code for replicability as open access on GitHub.
Paweł Szydło, Marcin Wątorek, Jarosław Kwapień, Stanisław Drożdż
A non-fungible token (NFT) market is a new trading invention based on the blockchain technology, which parallels the cryptocurrency market. In the present work, we study capitalization, floor price, the number of transactions, the inter-transaction times, and the transaction volume value of a few selected popular token collections. The results show that the fluctuations of all these quantities are characterized by heavy-tailed probability distribution functions, in most cases well described by the stretched exponentials, with a trace of power-law scaling at times, long-range memory, persistence, and in several cases even the fractal organization of fluctuations, mostly restricted to the larger fluctuations, however. We conclude that the NFT market-even though young and governed by somewhat different mechanisms of trading-shares several statistical properties with the regular financial markets. However, some differences are visible in the specific quantitative indicators.
The role of cryptocurrencies within the financial systems has been expanding rapidly in recent years among investors and institutions. It is therefore crucial to investigate the phenomena and develop statistical methods able to capture their interrelationships, the links with other global systems, and, at the same time, the serial heterogeneity. For these reasons, this paper introduces hidden Markov regression models for jointly estimating quantiles and expectiles of cryptocurrency returns using regime-switching copulas. The proposed approach allows us to focus on extreme returns and describe their temporal evolution by introducing time-dependent coefficients evolving according to a latent Markov chain. Moreover to model their time-varying dependence structure, we consider elliptical copula functions defined by state-specific parameters. Maximum likelihood estimates are obtained via an Expectation-Maximization algorithm. The empirical analysis investigates the relationship between daily returns of five cryptocurrencies and major world market indices.
Marcin Wątorek, Maria Skupień, Jarosław Kwapień, Stanisław Drożdż
This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures - logarithmic returns, volume, and transaction number, sampled every 10 seconds, were divided into intraday and intraweek periods and then further decomposed into recurring and noise components via correlation matrix formalism. The key findings include the distinctive market behavior from traditional stock markets due to the nonexistence of trade opening and closing. This was manifest in three enhanced-activity phases aligning with Asian, European, and U.S. trading sessions. An intriguing pattern of activity surge in 15-minute intervals, particularly at full hours, was also noticed, implying the potential role of algorithmic trading. Most notably, recurring bursts of activity in bitcoin and ether were identified to coincide with the release times of significant U.S. macroeconomic reports such as Nonfarm payrolls, Consumer Price Index data, and Federal Reserve statements. The most correlated daily patterns of activity occurred in 2022, possibly reflecting the documented correlations with U.S. stock indices in the same period. Factors that are external to the inner market dynamics are found to be responsible for the repeatable components of the market dynamics, while the internal factors appear to be substantially random, which manifests itself in a good agreement between the empirical eigenvalue distributions in their bulk and the random matrix theory predictions expressed by the Marchenko-Pastur distribution. The findings reported support the growing integration of cryptocurrencies into the global financial markets.
Considering that both the entropy-based market information and the Hurst exponent are useful tools for determining whether the efficient market hypothesis holds for a given asset, we study the link between the two approaches. We thus provide a theoretical expression for the market information when log-prices follow either a fractional Brownian motion or its stationary extension using the Lamperti transform. In the latter model, we show that a Hurst exponent close to 1/2 can lead to a very high informativeness of the time series, because of the stationarity mechanism. In addition, we introduce a multiscale method to get a deeper interpretation of the entropy and of the market information, depending on the size of the information set. Applications to Bitcoin, CAC 40 index, Nikkei 225 index, and EUR/USD FX rate, using daily or intraday data, illustrate the methodological content.
Stanisław Drożdż, Jarosław Kwapień, Marcin Wątorek
In relation to the traditional financial markets, the cryptocurrency market is a recent invention and the trading dynamics of all its components are readily recorded and stored. This fact opens up a unique opportunity to follow the multidimensional trajectory of its development since inception up to the present time. Several main characteristics commonly recognized as financial stylized facts of mature markets were quantitatively studied here. In particular, it is shown that the return distributions, volatility clustering effects, and even temporal multifractal correlations for a few highest-capitalization cryptocurrencies largely follow those of the well-established financial markets. The smaller cryptocurrencies are somewhat deficient in this regard, however. They are also not as highly cross-correlated among themselves and with other financial markets as the large cryptocurrencies. Quite generally, the volume V impact on price changes R appears to be much stronger on the cryptocurrency market than in the mature stock markets, and scales as $R(V) \sim V^α$ with $α\gtrsim 1$.
Blockchain enables peer-to-peer transactions in cyberspace without a trusted third party. The rapid growth of Ethereum and smart contract blockchains generally calls for well-designed Transaction Fee Mechanisms (TFMs) to allocate limited storage and computation resources. However, existing research on TFMs must consider the waiting time for transactions, which is essential for computer security and economic efficiency. Integrating data from the Ethereum blockchain and memory pool (mempool), we explore how two types of events affect transaction latency. First, we apply regression discontinuity design (RDD) to study the causal inference of the Merge, the most recent significant upgrade of Ethereum. Our results show that the Merge significantly reduces the long waiting time, network loads, and market congestion. In addition, we verify our results' robustness by inspecting other compounding factors, such as censorship and unobserved delays of transactions via private changes. Second, examining three major protocol changes during the merge, we identify block interval shortening as the most plausible cause for our empirical results. Furthermore, in a mathematical model, we show block interval as a unique mechanism design choice for EIP1559 TFM to achieve better security and efficiency, generally applicable to the market congestion caused by demand surges. Finally, we apply time series analysis to research the interaction of Non-Fungible token (NFT) drops and market congestion using Facebook Prophet, an open-source algorithm for generating time-series models. Our study identified NFT drops as a unique source of market congestion -- holiday effects -- beyond trend and season effects. Finally, we envision three future research directions of TFM.
Marcin Wątorek, Jarosław Kwapień, Stanisław Drożdż
In this study the cross-correlations between the cryptocurrency market represented by the two most liquid and highest-capitalized cryptocurrencies: bitcoin and ethereum, on the one side, and the instruments representing the traditional financial markets: stock indices, Forex, commodities, on the other side, are measured in the period: January 2020--October 2022. Our purpose is to address the question whether the cryptocurrency market still preserves its autonomy with respect to the traditional financial markets or it has already aligned with them in expense of its independence. We are motivated by the fact that some previous related studies gave mixed results. By calculating the $q$-dependent detrended cross-correlation coefficient based on the high frequency 10 s data in the rolling window, the dependence on various time scales, different fluctuation magnitudes, and different market periods are examined. There is a strong indication that the dynamics of the bitcoin and ethereum price changes since the March 2020 Covid-19 panic is no longer independent. Instead, it is related to the dynamics of the traditional financial markets, which is especially evident now in 2022, when the bitcoin and ethereum coupling to the US tech stocks is observed during the market bear phase. It is also worth emphasizing that the cryptocurrencies have begun to react to the economic data such as the Consumer Price Index readings in a similar way as traditional instruments. Such a spontaneous coupling of the so far independent degrees of freedom can be interpreted as a kind of phase transition that resembles the collective phenomena typical for the complex systems. Our results indicate that the cryptocurrencies cannot be considered as a safe haven for the financial investments.
In this paper we develop a linear expectile hidden Markov model for the analysis of cryptocurrency time series in a risk management framework. The methodology proposed allows to focus on extreme returns and describe their temporal evolution by introducing in the model time-dependent coefficients evolving according to a latent discrete homogeneous Markov chain. As it is often used in the expectile literature, estimation of the model parameters is based on the asymmetric normal distribution. Maximum likelihood estimates are obtained via an Expectation-Maximization algorithm using efficient M-step update formulas for all parameters. We evaluate the introduced method with both artificial data under several experimental settings and real data investigating the relationship between daily Bitcoin returns and major world market indices.
Non-Fungible Tokens (NFTs) are non-interchangeable assets, usually digital art, which are stored on the blockchain. Preliminary studies find that female and darker-skinned NFTs are valued less than their male and lighter-skinned counterparts. However, these studies analyze only the CryptoPunks collection. We test the statistical significance of race and gender biases in the prices of CryptoPunks and present the first study of gender bias in the broader NFT market. We find evidence of racial bias but not gender bias. Our work also introduces a dataset of gender-labeled NFT collections to advance the broader study of social equity in this emerging market.
Francesco Sanna Passino, Anastasia Mantziou, Daniyar Ghani, Philip Thiede · 6 authors
Cyber-systems are under near-constant threat from intrusion attempts. Attacks types vary, but each attempt typically has a specific underlying intent, and the perpetrators are typically groups of individuals with similar objectives. Clustering attacks appearing to share a common intent is very valuable to threat-hunting experts. This article explores Dirichlet distribution topic models for clustering terminal session commands collected from honeypots, which are special network hosts designed to entice malicious attackers. The main practical implications of clustering the sessions are two-fold: finding similar groups of attacks, and identifying outliers. A range of statistical models are considered, adapted to the structures of command-line syntax. In particular, concepts of primary and secondary topics, and then session-level and command-level topics, are introduced into the models to improve interpretability. The proposed methods are further extended in a Bayesian nonparametric fashion to allow unboundedness in the vocabulary size and the number of latent intents. The methods are shown to discover an unusual MIRAI variant which attempts to take over existing cryptocurrency coin-mining infrastructure, not detected by traditional topic-modelling approaches.
Our work presents two fundamental contributions. On the application side, we tackle the challenging problem of predicting day-ahead crypto-currency prices. On the methodological side, a new dynamical modeling approach is proposed. Our approach keeps the probabilistic formulation of the state-space model, which provides uncertainty quantification on the estimates, and the function approximation ability of deep neural networks. We call the proposed approach the deep state-space model. The experiments are carried out on established cryptocurrencies (obtained from Yahoo Finance). The goal of the work has been to predict the price for the next day. Benchmarking has been done with both state-of-the-art and classical dynamical modeling techniques. Results show that the proposed approach yields the best overall results in terms of accuracy.