Abstract
Bitcoin has attracted the attention of investors lately due to its significant market capitalization and high volatility. This work considers the modeling and forecasting of daily high and low Bitcoin prices using a fractionally cointegrated vector autoregressive (FCVAR) model. As a flexible framework, FCVAR is able to account for two fundamental patterns of high and low financial prices: their cointegrating relationship and the long memory of their difference (i.e., the range), which is a measure of realized volatility. The analysis comprises the period from January 2012 to February 2018. Empirical findings indicate a significant cointegration relationship between daily high and low Bitcoin prices, which are integrated on an order close to the unity, and the evidence of long memory for the range. Results also indicate that high and low Bitcoin prices are predictable, and the fractionally cointegrated approach appears as a potential forecasting tool forcryptocurrencies market practitioners.
Highlights
Bitcoin (BTC), the most popular cryptocurrency traded in the digital money markets, exhibited a capitalization of about $40.5 billion by mid-2017, representing 89% of the capitalization of all cryptocurrencies1
Since the “error correction” term in the cointegrated relationship between Bitcoin high and low prices, i.e. the range, may contain long memory, this paper considers the use of the fractional cointegration framework
The results suggest that a linear combination of the daily high and low prices is integrated of a non-zero order, and the range is in the stationary region (d − b < 0.5) – see Table 6
Summary
Bitcoin (BTC), the most popular cryptocurrency traded in the digital money markets, exhibited a capitalization of about $40.5 billion by mid-2017, representing 89% of the capitalization of all cryptocurrencies. Much research has been devoted to the analysis of the predictability of daily market closing prices, few studies based on econometric time series models examined the case of high and low prices, as for instance the works of Baruník& Dvoráková (2015), Caporin et al (2013), Cheung et al (2010), Cheung et al (2009), He& Hu (2009), and Cheung (2007). Considering highs and lows prices of equity shares traded on the Brazilian stock exchange, Maciel (2018) states that the FCVAR approach can improve forecasting, compared to traditional time series models.
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