Bitcoin time series dataset recording individual transactions denominated in Euro at the COINBASE market between April 23, 2015 and August 15, 2016 is analyzed. Markov switching model is applied to classify the regions of varying volatility represented by three hidden state regimes using univariate autoregressive model and dependent mixture model. Causality extraction and price prediction of daily BTCEUR exchange rates is performed by means of a recurrent neural network using the standard Elman model. Strong correlations is found between the normalized mean squared error of the Elman network (out-of-sample 5-day-ahead prediction) and the realized volatility (sum of minute returns squared throughout the trading day). The present approach is calibrated using simulated regime change in standard econometric models. Our results clearly demonstrate the applicability of recurrent neural networks to causality extraction even in the case of highly volatile cryptocurrency exchange rate time series data.
IntroductionBitcoin is a cryptocurrency released as an open-source software in 2009, which represents a transaction payment system as well as a sort of digital commodity (Bohme et al., 2016). The bitcoin market capitalization as of early 2017 has reached USD 20 billion (CoinDesk, 2017). Free of any interventions from regulatory authorities, such as central banks, the distributed block chain system on which Bitcoin is based meets varying levels of demand for transaction settlement, and the Bitcoin exchange rate series to major currencies such as USD, EUR or GBP are known to highly fluctuate -it is not uncommon that gains or losses in tens of percent occur within a week, if not during a single day. There exist various Bitcoin exchange markets, such as BitBay, Btcde, Kraken, LocalBtc, or Rock for EUR currency, to name just a few of the currently active BTCEUR exchanges. The highly volatile nature of the exchange rate represents an ideal environment for the study of the extreme events in the field of financial time series. Prediction of extreme events is a key issue not only in economics, but also in climatology, geosciences, civil engineering, space technology, etc. In spite of its importance, the topic is rather under-studied, in our opinion. In this work, we explore the applicability of computational intelligence methods from financial analysis to the series of Bitcoin exchange rates (data shown in Fig. 1). Since the Bitcoin price process is not stationary but exhibits an appreciation trend, we transform the time series data to the logarithmic returns. If the absolute value of the log return is large, it corresponds to an extreme event (bullish or bearish, based on the sign). Next we adopt the Hidden Markov Model to categorize the market regime into 3 modes: stable, intermediate, and volatile. This approach is excellent in ex-post analysis of the data, however lacks in the predictive power for future trend prediction. Consequently, we add the realized volatility as an intraday indicator of market stability, and d...