30 research outputs found
Multifractal cross-correlations of bitcoin and ether trading characteristics in the post-COVID-19 time
Unlike price fluctuations, the temporal structure of cryptocurrency trading
has seldom been a subject of systematic study. In order to fill this gap, we
analyse detrended correlations of the price returns, the average number of
trades in time unit, and the traded volume based on high-frequency data
representing two major cryptocurrencies: bitcoin and ether. We apply the
multifractal detrended cross-correlation analysis, which is considered the most
reliable method for identifying nonlinear correlations in time series. We find
that all the quantities considered in our study show an unambiguous
multifractal structure from both the univariate (auto-correlation) and
bivariate (cross-correlation) perspectives. We looked at the bitcoin--ether
cross-correlations in simultaneously recorded signals, as well as in
time-lagged signals, in which a time series for one of the cryptocurrencies is
shifted with respect to the other. Such a shift suppresses the
cross-correlations partially for short time scales, but does not remove them
completely. We did not observe any qualitative asymmetry in the results for the
two choices of a leading asset. The cross-correlations for the simultaneous and
lagged time series became the same in magnitude for the sufficiently long
scales
Decomposing cryptocurrency dynamics into recurring and noisy components
This paper investigates the temporal patterns of activity in the
cryptocurrency market with a focus on bitcoin, ether, dogecoin, and winklink
from January 2020 to December 2022. Market activity measures - logarithmic
returns, volume, and transaction number, sampled every 10 seconds, were divided
into intraday and intraweek periods and then further decomposed into recurring
and noise components via correlation matrix formalism. The key findings include
the distinctive market behavior from traditional stock markets due to the
nonexistence of trade opening and closing. This was manifest in three
enhanced-activity phases aligning with Asian, European, and US trading
sessions. An intriguing pattern of activity surge in 15-minute intervals,
particularly at full hours, was also noticed, implying the potential role of
algorithmic trading. Most notably, recurring bursts of activity in bitcoin and
ether were identified to coincide with the release times of significant US
macroeconomic reports such as Nonfarm payrolls, Consumer Price Index data, and
Federal Reserve statements. The most correlated daily patterns of activity
occurred in 2022, possibly reflecting the documented correlations with US stock
indices in the same period. Factors that are external to the inner market
dynamics are found to be responsible for the repeatable components of the
market dynamics, while the internal factors appear to be substantially random,
which manifests itself in a good agreement between the empirical eigenvalue
distributions in their bulk and the random matrix theory predictions expressed
by the Marchenko-Pastur distribution. The findings reported support the growing
integration of cryptocurrencies into the global financial markets
Multifractality in time series is due to temporal correlations
Based on the rigorous mathematical arguments formulated within the
Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that
in the uncorrelated time series the effects resembling multifractality
asymptotically disappear when the length of time series increases. The related
effects are also illustrated by numerical simulations. This documents that the
genuine multifractality in time series may only result from the long-range
temporal correlations and the fatter distribution tails of fluctuations may
broaden the width of singularity spectrum only when such correlations are
present. The frequently asked question of what makes multifractality in time
series - temporal correlations or broad distribution tails - is thus ill posed
Characteristics of price related fluctuations in Non-Fungible Token (NFT) market
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
Wavelet versus Detrended Fluctuation Analysis of multifractal structures
We perform a comparative study of applicability of the Multifractal Detrended
Fluctuation Analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM)
method in proper detecting of mono- and multifractal character of data. We
quantify the performance of both methods by using different sorts of artificial
signals generated according to a few well-known exactly soluble mathematical
models: monofractal fractional Brownian motion, bifractal Levy flights, and
different sorts of multifractal binomial cascades. Our results show that in
majority of situations in which one does not know a priori the fractal
properties of a process, choosing MFDFA should be recommended. In particular,
WTMM gives biased outcomes for the fractional Brownian motion with different
values of Hurst exponent, indicating spurious multifractality. In some cases
WTMM can also give different results if one applies different wavelets. We do
not exclude using WTMM in real data analysis, but it occurs that while one may
apply MFDFA in a more automatic fashion, WTMM has to be applied with care. In
the second part of our work, we perform an analogous analysis on empirical data
coming from the American and from the German stock market. For this data both
methods detect rich multifractality in terms of broad f(alpha), but MFDFA
suggests that this multifractality is poorer than in the case of WTMM.Comment: substantially extended version, to appear in Phys.Rev.