Resumo

The Bitcoin (BTC), as the most popular cryptocurrency traded in the digital money markets, showed a capitalization of about $40.5 billion by mid-2007, representing 89% of the capitalization of all cryptocurrencies. Launched in 2009, Bitcoin transactions are based on an information technology infrastructure and on the lack of a central authority. Bitcoin particular features, as the absence of a regulatory agency, made the digital money a volatile and speculative currency, resulting in a market quite sensitive to real (e.g., economic, social and political) and fake (e.g., rumours) news.

Due to the evidence of long memory of Bitcoin volatility, this work aims to investigate whether or not the high and low prices of Bitcoin are predictable and which approach is appropriate to model these prices. Hence, this paper suggests a fractionally cointegrated vector autoregressive model (FCVAR), as proposed by Johansen (2008) and Johansen and Nielsen (2010, 2012), to model and predict the relationship between Bitcoin highs and lows. The results are then compared against traditional benchmarks over different prediction horizons.

Daily high and low prices provide valuable information regarding the dynamic process of an asset throughout time. These prices can be seen as references values for investors in order to place buy or sell orders, e.g. through candlestick charts, a popular technical indicator (XIONG et al., 2017). He and Wan (2009) also stated that the highs and lows are referred to prices at which the excess of demand changes its direction. Additionally, high and low prices are related with the concept of volatility.

Daily high and low prices can be seen as references values for investors in order to place buy or sell orders, e.g. through candlestick charts, a popular technical indicator. The motivation of FCVAR is twofold. First, FCVAR modeling is able to capture the cointegrating relationship between high and low prices, i.e. in the short-term they may diverge, but in the long-term they have an embedded convergence path. Second, the range (the difference between high and low prices), as an efficient volatility measure, is assumed to display a long memory, which allows for greater flexibility.

FCVAR estimates indicate that daily high and low prices are integrated of an order close to the unity and suggest that a linear combination of the daily high and low prices (the range) is integrated of a non-zero order, and the range is in the stationary region. From the experimental results obtained, the FCVAR approach consistently outperforms all of other competitors. When comparing the performance of each method across the three prediction horizons (i.e., 1, 5, and 10), the superior performance of FCVAR over the remaining methods is still verified.

The findings indicate that daily high and low Bitcoin prices are integrated of an order close to the unity, and the range displays long memory and is in the stationary region. A significant cointegration relationship was found between daily high and low prices. The empirical FCVAR model shows that high and low prices move in opposite directions to restore equilibrium after a shock to the system occurs. Also, the results evidence the predictability of daily highs and lows of Bitcoin for different forecasting horizons, in which the fractionally approach conducts to better predictions.

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