On the predictability of high and low prices: The case of Bitcoin/Previsibilidade em precos maximos e minimos: O caso do Bitcoin.
| Autor | Maciel, Leandro |
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Introduction
Bitcoin (BTC), the most popular cryptocurrency traded in the digital money markets, exhibited a capitalization of about $40.5 billion by mid-2017, representing 89% of the capitalization of all cryptocurrencies (1). Launched in 2009, Bitcoin transactions are based on an information technology infrastructure and on the lack of a central authority. Instead of relying on central banks, a decentralized computer network validates the transactions and grows the money supply of Bitcoin (Yermack, 2017). Users and investors have perceived huge financial potential in the Bitcoin market, driving the Bitcoin price from US dollar parity in early 2011 to about 1,500 US$/BTC in mid-2017. Further, the number of transactions using Bitcoin has increased considerably and, according to Polasik et al. (2015), Bitcoin transactions per month increased from 12,000 to 2.1 million from August 2010 to August 2014, and in December 2015, approximately 200,000 Bitcoin transactions were carried out per day.
Bitcoin's particular features, in the absence of a regulatory agency, make the digital money a volatile and speculative currency, resulting in a market that is quite sensitive to real (e.g., economic, social and political) and fake (e.g., rumors) news. As stated by Alvarez-Ramirez et al. (2018) and Baek& Elbeck (2015), the poorly-defined liquidity conditions of the market and the lack of certain rules for investment realization add fragility to transactions, which are reflected as large price jumps and excessive volatility when compared to traditional currencies and assets. Despite that, a literature on cryptocurrencies has emerged, mostly focused on the legal aspects and the underlying blockchain technology.
Some authors, for example, discuss the efficiency of virtual money markets. Bartos (2015) indicates that Bitcoin returns follow the hypothesis of efficient markets by showing fast responses to publicly announced information in 2013-2014. On the other hand, based on automatic variance tests, Urquhart (2016) reveals that Bitcoin returns are significantly inefficient over the period from August 1st, 2010 to July 31st, 2016. However, when the sample is divided into two subsample periods, Urquhart (2016) finds that the Bitcoin market is efficient in the latter period--August 1st, 2013 to July 31st, 2016.
By verifying empirically whether or not there exist weekly price anomalies, Kurihara& Fukushima (2017) state that Bitcoin transactions are becoming more efficient, but its returns do not fulfill the efficient market hypothesis. Additionally, Urquhart (2017) find significant evidence of price clustering at round numbers as a Bitcoin price anomaly, with over 10% of prices ending with 00 decimals compared to other variations.
Bariviera et al. (2017) use detrended fluctuation analysis (DFA) over a sliding window to report that the Hurst exponent changed significantly during the first years of existence of Bitcoin, tending to stabilize from early 2014 to 2017. Also using DFA, Alvarez-Ramirez et al. (2018) estimate long-range correlations for price returns of Bitcoin. They find that the Bitcoin market exhibits periods of efficiency alternating with periods where the price dynamics are driven by anti-persistence.
The efficiency of Bitcoin market compared to gold, stock and foreign exchange markets is evaluated in the work of A-Yahyahee et al. (2018). They find that the long-memory feature and multifractality of the Bitcoin market is stronger, making the cryptocurrency more inefficient when compared to gold, stock and traditional currency markets.
Researchers have also devoted attention to the analysis of Bitcoin volatility. For instance, Balcilar et al. (2017) analyze the causal relationship between trading volume and Bitcoin returns, and trading volume and Bitcoin volatility. The causality-in-quantiles test reveals that volume can predict returns--except in Bitcoin bear and bull market regimes. It highlights the importance of modeling nonlinearities and accounting for the tail behavior when analyzing causal relationships between Bitcoin returns and trading volume. The authors additionally show, however, that volume cannot help predict the volatility of Bitcoin returns at any point of the conditional distribution.
Katsiampa (2017) explores the optimal conditional heteroskedasticity model with regards to goodness-of-fit to Bitcoin price data. The author shows that the best model is the AR-CGARCH model, highlighting the significance of including both a short-run and a long-run component for Bitcoin conditional variance. More recently, Lahmiri et al. (2018) investigate volatility nonlinear patterns in seven Bitcoin markets. The empirical findings identify the existence of long-range memory in Bitcoin volatility, irrespective of distributional inference. The same finding applies to Bitcoin entropy measurement, which indicates a high degree of randomness in the price series.
In general, the recent literature has stated that volatility of Bitcoin prices is an outcome of market sentiments, which can be attributed to the presence of significant "memory" (Katsiampa, 2017; Cheah et al., 2018; Cheah& Fry, 2015; Lahmiri et al., 2018). This emerges from a key element in the determination of Bitcoin prices: the assumption of full confidence of its users. Indeed, the literature has shown that Bitcoin is ideal for risk-averse investors in anticipation of negative shocks to the market (Dyhrberg, 2016a) and could be used as a hedging asset against market-specific risk (Dyhrberg, 2016b).
Due to the evidence of long memory of Bitcoin volatility, (2) 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. Although 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 Barunik& Dvorakova (2015), Caporin et al. (2013), Cheung et al. (2010), Cheung et al. (2009), He& Hu (2009), and Cheung (2007). Indeed, Caporin et al. (2013) argue that the lack of studies regarding daily high and low asset prices is surprising for at least three reasons: i) the long histories of high and low prices data are readily available; ii) many technical analysis strategies use high and low prices to construct resistance and support levels; and iii) these prices can measure market liquidity and transaction costs.
In particular, daily high and low prices provide valuable information regarding the dynamic process of an asset over time, which can be seen as references values for investors in trading analysis, e.g. through candlestick charts (Xiong et al., 2017; Cheung& Chinn, 2001). He& Wan (2009) state that highs and lows are referred to prices at which excess demand changes its direction. Additionally, these prices are related to the concept of volatility. Alizadeh et al. (2002) show that the difference between the highest and lowest (log) prices of an asset over a fixed sample interval, also known as the (log) range, is a highly efficient volatility measure. Brandt& Diebold (2006) and Shu& Zhang (2006) point out that the range-based volatility estimator appears robust to microstructure noise such as bid-ask bounce. This overcomes the limitations of traditional volatility models based on closing prices that fail to use the information contents inside the reference period of the prices, resulting in inaccurate forecasts.
Daily highs and lows can be used as stop-loss bandwidths, providing information about liquidity provisioning and the price discovery process. Further, Caporin et al. (2013) state that high (low) prices are more likely to correspond to ask (bid) quotes; thus, transaction costs and other frictions, such as price discreteness, the tick size (i.e., the minimal increments) or stale prices, might represent disturbing factors. Finally, high and low prices are more likely to be affected by unanticipated public announcements or other unexpected shocks. Therefore, aspects such as market resiliency and quality of the market infrastructure can be determinant (Caporin et al., 2013).
Hence, this paper suggests a fractionally cointegrated vector autoregressive model (FCVAR), as proposed by Johansen (2008) and Johansen& Nielsen (2010, 2012), to model and predict the relationship between Bitcoin highs and lows. The motivation of this approach is twofold. First, FCVAR modeling captures 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. (3) Barunik & Dvorakova (2015) give a more general fractional or long-memory framework, where the series are assumed to be integrated of order d and cointegrated of order less than d, i.e. CI(d - b), where d,b [member of] [Real part] and, 0
The usefulness of the FCAR framework for financial time series modeling has been addressed by the literature. Barunik & Dvorakova (2015) explore the fractional cointegration relationship between daily high and low of stock exchange indices. The authors find that the range of all indices display long memory and are mostly in the non-stationary region, supporting the idea that volatility might not be a stationary process. Considering highs and lows prices of equity shares traded on the Brazilian stock exchange, Maciel (2018) states that the FC-VAR approach can improve forecasting, compared to traditional time series models. Alternatively, Dolatabadi et al. (2016) use the FCVAR model to analyze the relationship between spot and futures prices in commodity markets, concluding that both prices are cointegrated, and the cointegration is of the fractional type.
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