Multifractals have been used to describe a set of highly unusual and severe fluctuations sandwiched between periods of relative tranquility. Some signals suggest that NFTs are already displaying a tendency to behave like true multifractals.
One of the most successful patterns found in multifractal analysis is the scaling range, which describes the fractional difference between consecutive measurements. If this divergence were fixed throughout all scales (i.e., always 0.2), it would be a fixed pattern, and it would carry no information about changes in dynamics. In contrast, fluctuations of the scaling range around its mean value tend to be larger at finer scales. In the case of multifractals, these fluctuations are thought to be self-similar in that they appear similar when measured over many different time intervals.
In contrast with the scaling behavior, it has been shown that multifractal methods can also characterize long-range memory processes. The presence of long-range memory (LRM) at different time scales can be used to identify multifractal properties in stock market data, although the data must first be preprocessed by applying wavelet decomposition. Wavelet analysis provides an efficient way of capturing short-term memory effects, meaning that the power spectrum is computed only for time scales up to some cut-off.
In the context of an NFT property like Bored Ape Yacht Club, a multifractal analysis can show that spiking price segments are preferentially longer than the average price segment. This means that, after a significant move (i.e., up or down), there is an increased probability that the following movements will be of medium strength rather than minor. Furthermore, it appears that fluctuations tend to display very long-range memory.
The multifractal system was created to generalize the fractal system to describe more complicated time series behaviors. High-volatility financial assets can be modeled using multifractal processes to capture the economic data's multifractal and non-fractal features.
The fractality of a time series can be quantified by computing its scaling exponent, which measures how closely power-law relationships fit the graph of fluctuations against changes in frequency. The scaling exponent is especially useful because it possesses a direct physical interpretation: fluctuations that scale with changes in frequency according to a power-law are scale-free, i.e., they do not become dampened or decayed with increasing changes in frequency.
Therefore, multifractal analysis is used for characterizing the long-term memory and correlation properties of financial time series by studying their multifractality and scaling behavior at different conditional and unconditional scales.
Multifractal analysis has already been applied to other complex systems, such as ocean waves, climate fluctuations, earthquakes, volcanic activity, stock market prices, and human brain activity. The results of these studies suggest that multifractals are universal phenomena found in many kinds of data.
NFTs: A multifractal approach
Price data from stock exchanges has been subjected to multifractal analysis. While the NFT market has properties similar to those observed in other financial markets, it is essential to note that NFTs are not an efficient market, and this fact should be considered when applying techniques used for analyzing movements.
In the NFT market, it has been shown that multifractals can provide helpful information about price movements and their memory properties.
The NFT market has expanded considerably since its inception, especially in recent months. The prices and returns of this virtual and speculative market have increased exponentially owing to chaos, randomness, and multi-fractionals in the market.
NFTs are a type of new financial asset that derives their value from the advancement of blockchain technology and economic model design, and are innovative financial assets. NFTs have been compared to a commodity, a collectible, a medium of exchange, and a technology; however, the term "cryptocollectible" is frequently used to describe the broader class of NFTs.
NFTs are non-fungible; each has unique characteristics, which cannot be replicated or destroyed (unlike currencies).
Because of this, it's hard to say whether NFTs are more like stocks or commodities. After considering significant tails, also known as fat-tailed distributions, which are frequently seen in financial market data, NFT price movements could be characterized by multifractal scaling laws.
Multifractal scaling laws are observed when self-similarity is observed at all scales, not just at large scales. They are characterized by power-law relationships between fluctuations in price and changes in frequency, i.e., price movements scale with changes in trading volume.
Researchers have discovered that financial assets, even stocks, and indices, typically contain a fraction of fat-tail events or heavy-tailed distributions. The presence of large deviations in price movements is frequently observed when many NFTs are examined simultaneously. Lastly, studying scaling properties concerning trading volume reveals the multifractal nature of NFTs.
NFTs could be used to visualize day-to-day price fluctuations of virtual assets over time, but the expected value and volatility measures typically used for pricing these assets may not adequately represent the NFTs' actual dynamics.
Observing these properties could help us better understand whether NFT prices are really bubbles or whether the observed dynamics result from multifractals.
It is difficult to find references in the academic literature that study how economic agents interact with NFTs, mainly when these agents apply different trading strategies or hold them for different periods. Researchers have studied agent-based models and their interactions with Bitcoin, but NFTs and their researchable data are too new at this point for deep research in this area.
Because of the unique properties of NFTs, they are likely to have a significant effect on how economic agents interact with them, their markets, and other digital assets. And understanding how these effects multiply when agents analyze different trading strategies is an exciting avenue for further study.
The NFT market has not been through a complete economic cycle because it is still young; therefore, its volatility level cannot be said to depend on interest rate fluctuations, inflation, or similar macroeconomic phenomena.
Technological innovation has played an essential role in determining price behavior in each NFT bull market. Advancements in blockchain networks may positively affect cryptocurrency prices, which is not always the case. This is because some technologies are adopted quickly while others suffer from interoperability problems.
On the other hand, it is worth mentioning that virtual currencies have always suffered significant drawdowns over shorter timeframes during all analyzed periods, no matter how much technology has improved or changed.
The price-to-return ratio is stable during the low-price period; however, as a result of rising volatility in returns, the level of uncertainty about returns has skyrocketed. Furthermore, both prices and returns have long-range correlations and multifractality.
NFTs are seen as an alternative investment option, and their prices depend on demand and supply conditions. This, of course, makes them very vulnerable to sudden drops similar to the ones seen in January 2018. However, the fact that prices are still showing high volatility means that NFTs are yet to establish themselves as reliable assets for real-world applications.
The historical performance is not necessarily an indicator of future returns, even if all other factors remain unchanged. The mere possibility of technological changes or updates should be included in the expected return calculation. These changes may positively or negatively affect virtual currency prices, but it is currently impossible to say whether they will do so.