Abstract
Information transfer between time series is calculated using the asymmetric information-theoretic measure known as transfer entropy. Geweke’s autoregressive formulation of Granger causality is used to compute linear transfer entropy, and Schreiber’s general, non-parametric, information-theoretic formulation is used to quantify nonlinear transfer entropy. We first validate these measures against synthetic data. Then we apply these measures to detect statistical causality between social sentiment changes and cryptocurrency returns. We validate results by performing permutation tests by shuffling the time series, and calculate the Z-score. We also investigate different approaches for partitioning in non-parametric density estimation which can improve the significance. Using these techniques on sentiment and price data over a 48-month period to August 2018, for four major cryptocurrencies, namely bitcoin (BTC), ripple (XRP), litecoin (LTC) and ethereum (ETH), we detect significant information transfer, on hourly timescales, with greater net information transfer from sentiment to price for XRP and LTC, and instead from price to sentiment for BTC and ETH. We report the scale of nonlinear statistical causality to be an order of magnitude larger than the linear case.
Highlights
Causality is a central concept in natural sciences, commonly understood to describe where a process, evolving in time, has royalsocietypublishing.org/journal/rsos R
Having confirmed that the information-theoretic approach is able to detect both linear and nonlinear causalities, we apply the technique to investigate the effect of changes in social media sentiment on cryptocurrency returns, and vice versa
The techniques were applied to historical data describing social media sentiment and cryptocurrency prices to detect information transfer between changes in sentiment and price returns
Summary
Causality is a central concept in natural sciences, commonly understood to describe where a process, evolving in time, has royalsocietypublishing.org/journal/rsos R. We consider a statistical form of causality, which can be observed in codependent time series where a response in the dependent series is more likely to follow after some change in the driving series. The direction of information transfer is forced by requiring the cause to precede the effect This concept was conceived first by Wiener in 1956 [3], and formalized by Granger in 1969 [4] who was subsequently awarded the Nobel memorial prize in economics for his work on the analysis of time series. The first approach involves the application of the Granger–Geweke causality test, which assumes linearity and employs vector auto-regressive techniques to estimate the extent to which knowing the driving time series can improve predictions of the dependent series. Linear regression estimates the coefficient 4 parameters b(kY) which minimize the sum of squared residuals
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