In this paper, we analyze and predict the cyclical behavior of the Bitcoin price using real data and state-of-the-art methodologies in time series analysis. We first identify short, medium and long cycles from historical Bitcoin prices. We then transform the price data into better fitted time series and reconstruct the extracted fitted time series into high-frequency, low-frequency, and residue components. We optimize the hyper-parameters that control the learning process and predict the Bitcoin prices in future cycles using a recurrent neural network model, i.e., Long Short Term Memory (LSTM) with the reconstructed components as the inputs. Numerical studies show that our refined inputs and hyper-parameters result in better predictions than raw prices and default hyper-paramete...[ Read more ]

In this paper, we analyze and predict the cyclical behavior of the Bitcoin price using real data and state-of-the-art methodologies in time series analysis. We first identify short, medium and long cycles from historical Bitcoin prices. We then transform the price data into better fitted time series and reconstruct the extracted fitted time series into high-frequency, low-frequency, and residue components. We optimize the hyper-parameters that control the learning process and predict the Bitcoin prices in future cycles using a recurrent neural network model, i.e., Long Short Term Memory (LSTM) with the reconstructed components as the inputs. Numerical studies show that our refined inputs and hyper-parameters result in better predictions than raw prices and default hyper-parameters. Assume that one plans to invest in Bitcoin futures with different maturities, e.g., short, medium, and long periods that coincide with the cycle lengths. We study the portfolio decision using an Eigen-adjusted covariance matrix of the investment options and perform backtesting on historical data.