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arxiv: 2606.25466 · v1 · pith:CXPCZSE7new · submitted 2026-06-24 · 💱 q-fin.TR · q-fin.GN

Time-dependent weighted directed networks of cryptocurrency interaction from high-frequency returns

Shubhangam Shukla , Mahesh Peyyala , Abhijit Chakraborty This is my paper

Pith reviewed 2026-06-25 19:55 UTC · model grok-4.3

classification 💱 q-fin.TR q-fin.GN
keywords cryptocurrencyGranger causalitydirected networkshigh-frequency returnsinfluence rankingEthereumBitcointemporal variability
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The pith

Granger-causality networks from high-frequency returns show Ethereum as the most influential cryptocurrency while Bitcoin's relative importance declines steadily from 2020 to 2025.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds time-dependent directed and weighted networks whose edges are the statistically significant Granger causal links between log-returns of multiple cryptocurrencies. These networks display strong heterogeneity, with a small number of assets accounting for most of the outgoing influence. Ranking nodes by out-strength produces a hierarchy in which Ethereum occupies the top position across most intervals, Bitcoin slips downward, and other coins move in and out of the leading ranks. The structure changes markedly over time, indicating that market leadership is competitive rather than fixed. The same networks also recover the heavy-tailed character of normalized returns that is familiar from other financial markets.

Core claim

Directed and weighted networks constructed from statistically significant Granger causal relationships between cryptocurrency log-returns reveal a dynamically evolving hierarchy of influence in which Ethereum consistently ranks as the most influential asset, Bitcoin exhibits a gradual decline in relative importance, and the ranking structure shows substantial temporal variability with multiple cryptocurrencies entering and exiting top positions.

What carries the argument

Directed weighted networks whose edges are statistically significant Granger causal links between log-returns, with nodal out-strength serving as the measure of influence.

If this is right

  • A small subset of cryptocurrencies accounts for a disproportionate share of directed influence in the market.
  • Market leadership is non-stable, with frequent changes in which assets occupy the highest ranks.
  • Normalized returns remain heavy-tailed even after network construction, consistent with known financial stylized facts.
  • The organization of the cryptocurrency ecosystem is competitive rather than dominated by any permanent leader.
  • Out-strength rankings derived from these networks provide a quantitative description of evolving influence flows.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The observed temporal variability implies that any static snapshot of influence would quickly become outdated for monitoring or risk purposes.
  • If the networks capture genuine predictive structure, they could be used to test whether influence measured this way improves forecasts of volatility spillovers between assets.
  • The concentration of out-strength in a few nodes raises the question of how resilient the overall market remains when those central assets experience large shocks.
  • Extending the same Granger-network construction to include traditional financial assets would show whether crypto influence remains internally driven or couples to broader markets.

Load-bearing premise

Statistically significant Granger causal relationships between log-returns accurately quantify the flow of influence across assets without being driven by common external shocks, microstructure noise, or multiple-testing artifacts.

What would settle it

If the detected Granger causalities and the resulting out-strength rankings vanish or reorder after the returns are orthogonalized to common market factors or after microstructure noise is removed, the claimed influence hierarchy would be falsified.

Figures

Figures reproduced from arXiv: 2606.25466 by Abhijit Chakraborty, Mahesh Peyyala, Shubhangam Shukla.

Figure 1
Figure 1. Figure 1: Complementary cumulative distribution functions (CCDF) of the normalized 1-minute log-returns r. Panels (a) and (b) show the positive and negative tails for XBT, respectively, while panels (c) and (d) cor￾respond to XRP. The red lines represent power-law fits of the form P(r) ∼ r 1−γ , with estimated exponents γ = 3.91, 3.78, 4.08, and 3.66 for panels (a)–(d), respectively. The exponents are obtained using… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Normalized log-return of ETH (grey), along with the restricted model (red) defined in Eq. 2, where the target variable Y represents log-return time series for ETH, and the full model (blue) defined in Eq. 3, where X represents log-return time series for XBT. In both models, the error term is excluded. Panels (b) and (c) show the corresponding residuals (error terms) for the full model and restricted mo… view at source ↗
Figure 3
Figure 3. Figure 3: Complementary cumulative distribution functions (CCDF) of key network measures: (a) link weight w, (b) nodal out-strength sout, and (c) nodal in-strength sin. Results are shown for a representative week (24–30 March 2025); other weeks exhibit qualitatively similar behaviour. presents the distribution of link weights w, while panels (b) and (c) show the distributions of nodal out-strength sout and in-streng… view at source ↗
Figure 4
Figure 4. Figure 4: Scatter plot of nodal out-strength sout versus in-strength sin for all nodes. The red line represents a power-law fit of the form sout ∼ s α in . The estimated exponent α = 0.91 indicates a nontrivial sublinear relationship between the two quantities. Results are shown for a representative week (24–30 March 2025); other weeks exhibit qualitatively similar behaviour. once among the top five most influential… view at source ↗
Figure 5
Figure 5. Figure 5: Ranking of cryptocurrencies based on their average quarterly out-strength (influence) over the period 2020–2025. Ethereum (ETH) consistently ranks as the most influential cryptocurrency, while Bitcoin (XBT) shows a gradual decline in influence. The rankings exhibit significant temporal variability, particularly between Q3 2022 and Q1 2025, with multiple cryptocurrencies entering and exiting the top ranks. … view at source ↗
Figure 6
Figure 6. Figure 6: Robustness of the inferred network structure after removing the common market factor via first prin￾cipal component (PC1) regression. Panel (a) compares the nodal out-strength sout computed from the orig￾inal log-returns (PC unregressed) against those computed from the PC1-filtered idiosyncratic residuals (PC regressed) for all nodes across the network. Panel (b) shows the corresponding comparison for indi… view at source ↗
read the original abstract

We investigate the evolving structure of interactions in cryptocurrency markets using a network-based framework constructed from high-frequency price data spanning 2020-2025. Directed and weighted networks are constructed from statistically significant Granger causal relationships between cryptocurrency log-returns, enabling us to quantify the flow of influence across assets. We find that normalized returns exhibit heavy-tailed distributions, consistent with the presence of large intermittent fluctuations and in line with stylized facts of financial markets. The resulting networks display pronounced heterogeneity in link weights and nodal strengths, indicating that a small subset of cryptocurrencies contributes disproportionately to market dynamics. By ranking cryptocurrencies based on their nodal out-strength, we uncover a dynamically evolving hierarchy of influence. Ethereum consistently emerges as the most influential asset, while Bitcoin shows a gradual decline in its relative importance. The ranking structure exhibits substantial temporal variability, with multiple cryptocurrencies entering and exiting the top positions over time. Our findings reveal a highly competitive and non-stable organization of the cryptocurrency ecosystem.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript constructs time-dependent directed weighted networks from high-frequency cryptocurrency log-returns (2020-2025) by retaining only statistically significant Granger-causal links. It reports heavy-tailed normalized returns, heterogeneous link weights and nodal strengths, and a ranking of assets by out-strength that identifies Ethereum as consistently most influential, Bitcoin as declining in relative importance, and substantial temporal variability in the top ranks, concluding that the ecosystem exhibits a competitive, non-stable organization.

Significance. If the Granger-causality links can be shown to isolate directed influence rather than common shocks or testing artifacts, the work would supply a concrete, time-resolved hierarchy of influence in cryptocurrency markets and document its instability, which is of interest for both market microstructure and systemic-risk studies.

major comments (2)
  1. [Abstract] Abstract: the central claim that out-strength rankings yield a reliable hierarchy rests on pairwise Granger tests performed across many asset pairs, lags, and rolling windows, yet the text supplies no indication of multiple-testing correction (FDR or Bonferroni) or of the exact test count; without this, the reported temporal variability and specific rankings (Ethereum dominant, Bitcoin declining) cannot be distinguished from false-positive artifacts.
  2. [Abstract] Abstract: the networks are built from raw log-returns without any reported orthogonalization to a latent market factor or first principal component; in cryptocurrency data dominated by common shocks, significant pairwise links can arise from shared exposure rather than direct causation, directly undermining the interpretation of out-strength as a measure of influence flow.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'normalized returns exhibit heavy-tailed distributions' is stated without reference to the normalization procedure or the specific tail index estimated, which would help readers assess consistency with known financial stylized facts.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important methodological considerations for strengthening the interpretation of our Granger-causality networks. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that out-strength rankings yield a reliable hierarchy rests on pairwise Granger tests performed across many asset pairs, lags, and rolling windows, yet the text supplies no indication of multiple-testing correction (FDR or Bonferroni) or of the exact test count; without this, the reported temporal variability and specific rankings (Ethereum dominant, Bitcoin declining) cannot be distinguished from false-positive artifacts.

    Authors: We agree that multiple testing is a critical issue given the scale of pairwise tests across assets, lags, and rolling windows. The original manuscript does not report any correction procedure or the exact test count. In the revised version we will apply FDR correction at the conventional 5% level and explicitly document the total number of tests performed per window, allowing readers to assess whether the reported rankings and temporal variability remain robust. revision: yes

  2. Referee: [Abstract] Abstract: the networks are built from raw log-returns without any reported orthogonalization to a latent market factor or first principal component; in cryptocurrency data dominated by common shocks, significant pairwise links can arise from shared exposure rather than direct causation, directly undermining the interpretation of out-strength as a measure of influence flow.

    Authors: The referee correctly notes that common shocks can induce spurious pairwise Granger links. Our current construction follows the direct application of Granger causality to raw log-returns, which is standard in several existing cryptocurrency network studies. To address the concern, the revision will add a robustness section in which returns are first orthogonalized to the first principal component (or a market-factor proxy) before re-estimating the networks; we will then compare the resulting out-strength rankings and temporal variability with the original results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is data-driven from observed returns

full rationale

The paper constructs directed networks directly from statistically significant Granger causal links on log-returns, then computes out-strength rankings; no equations, fitted parameters, or self-citations are shown that would make the hierarchy or temporal variability equivalent to the inputs by construction. The abstract and description indicate an empirical pipeline without self-definitional steps, fitted-input predictions, or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the validity of Granger causality as a measure of influence and on the assumption that high-frequency log-returns are stationary enough for the tests; no free parameters, invented entities, or non-standard axioms are mentioned.

axioms (1)
  • domain assumption Granger causality on log-returns captures directed influence between assets
    Invoked when the paper states that significant Granger links quantify flow of influence

pith-pipeline@v0.9.1-grok · 5698 in / 1095 out tokens · 24773 ms · 2026-06-25T19:55:11.511219+00:00 · methodology

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Reference graph

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