Forecasting Bitcoin closing price series using linear regression and neural networks models

In this article we forecast daily closing price series of Bitcoin, Litecoin and Ethereum cryptocurrencies, using data on prices and volumes of prior days. Cryptocurrencies price behaviour is still largely unexplored, presenting new opportunities for researchers and economists to highlight similarities and differences with standard financial prices. We compared our results with various benchmarks: one recent work on Bitcoin prices forecasting that follows different approaches, a well-known paper that uses Intel, National Bank shares and Microsoft daily NASDAQ closing prices spanning a 3-year interval and another, more recent paper which gives quantitative results on stock market index predictions. We followed different approaches in parallel, implementing both statistical techniques and machine learning algorithms: the Simple Linear Regression (SLR) model for uni-variate series forecast using only closing prices, and the Multiple Linear Regression (MLR) model for multivariate series using both price and volume data. We used two artificial neural networks as well: Multilayer Perceptron (MLP) and Long short-term memory (LSTM). While the entire time series resulted to be indistinguishable from a random walk, the partitioning of datasets into shorter sequences, representing different price "regimes", allows to obtain precise forecast as evaluated in terms of Mean Absolute Percentage Error(MAPE) and relative Root Mean Square Error (relativeRMSE). In this case the best results are obtained using more than one previous price, thus confirming the existence of time regimes different from random walks. Our models perform well also in terms of time complexity, and provide overall results better than those obtained in the benchmark studies, improving the state-of-the-art.