Unlike price fluctuations, the temporal structure of cryptocurrency trading has seldom been a sub... more 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 t...
Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are inv... more Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on this matrix are applied for different positions of a moving window. The cryptocurrencies become more strongly cross-correlated among themselves than they used to be before. The average cross-correlations increase with time on a specific time scale in a way that resembles the Epps effect amplification when going from past to present. The minimal spanning trees also change their topology and, for the short time scales, they become more centralized with increasing maximum node degrees, while for the long time scales they become more distributed, but also more correlated at the same time. Apart from the inter-market dependencies, the detrended cross-correlations between the cryptocurrency market and so...
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contr... more We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a cu...
Social systems are characterized by an enormous network of connections and factors that can influ... more Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. Among them the whole economical sphere of human activity seems to be the most interrelated and complex. All financial markets, including the youngest one, the cryptocurrency market, belong to this sphere. The complexity of the cryptocurrency market can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. In this work, we approach the subject from all three...
Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange... more Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high-frequency exchange rates of eight major world currencies over 2010–2018 period are used to study cross-correlations. The study is motivated by fundamental questions in complex systems’ response to significant environmental changes and by potential applications in investment strategies, including detecting triangular arbitrage opportunities. Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluctuation levels. However, hierarchical organization of ties expressed in terms of dendrograms, with a novel application of the multiscale cross-correlation coefficient, is more pronounced at large fluctuations. The cross-correlations are quantified to be stronger on average between those exchange rate pairs that are bound within triangular relations. Some pairs from outside triangular relations ...
Based on the high-frequency recordings from Kraken, a cryptocurrency exchange and professional tr... more Based on the high-frequency recordings from Kraken, a cryptocurrency exchange and professional trading platform that aims to bring Bitcoin and other cryptocurrencies into the mainstream, the multiscale cross-correlations involving the Bitcoin (BTC), Ethereum (ETH), Euro (EUR) and US dollar (USD) are studied over the period between 1 July 2016 and 31 December 2018. It is shown that the multiscaling characteristics of the exchange rate fluctuations related to the cryptocurrency market approach those of the Forex. This, in particular, applies to the BTC/ETH exchange rate, whose Hurst exponent by the end of 2018 started approaching the value of 0.5, which is characteristic of the mature world markets. Furthermore, the BTC/ETH direct exchange rate has already developed multifractality, which manifests itself via broad singularity spectra. A particularly significant result is that the measures applied for detecting cross-correlations between the dynamics of the BTC/ETH and EUR/USD exchang...
We closely examine and compare two promising techniques helpful in estimating the moment an asset... more We closely examine and compare two promising techniques helpful in estimating the moment an asset bubble bursts. Namely, the Log-Periodic Power Law model and Generalized Hurst Exponent approaches are considered. Sequential LPPL fitting to empirical financial time series exhibiting evident bubble behavior is presented. Estimating the critical crash-time works satisfactorily well also in the case of GHE, when substantial „decorrelation“ prior to the event is visible. An extensive simulation study carried out on empirical data: stock indices and commodities, confirms very good performance of the two approaches.
Chaos: An Interdisciplinary Journal of Nonlinear Science
We analyze tick-by-tick data representing major cryptocurrencies traded on some different cryptoc... more We analyze tick-by-tick data representing major cryptocurrencies traded on some different cryptocurrency trading platforms. We focus on such quantities like the inter-transaction times, the number of transactions in time unit, the traded volume, and volatility. We show that the inter-transaction times show long-range power-law autocorrelations. These lead to multifractality expressed by the right-side asymmetry of the singularity spectra [Formula: see text] indicating that the periods of increased market activity are characterized by richer multifractality compared to the periods of quiet market. We also show that neither the stretched exponential distribution nor the power-law-tail distribution is able to model universally the cumulative distribution functions of the quantities considered in this work. For each quantity, some data sets can be modeled by the former and some data sets by the latter, while both fail in other cases. An interesting, yet difficult to account for, observa...
Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling fac... more Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling factor 2, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so called commodity currencies expressed in terms of the US dollar appears to take place with the oscillation pattern which largely is mirror reflected relative to oil price oscillation pattern. This documents recent strong anti-correlation between the dynamics of the oil price and of the USD. A related forecast made at the time of FENS 2015 conference (begining of November) turned out to be quite satisfactory. These findings provide also further indication that such a log-periodically accelerating down-trend signals termination of the corresponding decreases.
Speculative bubbles and the subsequent crashes are an integral
part of human history. Greed and f... more Speculative bubbles and the subsequent crashes are an integral part of human history. Greed and fear present in the nancial markets naturally favor the occurrence of extreme events. Despite the research conducted for a long time in this topic, there is still no clear consensus on the de nition and the causes of speculative bubbles. Their correct identi cation and forecasting in advance are still unresolved problems. In my presentation I will discuss two practical models: Log-Periodic Power Law and Generalized Hurst Exponent. They were tested on 10 historical bubbles and then applied to the current situation on nancial markets. I will describe my methods and show the most important results. Especially interesting was detection of peaks on German and Chinese stock markets in 2015 which was achieved in advance.
Bąble spekulacyjne i następujące po nich krachy są nieodłączoną częścią historii ludzkości. Chciw... more Bąble spekulacyjne i następujące po nich krachy są nieodłączoną częścią historii ludzkości. Chciwość i strach obecne na rynkach finansowych w naturalny sposób sprzyjają występowaniu zdarzeń ekstremalnych. W referacie omówione zostanie co to jest bańka spekulacyjna? Jak powstaje? Przedstawione zostaną próby testowania obecności bańki, sygnały świadczące o jej możliwym końcu oraz modele opisujące dynamikę cen w trakcie bąbla i krachu.
Unlike price fluctuations, the temporal structure of cryptocurrency trading has seldom been a sub... more 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 t...
Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are inv... more Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on this matrix are applied for different positions of a moving window. The cryptocurrencies become more strongly cross-correlated among themselves than they used to be before. The average cross-correlations increase with time on a specific time scale in a way that resembles the Epps effect amplification when going from past to present. The minimal spanning trees also change their topology and, for the short time scales, they become more centralized with increasing maximum node degrees, while for the long time scales they become more distributed, but also more correlated at the same time. Apart from the inter-market dependencies, the detrended cross-correlations between the cryptocurrency market and so...
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contr... more We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a cu...
Social systems are characterized by an enormous network of connections and factors that can influ... more Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. Among them the whole economical sphere of human activity seems to be the most interrelated and complex. All financial markets, including the youngest one, the cryptocurrency market, belong to this sphere. The complexity of the cryptocurrency market can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. In this work, we approach the subject from all three...
Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange... more Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high-frequency exchange rates of eight major world currencies over 2010–2018 period are used to study cross-correlations. The study is motivated by fundamental questions in complex systems’ response to significant environmental changes and by potential applications in investment strategies, including detecting triangular arbitrage opportunities. Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluctuation levels. However, hierarchical organization of ties expressed in terms of dendrograms, with a novel application of the multiscale cross-correlation coefficient, is more pronounced at large fluctuations. The cross-correlations are quantified to be stronger on average between those exchange rate pairs that are bound within triangular relations. Some pairs from outside triangular relations ...
Based on the high-frequency recordings from Kraken, a cryptocurrency exchange and professional tr... more Based on the high-frequency recordings from Kraken, a cryptocurrency exchange and professional trading platform that aims to bring Bitcoin and other cryptocurrencies into the mainstream, the multiscale cross-correlations involving the Bitcoin (BTC), Ethereum (ETH), Euro (EUR) and US dollar (USD) are studied over the period between 1 July 2016 and 31 December 2018. It is shown that the multiscaling characteristics of the exchange rate fluctuations related to the cryptocurrency market approach those of the Forex. This, in particular, applies to the BTC/ETH exchange rate, whose Hurst exponent by the end of 2018 started approaching the value of 0.5, which is characteristic of the mature world markets. Furthermore, the BTC/ETH direct exchange rate has already developed multifractality, which manifests itself via broad singularity spectra. A particularly significant result is that the measures applied for detecting cross-correlations between the dynamics of the BTC/ETH and EUR/USD exchang...
We closely examine and compare two promising techniques helpful in estimating the moment an asset... more We closely examine and compare two promising techniques helpful in estimating the moment an asset bubble bursts. Namely, the Log-Periodic Power Law model and Generalized Hurst Exponent approaches are considered. Sequential LPPL fitting to empirical financial time series exhibiting evident bubble behavior is presented. Estimating the critical crash-time works satisfactorily well also in the case of GHE, when substantial „decorrelation“ prior to the event is visible. An extensive simulation study carried out on empirical data: stock indices and commodities, confirms very good performance of the two approaches.
Chaos: An Interdisciplinary Journal of Nonlinear Science
We analyze tick-by-tick data representing major cryptocurrencies traded on some different cryptoc... more We analyze tick-by-tick data representing major cryptocurrencies traded on some different cryptocurrency trading platforms. We focus on such quantities like the inter-transaction times, the number of transactions in time unit, the traded volume, and volatility. We show that the inter-transaction times show long-range power-law autocorrelations. These lead to multifractality expressed by the right-side asymmetry of the singularity spectra [Formula: see text] indicating that the periods of increased market activity are characterized by richer multifractality compared to the periods of quiet market. We also show that neither the stretched exponential distribution nor the power-law-tail distribution is able to model universally the cumulative distribution functions of the quantities considered in this work. For each quantity, some data sets can be modeled by the former and some data sets by the latter, while both fail in other cases. An interesting, yet difficult to account for, observa...
Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling fac... more Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling factor 2, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so called commodity currencies expressed in terms of the US dollar appears to take place with the oscillation pattern which largely is mirror reflected relative to oil price oscillation pattern. This documents recent strong anti-correlation between the dynamics of the oil price and of the USD. A related forecast made at the time of FENS 2015 conference (begining of November) turned out to be quite satisfactory. These findings provide also further indication that such a log-periodically accelerating down-trend signals termination of the corresponding decreases.
Speculative bubbles and the subsequent crashes are an integral
part of human history. Greed and f... more Speculative bubbles and the subsequent crashes are an integral part of human history. Greed and fear present in the nancial markets naturally favor the occurrence of extreme events. Despite the research conducted for a long time in this topic, there is still no clear consensus on the de nition and the causes of speculative bubbles. Their correct identi cation and forecasting in advance are still unresolved problems. In my presentation I will discuss two practical models: Log-Periodic Power Law and Generalized Hurst Exponent. They were tested on 10 historical bubbles and then applied to the current situation on nancial markets. I will describe my methods and show the most important results. Especially interesting was detection of peaks on German and Chinese stock markets in 2015 which was achieved in advance.
Bąble spekulacyjne i następujące po nich krachy są nieodłączoną częścią historii ludzkości. Chciw... more Bąble spekulacyjne i następujące po nich krachy są nieodłączoną częścią historii ludzkości. Chciwość i strach obecne na rynkach finansowych w naturalny sposób sprzyjają występowaniu zdarzeń ekstremalnych. W referacie omówione zostanie co to jest bańka spekulacyjna? Jak powstaje? Przedstawione zostaną próby testowania obecności bańki, sygnały świadczące o jej możliwym końcu oraz modele opisujące dynamikę cen w trakcie bąbla i krachu.
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Papers by Marcin Wątorek
part of human history. Greed and fear present in the nancial
markets naturally favor the occurrence of extreme events. Despite the research conducted for a long time in this topic, there is still no clear consensus on the de nition and the causes of speculative bubbles. Their correct identi cation and forecasting in advance are still unresolved problems.
In my presentation I will discuss two practical models: Log-Periodic Power Law and Generalized Hurst Exponent. They were tested on 10 historical bubbles and then applied to the current
situation on nancial markets. I will describe my methods and show the most important results. Especially interesting was detection of peaks on German and Chinese stock markets in 2015 which was achieved in advance.
part of human history. Greed and fear present in the nancial
markets naturally favor the occurrence of extreme events. Despite the research conducted for a long time in this topic, there is still no clear consensus on the de nition and the causes of speculative bubbles. Their correct identi cation and forecasting in advance are still unresolved problems.
In my presentation I will discuss two practical models: Log-Periodic Power Law and Generalized Hurst Exponent. They were tested on 10 historical bubbles and then applied to the current
situation on nancial markets. I will describe my methods and show the most important results. Especially interesting was detection of peaks on German and Chinese stock markets in 2015 which was achieved in advance.