Abstract
In this article, we analyze the time series of minute price returns on the Bitcoin market through the statistical models of the generalized autoregressive conditional heteroscedasticity (GARCH) family. 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, the Bitcoin trade volume, and the Bitcoin bid–ask spread, as external information signals, we test for improvement in volatility prediction of several GARCH model variants on a minute-level Bitcoin price time series. Statistical tests show that GARCH(1,1) and cGARCH(1,1) react the best to the addition of external signals to model the volatility process on out-of-sample data.
Highlights
The first mathematical description of the evolution of price changes in a market dates back to Bachelier [1], Mandelbrot [2], and truncated Lévy processes [3]
We focus this study on understanding Bitcoin volatility process and the statistical quantification of the predictive power of the class of generalized autoregressive conditional heteroscedasticity (GARCH) models with exogenous signals from social media tweets, trading volume, and order book on a minute level timescale
The mathematical models of information effects continued to advance in the 70s as well, by the proposition of the Mixture of Distribution Hypothesis [4], which states that the dynamics of price returns are governed by the information flow available to the traders
Summary
The first mathematical description of the evolution of price changes in a market dates back to Bachelier [1] (later rediscovered as Brownian motion, or random walk model), Mandelbrot [2] (price increments are Lévy stable distribution), and truncated Lévy processes [3]. Contrary to other studies about news jump dynamics and impact on daily returns [8, 9], we will model the volatility and external signals on a minute-level granularity. On this timescale, our external signals are not modeled with Poisson-like dynamics, but added directly as an exogenous observable variable It−1 to form GARCHX model. We focus this study on understanding Bitcoin volatility process and the statistical quantification of the predictive power of the class of GARCH models with exogenous signals from social media tweets, trading volume, and order book on a minute level timescale.
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