NONLINEAR ANALYSIS AND PREDICTION OF BITCOIN RETURN’S VOLATILITY

Abstract

This paper mainly studies the market nonlinearity and the prediction model based on the intrinsic generation mechanism (chaos) of Bitcoin’s daily return’s volatility from June 27, 2013 to November 7, 2019 with an econophysics perspective, so as to avoid the forecasting model misspecification. Firstly, this paper studies the multifractal and chaotic nonlinear characteristics of Bitcoin volatility by using multifractal detrended fluctuation analysis (MFDFA) and largest Lyapunov exponent (LLE) methods. Then, from the perspective of nonlinearity, the measured values of multifractal and chaos show that the volatility of Bitcoin has short-term predictability. The study of chaos and multifractal dynamics in nonlinear systems is very important in terms of their predictability. The chaos signals may have short-term predictability, while multifractals and self-similarity can increase the likelihood of accurately predicting future sequences of these signals. Finally, we constructed a number of chaotic artificial neural network models to forecast the Bitcoin return’s volatility avoiding the model misspecification. The results show that chaotic artificial neural network models have good prediction effect by comparing these models with the existing Artificial Neural Network (ANN) models. This is because the chaotic artificial neural network models can extract hidden patterns and accurately model time series from potential signals, while the benchmark ANN models are based on Gaussian kernel local approximation of non-stationary signals, so they cannot approach the global model with chaotic characteristics. At the same time, the multifractal parameters are further mined to obtain more market information to guide financial practice. These above findings matter for investors (especially for investors in quantitative trading) as well as effective supervision of financial institutions by government.