Scaling Laws And Statistical Properties of The Transaction Flows And Holding Times of Bitcoin

ArXiv ID: 2401.04702 “View on arXiv”

Authors: Unknown

Abstract

We study the temporal evolution of the holding-time distribution of bitcoins and find that the average distribution of holding-time is a heavy-tailed power law extending from one day to over at least $200$ weeks with an exponent approximately equal to $0.9$, indicating very long memory effects. We also report significant sample-to-sample variations of the distribution of holding times, which can be best characterized as multiscaling, with power-law exponents varying between $0.3$ and $2.5$ depending on bitcoin price regimes. We document significant differences between the distributions of book-to-market and of realized returns, showing that traders obtain far from optimal performance. We also report strong direct qualitative and quantitative evidence of the disposition effect in the Bitcoin Blockchain data. Defining age-dependent transaction flows as the fraction of bitcoins that are traded at a given time and that were born (last traded) at some specific earlier time, we document that the time-averaged transaction flow fraction has a power law dependence as a function of age, with an exponent close to $-1.5$, a value compatible with priority queuing theory. We document the existence of multifractality on the measure defined as the normalized number of bitcoins exchanged at a given time.

Keywords: Bitcoin, Holding-time Distribution, Disposition Effect, Multifractality, Power Law, Cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs a rigorous mathematical formulation (difference equations, distribution theory, multifractality) and leverages complete, public blockchain data to analyze transaction flows and holding times with strong empirical evidence.

  flowchart TD
    A["Research Goal: Study Temporal Dynamics<br>Holding Times & Transaction Flows in Bitcoin"] --> B
    subgraph B ["Methodology & Data"]
        B1["Data Source: Bitcoin Blockchain"]
        B2["Key Metrics: Holding Times<br>Transaction Flows<br>Realized Returns"]
    end
    B --> C["Computational Analysis"]
    subgraph C ["Computational Analysis"]
        direction LR
        C1["Fitting<br>Power-Law Distributions"]
        C2["Analyzing<br>Price Regimes"]
        C3["Testing for<br>Multifractality"]
    end
    C --> D["Key Findings & Outcomes"]
    subgraph D ["Key Findings & Outcomes"]
        D1["Holding Time: Heavy-tailed<br>Power Law (t ≈ -0.9)<br>Multiscaling across regimes"]
        D2["Transaction Flow: Age-dependent<br>Power Law (t ≈ -1.5)<br>Matches Priority Queuing"]
        D3["Trader Performance:<br>Disposition Effect detected<br>Far from optimal"]
        D4["Market Structure:<br>Strong Multifractality present"]
    end