Hilbert Martin, Darmon David
Communication, Computational Social Science, University of California, Davis, CA 95616, USA.
Department of Mathematics, Monmouth University, West Long Branch, NJ 07764, USA.
Entropy (Basel). 2020 Apr 26;22(5):499. doi: 10.3390/e22050499.
The machine-learning paradigm promises traders to reduce uncertainty through better predictions done by ever more complex algorithms. We ask about detectable results of both uncertainty and complexity at the aggregated market level. We analyzed almost one billion trades of eight currency pairs (2007-2017) and show that increased algorithmic trading is associated with more complex subsequences and more predictable structures in bid-ask spreads. However, algorithmic involvement is also associated with more future uncertainty, which seems contradictory, at first sight. On the micro-level, traders employ algorithms to reduce their local uncertainty by creating more complex algorithmic patterns. This entails more predictable structure and more complexity. On the macro-level, the increased overall complexity implies more combinatorial possibilities, and therefore, more uncertainty about the future. The chain rule of entropy reveals that uncertainty has been reduced when trading on the level of the fourth digit behind the dollar, while new uncertainty started to arise at the fifth digit behind the dollar (aka 'pip-trading'). In short, our information theoretic analysis helps us to clarify that the seeming contradiction between decreased uncertainty on the micro-level and increased uncertainty on the macro-level is the result of the inherent relationship between complexity and uncertainty.
机器学习范式有望通过更复杂的算法做出更好的预测，从而帮助交易员降低不确定性。我们探讨了在市场总体层面上不确定性和复杂性的可检测结果。我们分析了2007年至2017年期间八种货币对的近10亿笔交易，结果表明，算法交易的增加与更复杂的子序列以及买卖价差中更具可预测性的结构相关。然而，算法参与也与更多的未来不确定性相关，乍一看这似乎自相矛盾。在微观层面，交易员通过创建更复杂的算法模式来使用算法降低其局部不确定性。这会带来更具可预测性的结构和更多的复杂性。在宏观层面，整体复杂性的增加意味着更多的组合可能性，因此也意味着对未来更多的不确定性。熵的链式法则表明，在美元后第四位数字的交易层面上不确定性有所降低，而在美元后第五位数字（即“点差交易”）上开始出现新的不确定性。简而言之，我们的信息论分析有助于我们阐明微观层面不确定性降低与宏观层面不确定性增加之间看似矛盾的现象，是复杂性与不确定性之间内在关系的结果。
