In recent years, many researchers have studied the phenomenon of wash trading on NFTs (Non Fungible Tokens) from an “ex-ante” perspective. The latter aims to identify and classify wash trading activities before or as they occur. In this paper, we propose an “ex-post” analysis of wash trading on NFTs. This perspective aims to analyze wash trading activities carried out in the past to see whether such illicit and risky activities brought significant profit to those who did them. To the best of our knowledge, this is the ifrst paper in the literature to analyze wash trading on NFTs from an “ex-post”, instead of an “ex-ante”, perspective.
phenomenon. In other words, they sought to identify and classify wash trading activities before
or as they occur [
An NFT2 is defined by several features (think, for instance, of sales volume, price, owner number, etc.). Since the values of these features vary over time, it will be necessary to manage the temporal dimension of this phenomenon. In addition, the various features may be related to each other by diferent relationships (think, for instance, of correlation, causality, distance, etc.). In the following, we will use the term “facet” to refer to such relationships because each of them allows us to view the phenomenon from a certain angle or dimension (a facet, in fact). These facets, when applied to the features of NFTs, allow us to perform a “structured” analysis of the wash trading phenomenon. However, such analysis would not be possible if we did not have a congruent model to represent NFTs. Therefore, in this paper, we will also define such a model.
The outline of this paper is as follows: in Section 2, we present the model and framework used to conduct our analysis. In Section 3, we describe some of the experiments we conducted along with a discussion of the results obtained. Finally, in Section 4, we draw our conclusion and sketch some possible future developments.
Before illustrating our framework for investigating wash trading on NFTs, it is necessary to describe the underlying model by which we represent a set of NFT collections.
An NFT collection is a set of NFTs of the same type created by the same author. Specifically, let = {1, 2, · · · , } be a set of NFT collections of interest. Our model assumes that all NFT collections are characterized by the same set ℱ = {1, 2, · · · , } of features. A generic NFT collection ∈ can be represented as:
= ⟨ , ℱ ⟩ 1https://blog.chainalysis.com/reports/2022-crypto-crime-report-preview-nft-wash-trading-money-laundering/ 2In this paper, when we talk about an NFT, we mean a collection of homogeneous NFTs; therefore, in the following, we will use the terms “NFT” and “NFT collection” interchangeably.
is the name of and is unique. ℱ consists of numerical features whose values
may vary over time. Borrowing the concepts of time series analysis [
As mentioned in the Introduction, the temporal dimension is crucial in our model. Given a time interval of interest, we can think of modeling it as an ordered sequence of time slices = 1, · · · , . For example, could be a certain month, say April 2023. In this case, it could be represented by a succession of 30 time slices, one for each day. Our time model must have a mechanism for indexing the sequence of time slices so that a particular interval of contiguous time slices of (e.g., the first decade of April 2023) can be selected. To this end, it provides the notation [..], 1 ≤ ≤ ≤ , to represent the interval of contiguous time slices beginning at and ending at . If = , then it means that we want to select a single time slice. In this case, we will use the abbreviated notation or [], instead of [..]. If = 1 and = , then it means that we want to select the whole interval of interest. In this case, we will use the abbreviated notation , instead of [1..], to represent that interval.
The notation defined above for time intervals can be extended to the features of an NFT collection. Specifically, given the collection ∈ , we indicate by ℱ [..] the trend of the values of ℱ assumed by in the time interval [..]. In turn, [..], 1 ≤ ≤ , indicates the values of assumed by in the time interval [..]. Clearly, ℱ [..] = {1[..], 2[..], · · · , [..]}. We adopt the notation ℱ [], or ℱ, (resp., [], or ) to indicate the values of ℱ (resp., the value of ) assumed by during the time slice , i.e., ℱ [] = ℱ [..] (resp., [] = [..]). Finally, we adopt the abbreviated notation ℱ (resp., ) to indicate the trend of the values of ℱ (resp., the value of ) assumed by during the overall time interval , i.e., ℱ = ℱ [1..] (resp., = [1..]).
The facets that our framework uses to investigate the wash trading on NFTs phenomenon are three, namely correlation, causality and distance between features. They capture and allow us to analyze diferent aspects of the phenomenon. However, our framework is extensible and allows one or more of these facets to be removed and/or new facets to be added.
The first facet used in our framework is correlation. Correlation analysis is performed
by means of two techniques. The first computes the correlation between two features by
calculating the Pearson coeficient between the corresponding time series [
The second facet used in our framework is the causal relationship between two features. It
expresses the fact that the values of one of them depend on the values of the other. To compute
the causality degree between a pair of features and , we consider the test proposed by
Granger [
The third facet used in our framework is the distance between two features. Since, in our
model, features represent time series, it is not possible to employ classical distance metrics, such
as the Euclidean, Manhattan or Minkowski distance because they are incapable of determining
whether two time series align but with some delay from each other. Therefore, it is necessary
to consider a distance metrics that takes this factor into account. Among those available in the
literature, we decided to use the Dynamic Time Warping (DTW) distance [
We built the dataset for the experiments by extracting data from Cryptoslam3, an aggregator of data on NFT sales involving the Ethereum, WAS and FLOW blockchains. Specifically, we downloaded data on all NFT sales made from the appearance of each NFT collection in the market until February 7, 2023. Then, from all NFT collections thus downloaded, we selected the top 2000 ones based on their USD sales volumes. In this way, we constructed a ranking from which to draw NFT collections for analysis. Because the amounts of money in the dataset were expressed some in USD and some in ETH, we downloaded the daily ETH/USD exchange rate from Yahoo Finance in order to uniform them. The complete dataset thus constructed consisted of 672,098 rows, with an average of 336 rows for each NFT collection.
At this point, we identified the features of NFT collections useful for studying the phenomenon of our interest. Specifically, we identified the following features: (i) Name: it denotes the name of the NFT collection to which all next features refer; (ii) Date: it represents the day to which all next features refer; (iii) Sales: it indicates the sales volume expressed in USD; (iv) ETH: it denotes the ETH/USD exchange rate; (v) Floor Price: it represents the minimum price of an NFT in the collection; (vi) Active Wallets: it indicates the number of active wallets; (vii) Sales Txns: it denotes the number of sale transactions; (viii) Total Owners: it represents the total number of owners; (ix) Wash Sales: it denotes the volume of wash sales expressed in USD; (x) Wash Txns: it indicates the number of transactions made to perform wash trading. The set ℱ of the features of interest for our analysis is given by all these features except the first two.
After that, we homogenized the time slices. In fact, the various features had been surveyed at diferent cadences. To this end, we chose to adopt the daily cadence for all of them to ensure consistency.
The first test we performed focused on the correlation facet. In Section 2, we have seen that there are two correlation metrics, namely the Pearson coeficient and cross-correlation. We began this test by calculating, for each NFT collection, the Pearson coeficient related to each pair of features. Then, we averaged the corresponding values over all available NFT collections. The results obtained are shown in Figure 1. As can be seen from this figure, the correlation between Wash Sales and Sales is very low.
After that, we analyzed the cross-correlation between features. In particular, we considered
three cases corresponding to a number ℎ of lags equal to 0, 1 and 2. For each case, we computed
the value of cross-correlation for each pair of features and for each NFT collection. Finally, we
averaged the values thus obtained over all NFT collections. The results for ℎ = 0 are shown in
Figure 1, since, in this case, cross-correlation coincides with the Pearson coeficient. The results
for ℎ = 2 are shown in Figure 2. Those for ℎ = 1 are not shown because of space limitations;
they can be found in [
The second test we conducted focused on causality. Specifically, we applied the Granger causality test to verify whether Wash Sales Granger-causes Sales. If this happened, we would have a clue that it is worthwhile to carry out wash trading activities on NFTs. If not, we would have a second clue, in addition to that provided by correlation analysis, that it is not worthwhile. To carry out this verification, we considered the following null hypothesis: H0: “Wash Sales does not Granger-cause Sales”. For each NFT collection we calculated the p-value associated with the null hypothesis. Then, we computed for how many NFT collections the p-value was less than 0.05. We performed this calculation both using a linear autoregressive model (VAR) and adopting two deep learning models, namely MultiLayer Perceptron (MLP) and Long Short-Term Memory (LSTM). Finally, we considered diferent values of (representing the maximum number of lagged observations), namely = 1, = 2 and = 3. The results obtained are shown in Table 1.
Model = 1 = 2 = 3
From the analysis of this table, we can deduce that the null hypothesis is almost always confirmed with all the three models considered. This implies that we have a second clue that wash trading on NFTs is not worth doing. However, before drawing any firm conclusion on this, we thought it was appropriate to consider the third facet, namely distance.
The third test we conducted focused on distance. Specifically, we calculated the value of DTW for each pair of features and for each NFT collection in the dataset. Then, we averaged the DTW values thus obtained over all the NFT collections. The final results are shown in Figure 3. From the analysis of this figure, we can observe that the DTW value for the pair (Wash Sales, Sales) is not only high but even the highest among all pairs of features.
All these experiments allow us to conclude that our framework is capable of supporting NFT sales analysis and, in particular, wash trading investigation. In fact, it obtained interesting and concordant results for all the three facets considered. First the Pearson coeficient and cross-correlation values, then the causality values and finally the distance values say us that there is no significant relationships between Wash Sales and Sales. This allows us to conclude that it is very unlikely that there is an impact of wash trading activities on the economic values of an NFT collection.
In this paper, we have proposed an “ex-post” analysis of the wash trading on NFTs phenomenon. While in the literature there are several papers that present “ex-ante” analyses of this phenomenon, to the best of our knowledge this is the first paper that provides an “ex-post” perspective. The latter had been considered in the past by blogs and magazines that, however, had only presented simple statistics on this phenomenon. Instead, we have proposed a framework, with a well-defined underlying data model, capable of supporting this type of analysis. A key concept in our model is the facet one, which is a novelty introduced by our very framework. At the end of our analysis, we were able to conclude that it is not worthwhile to engage in such an illicit and risky practice as wash trading on NFTs.
The results obtained in this paper are not to be considered as an ending point, but rather as a starting point for further research on the wash trading on NFTs phenomenon. An initial development could involve analyzing the relationships between other features of NFTs, such as rarity and asset type, and wash trading activity. Indeed, some types of NFTs might be more prone to wash trading than others. Categorizing NFTs based on their features may allow a ifne-grained study on the phenomenon of wash trading for the various types of NFTs. This could help determine the extent to which a new NFT collection might be subject to speculation. A next development could regard the application of machine learning algorithms to extract knowledge patterns related to the features involved in the wash trading phenomenon. Finally, we would like to study what factors underlie the pricing of NFTs, focusing in particular on the community that supports an NFT project. Specifically, we plan to analyze the social media ecosystem around an NFT project and characterize the behavior of users who participate in it, as well as the characteristics of the content they produce.