Itô Stochastic Differential Equation Modeling for Bitcoin Data

Abstract

In this study, Bitcoin data is examined by Stochastic Differential Equation Modeling(SDEM). At first, the parameters of SDE established for the given Bitcoin data areestimated by using maximum likelihood estimation method. Then, we have obtainedreasonable Stochastic Differential Equation (SDE) based on the Bitcoin data. Finally, byapplying Euler-Maruyama Approximation Method trajectories of SDE according to thefixed time are achieved. The performances of trajectories are established by Chi-Squarecriteria. The results are acquired by using statistical software R-Studio.<br>