Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

What Is Mature and What Is Still Emerging in the Cryptocurrency Market?

In relation to the traditional financial markets, the cryptocurrency market is a recent invention and the trading dynamics of all its components are readily recorded and stored. This fact opens up a unique opportunity to follow the multidimensional trajectory of its development since inception up to the present time. Several main characteristics commonly recognized as financial stylized facts of mature markets were quantitatively studied here. In particular, it is shown that the return distributions, volatility clustering effects, and even temporal multifractal correlations for a few highest-capitalization cryptocurrencies largely follow those of the well-established financial markets. The smaller cryptocurrencies are somewhat deficient in this regard, however. They are also not as highly cross-correlated among themselves and with other financial markets as the large cryptocurrencies. Quite generally, the volume V impact on price changes R appears to be much stronger on the cryptocurrency market than in the mature stock markets, and scales as R(V)∼Vα with α≳1.

Cryptocurrency Market Consolidation in 2020-2021

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 some traditional markets, like the stock markets, commodity markets, and Forex, are also analyzed. The cryptocurrency market shows higher levels of cross-correlations with the other markets during the same turbulent periods, in which it is strongly cross-correlated itself.

Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19

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 perspectives based on data from a recent time interval between January 2019 and June 2020. This period includes the peculiar time of the Covid-19 pandemic; therefore, we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.

The Evolution Characteristics of Systemic Risk in China's Stock Market Based on a Dynamic Complex Network

The stock market is a complex system with unpredictable stock price fluctuations. When the positive feedback in the market amplifies, the systemic risk will increase rapidly. During the last 30 years of development, the mechanism and governance system of China’s stock market have been constantly improving, but irrational shocks have still appeared suddenly in the last decade, making investment decisions risky. Therefore, based on the daily return of all a-shares in China, this paper constructs a dynamic complex network of individual stocks, and represents the systemic risk of the market using the average weighting degree, as well as the adjusted structural entropy, of the network. In order to eliminate the influence of disturbance factors, empirical mode decomposition (EMD) and grey relational analysis (GRA) are used to decompose and reconstruct the sequences to obtain the evolution trend and periodic fluctuation of systemic risk. The results show that the systemic risk of China’s stock market as a whole shows a downward trend, and the periodic fluctuation of systemic risk has a long-term equilibrium relationship with the abnormal fluctuation of the stock market. Further, each rise of systemic risk corresponds to external factor shocks and internal structural problems.

Multifractal temporally weighted detrended cross-correlation analysis of multivariate time series

Fractal and multifractal properties of various systems have been studied extensively. In this paper, first, the multivariate multifractal detrend cross-correlation analysis (MMXDFA) is proposed to investigate the multifractal features in multivariate time series. MMXDFA may produce oscillations in the fluctuation function and spurious cross correlations. In order to overcome these problems, we then propose the multivariate multifractal temporally weighted detrended cross-correlation analysis (MMTWXDFA). In relation to the multivariate detrended cross-correlation analysis and multifractal temporally weighted detrended cross-correlation analysis, an innovation of MMTWXDFA is the application of the signed Manhattan distance to calculate the local detrended covariance function. To evaluate the performance of the MMXDFA and MMTWXDFA methods, we apply them on some artificially generated multivariate series. Several numerical tests demonstrate that both methods can identify their fractality, but MMTWXDFA can detect long-range cross correlations and simultaneously quantify the levels of cross correlation between two multivariate series more accurately.

Multifractal analysis of financial markets: a review

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

Signatures of the Crypto-Currency Market Decoupling from the Forex

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 exchange rates do not show any noticeable relationships. This could be taken as an indication that the cryptocurrency market has begun decoupling itself from the Forex.

Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015

This paper applies effective transfer entropy to research the information transfer in the Chinese stock market around its crash in 2015. According to the market states, the entire period is divided into four sub-phases: the tranquil, bull, crash, and post-crash periods. Kernel density estimation is used to calculate the effective transfer entropy. Then, the information transfer network is constructed. Nodes’ centralities and the directed maximum spanning trees of the networks are analyzed. The results show that, in the tranquil period, the information transfer is weak in the market. In the bull period, the strength and scope of the information transfer increases. The utility sector outputs a great deal of information and is the hub node for the information flow. In the crash period, the information transfer grows further. The market efficiency in this period is worse than that in the other three sub-periods. The information technology sector is the biggest information source, while the consumer staples sector receives the most information. The interactions of the sectors become more direct. In the post-crash period, information transfer declines but is still stronger than the tranquil time. The financial sector receives the largest amount of information and is the pivot node.

Construction of Complex Network with Multiple Time Series Relevance

Multivariate time series data, which comprise a set of ordered observations for multiple variables, are pervasively generated in weather conditions, traffic, financial stocks, etc. Therefore, it is of great significance to analyze the correlation between multiple time series. Financial stocks generate a significant amount of multivariate time series data that can be used to build networks that reflect market behavior. However, traditional commercial complex networks cannot fully utilize the multiple attributes of stocks and redundant filter relationships and reveal a more authentic financial stock market. We propose a fusion similarity of multiple time series and construct a threshold network with similarity. Furthermore, we define the connectivity efficiency to choose the best threshold, establishing a high connectivity efficiency network with the optimal network threshold. By searching the central node in the threshold network, we have found that the network center nodes constructed by our proposed method have a more comprehensive industry coverage than the traditional techniques to build the systems, and this also proves the superiority of this method.

Characterisation of survivability resilience with dynamic stock interdependence in financial networks

This paper examines the dynamic evolutionary process in the London Stock Exchange and uses network statistical measures to model the resilience of stock. A large historical dataset of companies was collected over 40 years (1977-2017) and conceptualised into weighted, temporally evolving and signed networks using correlation-based interdependences. Our results revealed a "fission-fusion" market growth in network topologies, which indicated the dynamic and complex characteristics of its evolutionary process. In addition, our regression and modelling results offer insights for construction a "characterisation tool" which can be used to predict stocks that have delisted and continuing performance relatively well, but were less adequate for stocks with normal performance. Moreover, the analysis of deviance suggested that the survivability resilience could be described and approximated by degree-related centrality measures. This study introduces a novel alternative for looking at the bankruptcy in the stock market and is potentially helpful for shareholders, decision- and policy-makers.

Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects

Based on 1-min price changes recorded since year 2012, the fluctuation properties of the rapidly emerging Bitcoin market are assessed over chosen sub-periods, in terms of return distributions, volatility autocorrelation, Hurst exponents, and multiscaling effects. The findings are compared to the stylized facts of mature world markets. While early trading was affected by system-specific irregularities, it is found that over the months preceding April 2018 all these statistical indicators approach the features hallmarking maturity. This can be taken as an indication that the Bitcoin market, and possibly other cryptocurrencies, carry concrete potential of imminently becoming a regular market, alternative to the foreign exchange. Since high-frequency price data are available since the beginning of trading, the Bitcoin offers a unique window into the statistical characteristics of a market maturation trajectory.

Dynamics of investor spanning trees around dot-com bubble

We identify temporal investor networks for Nokia stock by constructing networks from correlations between investor-specific net-volumes and analyze changes in the networks around dot-com bubble. The analysis is conducted separately for households, financial, and non-financial institutions. Our results indicate that spanning tree measures for households reflected the boom and crisis: the maximum spanning tree measures had a clear upward tendency in the bull markets when the bubble was building up, and, even more importantly, the minimum spanning tree measures pre-reacted the burst of the bubble. At the same time, we find less clear reactions in the minimal and maximal spanning trees of non-financial and financial institutions around the bubble, which suggests that household investors can have a greater herding tendency around bubbles.