Using Correlated Stochastic Differential Equations to Model Cryptocurrency Rates and Social Media Activities

Increasingly interconnected financial systems and online social networks present both critical challenges and opportunities. Volatility in the former (e.g., cryptocurrency rates) can give rise to increased volume of activities in online social networks on relevant topics, while sentiments and rumors in online social networks can also have a significant impact on the corresponding financial time series. 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.