The growing interconnectivity of socio-economic systems requires one to treat multiple relevant social and economic variables simultaneously as parts of a strongly interacting complex system. Here, we analyze and exploit correlations between the price fluctuations of selected cryptocurrencies and social media activities, and develop a predictive framework using noise-correlated stochastic differential equations. We employ the standard Geometric Brownian Motion to model cryptocurrency rates, while for social media activities and trading volume of cryptocurrencies we use the Geometric Ornstein-Uhlenbeck process. In our model, correlations between the different stochastic variables are introduced through the noise in the respective stochastic differential equation. Using a Maximum Likelihood Estimation on historical data of the corresponding cryptocurrencies and social media activities we estimate parameters, and using the observed correlations, forecast selected time series. We successfully analyze and predict cryptocurrency related social media and the cryptocurrency market itself with a reasonable degree of accuracy. In particular, we show that our method has impressive accuracy in predicting whether a cryptocurrency market will increase or decrease a day in the future, a significant result with regards to investing and trading cryptocurrencies.

中文翻译：

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使用相关的随机微分方程预测加密货币汇率和社交媒体活动

社会经济系统日益增长的相互联系要求人们同时将多个相关的社会和经济变量视为一个相互作用强烈的复杂系统的一部分。在这里，我们分析和利用所选加密货币的价格波动与社交媒体活动之间的相关性，并使用与噪声相关的随机微分方程建立预测框架。我们使用标准的几何布朗运动来对加密货币汇率建模，而对于社交媒体活动和加密货币的交易量，我们使用几何Ornstein-Uhlenbeck流程。在我们的模型中，不同随机变量之间的相关性是通过相应随机微分方程中的噪声引入的。对对应的加密货币和社交媒体活动的历史数据使用最大似然估计，我们估计参数，并使用观察到的相关性预测所选时间序列。我们以合理的准确度成功地分析和预测了与加密货币相关的社交媒体和加密货币市场本身。特别是，我们表明，我们的方法在预测加密货币市场未来一天会增加还是减少方面具有惊人的准确性，这在投资和交易加密货币方面是一个重大成果。我们以合理的准确度成功地分析和预测了与加密货币相关的社交媒体和加密货币市场本身。特别是，我们表明，我们的方法在预测加密货币市场未来一天会增加还是减少方面具有惊人的准确性，这在投资和交易加密货币方面是一个重大成果。我们以合理的准确度成功地分析和预测了与加密货币相关的社交媒体和加密货币市场本身。特别是，我们证明了我们的方法在预测加密货币市场未来一天会增加还是减少方面具有惊人的准确性，这在投资和交易加密货币方面是一个重大成果。