The Comparison of Cryptocurrency Returns Prediction Based on Geometric Brownian Motion and Wavelet Transform

In the present study the accuracy of predicting cryptocurrencies return was compared through two approaches of Geometric Broanian Motion (GBM) and Wavelet Transforms (WT). In order to do that, 5 cryptocurrencies of BTC, ETH, XRP, BCH and EOS as representatives of risky assets were studied with daily frequency during the one year period of 2018 to 2019. Two measures of RMSE and MAE were employed to compare the accuracy of approaches in prediction of returns. In geometric Brownian modeling, the Brownian process-based stochastic differential model for asset prices leads to the fact that the logarithmic return of an asset has a normal distribution with time-dependent parameters. The results of logarithmic returns prediction by both of methods showed that WTs have less error than GBM in returns prediction of BTC, ETH, XRP and BCH cryptocurrencies and for each of accuracy measures, an specific approach has desirable performance for prediction of EOS returns. citing these results it can be concluded that WT in prediction of risky assts returns has less error than GBM method.