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, 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 a somewhat different mechanisms of trading - shares several statistical properties with the regular financial markets. However, some differences are visible in the specific quantitative indicators.
Majority of the observables for all the collections show a persistent behaviour with 0.6 6 H 6 0.8 this is true for the capitalization increments, the number of trades, intertransaction times, and transaction volume value. For the unsigned observables like t, Nt , and Vt, it is an expected, natural result if one takes into consideration the positive autocorrelations reported above. For the signed observables like ct, however, this outcome is less expected. It can be accounted for by the fact that, even if separated by a substantial lag, the transaction prices of different tokens from the same collection go in the same direction, which leads to a certain inertia in the evolution of its capitalization. This inertia causes, in turn, the 6 Characteristics of price related uctuations in Non-Fungible Token (NFT) market a) 10 1 SOL |c | USD
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|c | TABLE III. Values of the Hurst exponent together with its standard error calculated for time series representing each observable and collection. 10 2 ) A( N t cSOL t cUSD t rSOL t rUSD t Nt t V SOL t V USD t LF 0.67 0.02 0.84 0.04 0.61 0.03 0.77 0.04 0.81 0.04 0.68 0.03 0.82 0.02 0.57 0.05 0.79 0.04 0.81 0.04 0, 47 0.01 0.47 0.01 0.45 0.01 0.49 0.01 0.42 0.01 0.49 0.01 0.47 0.01 0.49 0.01 0.51 0.01 0.46 0.01 0.74 0.02 0.69 0.01 0.62 0.01 0.81 0.01 0.76 0.02 0.65 0.01 0.66 0.01 0.68 0.01 0.70 0.01 0.68 0.01 0.65 0.01 0.74 0.02 0.65 0.02 0.82 0.03 0.67 0.01 0.69 0.01 0.8 0.01 0.69 0.03 0.82 0.04 0.66 0.02 BL FF OKB SM 10 1 10 2 BL FF LF OKB SM considered as the closest possible counterpart of the transaction price in the case of other assets. b) 1 10 10 2 10 3 1 [1h] SOL |r | 10 10 2 10 3 USD |r | C. Multifractal properties 10 1 10 2 ) A( 10 1 SOL V USD
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V The existence of nonlinear long-range correlations (Fig. 3) indicates a possibility of multifractal structures. We thus applied MFDFA to the time series of logarithmic increments of capitalization, oor price returns, transaction volume value aggregated hourly, the number of transactions aggregated hourly, and inter-transaction times for each collection. In any multifractal approach, the fundamental issue is identication of scaling in a plot of the relevant function. In MFDFA it is the uctuation function given by Eq. (4). We calculated Fq(s) for all 8 types of data for each collection. 10 2
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BL FF LF OKB SM 1 10 10 2 10 3 1 [1h] 10 10 2 10 FIG. 3. (a) Autocorrelation function for absolute values of logarithSOL mic increments of collection capitalization expressed in solana |c t | (top left) and US dollar |c t | (top right), the number of transactions aggregated hourly Nt (bottom left), and inter-transaction times t (bottom right). (b) Autocorrelation function for absolute values of USD oor price returns expressed in SOL |r | t (top right) and volume value expressed in solana V (bottom left) and US dollar V USD SOL t | (top left) and USD |r SOL t
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