  In this paper, we analyze the time-series of minute price returns on the
Bitcoin market through the statistical models of generalized autoregressive
conditional heteroskedasticity (GARCH) family. Several mathematical models have
been proposed in finance, to model the dynamics of price returns, each of them
introducing a different perspective on the problem, but none without
shortcomings. We combine an approach that uses historical values of returns and
their volatilities - GARCH family of models, with a so-called "Mixture of
Distribution Hypothesis", which states that the dynamics of price returns are
governed by the information flow about the market. Using time-series of
Bitcoin-related tweets and volume of transactions as external information, we
test for improvement in volatility prediction of several GARCH model variants
on a minute level Bitcoin price time series. Statistical tests show that the
simplest GARCH(1,1) reacts the best to the addition of external signal to model
volatility process on out-of-sample data.
