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Information transfer between time series is calculated by using theasymmetric information-theoretic measure known as transfer entropy. Geweke'sautoregressive formulation of Granger causality is used to find linear transferentropy, and Schreiber's general, non-parametric, information-theoreticformulation is used to detect non-linear transfer entropy.  We first validate these measures against synthetic data. Then we apply thesemeasures to detect causality between social sentiment and cryptocurrencyprices. We perform significance tests by comparing the information transferagainst a null hypothesis, determined via shuffled time series, and calculatethe Z-score. We also investigate different approaches for partitioning innonparametric density estimation which can improve the significance of results.  Using these techniques on sentiment and price data over a 48-month period toAugust 2018, for four major cryptocurrencies, namely bitcoin (BTC), ripple(XRP), litecoin (LTC) and ethereum (ETH), we detect significant informationtransfer, on hourly timescales, in directions of both sentiment to price and ofprice to sentiment. We report the scale of non-linear causality to be an orderof magnitude greater than linear causality.

Information-theoretic measures for non-linear causality detection: application to social media sentiment and cryptocurrency prices