Group transfer entropy with an application to cryptocurrencies

Abstract The detection of informational leadership is a core issue in financial market microstructure. We use effective group transfer entropy (EGTE) as a measure for the predictability of a stochastic process using lagged observations on multiple related processes within the same system. We propose an appropriate bootstrap to derive confidence bounds and show by means of a simulation study that standard linear approaches in economics and finance, such as vector autoregressions and Granger-causality tests, are not well suited to detect information transfer. We empirically examine the markets for cryptocurrencies using intraday data and reveal that the dependencies are mostly of nonlinear nature, highlighting the applicability of EGTE in the context of this new financial product.

[1]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[2]  Roland Mestel,et al.  Price discovery of cryptocurrencies: Bitcoin and beyond , 2018 .

[3]  Mikhail Prokopenko,et al.  On Thermodynamic Interpretation of Transfer Entropy , 2013, Entropy.

[4]  P. Hall,et al.  On blocking rules for the bootstrap with dependent data , 1995 .

[5]  Andrew Harvey,et al.  Testing for the Presence of a Random Walk in Series with Structural Breaks , 1998 .

[6]  Atul Malhotra,et al.  Transfer Entropy Estimation and Directional Coupling Change Detection in Biomedical Time Series , 2012, Biomedical engineering online.

[7]  J. MacKinnon.  Bootstrap Methods in Econometrics , 2006 .

[8]  Ananth N. Madhavan,et al.  Why Do Security Prices Change? A Transaction-Level Analysis of Nyse Stocks , 1996 .

[9]  Thadavillil Jithendranathan,et al.  A study of linkages between frontier markets and the U.S. equity markets using multivariate GARCH and transfer entropy , 2015 .

[10]  Aurel A. Lazar,et al.  Information theory in neuroscience , 2011, Journal of Computational Neuroscience.

[11]  S. Kim,et al.  Time series analysis of the Antarctic Circumpolar Wave via symbolic transfer entropy , 2018, Physica A: Statistical Mechanics and its Applications.

[12]  J. Grammig,et al.  Telltale Tails: A New Approach to Estimating Unique Market Information Shares , 2013, Journal of Financial and Quantitative Analysis.

[13]  Andrew Urquhart.  The Inefficiency of Bitcoin , 2016 .

[14]  T. Dimpfl,et al.  Using Transfer Entropy to Measure Information Flows Between Financial Markets , 2013 .

[15]  Ke-Li Xu,et al.  A Fractionally Cointegrated VAR Analysis of Price Discovery in Commodity Futures Markets , 2015 .

[16]  F. Longin,et al.  Extreme Correlation of International Equity Markets , 2000 .

[17]  Matthäus Staniek,et al.  Symbolic transfer entropy. , 2008, Physical review letters.

[18]  Yifan Li,et al.  Use of Mutual Information and Transfer Entropy to Assess Interaction between Parasympathetic and Sympathetic Activities of Nervous System from HRV , 2017, Entropy.

[19]  Christian Schlag,et al.  Internationally cross-listed stock prices during overlapping trading hours: price discovery and exchange rate effects , 2005 .

[20]  J M Nichols,et al.  Detecting nonlinearity in structural systems using the transfer entropy. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Ladislav Kristoufek,et al.  On Bitcoin markets (in)efficiency and its evolution , 2018, Physica A: Statistical Mechanics and its Applications.

[22]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[23]  R. Roll,et al.  A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market , 2008 .

[24]  A. Seth,et al.  Granger causality and transfer entropy are equivalent for Gaussian variables. , 2009, Physical review letters.

[25]  Olivier J. J. Michel,et al.  On directed information theory and Granger causality graphs , 2010, Journal of Computational Neuroscience.

[26]  Keshab Shrestha,et al.  A new information share measure , 2009 .

[27]  Wang Chun Wei.  Liquidity and market efficiency in cryptocurrencies , 2018, Economics Letters.

[28]  W. Fuller,et al.  LIKELIHOOD RATIO STATISTICS FOR AUTOREGRESSIVE TIME SERIES WITH A UNIT ROOT , 1981 .

[29]  Joel Hasbrouck,et al.  One Security, Many Markets: Determining the Contributions to Price Discovery , 1995 .

[30]  Dror Y. Kenett,et al.  Dependency Relations among International Stock Market Indices , 2015 .

[31]  H. Kantz,et al.  Analysing the information flow between financial time series , 2002 .

[32]  Thomas Dimpfl,et al.  The impact of the financial crisis on transatlantic information flows: An intraday analysis , 2014 .