Correlations versus noise in the NFT market

TL;DR

The study investigates cross-collection correlations in the Ethereum NFT market to separate genuine collective dynamics from randomness. It applies Random Matrix Theory, Pearson and detrended cross-correlation matrices $\mathbf{C}$ and $\mathbf{C}^{\rho}(q,s)$, multifractal detrended fluctuation analysis (MFDFA) with $\rho(q,s)$, and minimal spanning trees (MST) to 90 collections over ~500 days using time series $c_{\Delta t}$ and $N_{\Delta t}$. Findings show weaker cross-correlations than in traditional markets, with eigenvalue spectra largely resembling the Marchenko-Pastur distribution but featuring a market-factor eigenvalue $\lambda_1$ and notable anti-correlations; large fluctuations exhibit stronger cross-collection coupling, especially for $q=4$. MSTs reveal decentralized networks lacking a dominant hub, a feature that persists after accounting for the market factor, reflecting NFT-specific information transmission mechanisms and distinct dynamics from cryptocurrencies and stocks.

Abstract

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.

Figures (15)

• Figure 1: (a) Collection capitalization $K(t)$ and (b) the number of transactions $N_{\Delta t=24h}(t)$ for all the considered NFT collections with the most frequently traded ones listed explicitly. Inset in (b) displays fluctuations of the number of transactions around January 6, 2023, highlighting a significant surge in activity for the aforementioned collections during this period.
• Figure 2: Daily pattern of the number of transactions in 1 hour interval averaged over all trading days $\langle N_{\Delta t=1h} \rangle$.
• Figure 3: Complementary cumulative distribution functions for (a) absolute logarithmic increments of collection capitalization expressed in USD $|c_{\Delta t=1h}(t)|$ and (b) the number of transactions aggregated hourly $N_{\Delta t=1h}(t)$.
• Figure 4: Autocorrelation functions of $c_{\Delta t=1h}$ (a) and $N_{\Delta t=1h}$ (b) for all the collections.
• Figure 5: Fluctuation functions $F(q,s)$ with $q \in [-4,4]$ calculated for the number of transactions $N_{\Delta t=1h}$ and logarithmic increments of the total collection capitalization $c_{\Delta t=1h}$ for Mutant Ape Yacht Club collection. In main panels, thick green lines represent $F(q=2,s)$, which are utilized in the estimation of the Hurst exponent $H$ with the standard error. Vertical red dashed lines point out to a scale range where the family of $F(q,s)$ exhibit power-law dependence for different values of $q$, from which the singularity spectrum $f(\alpha)$ can be calculated (insets).