**1. Introduction**

Bitcoin, the world's first decentralised and currently biggest digital currency, is similar to synthetic commodity money, which shares the attributes of both commodity (e.g., gold) and fiat money (e.g., US dollar) (Selgin 2015). Bitcoin was introduced in 2008 by a group of programmers using the pseudonym 'Satoshi Nakamoto' (Cheah and Fry 2015). Some argue that it has the same finite economic attributes of gold and labelled as digital gold (Popper 2015). Meanwhile, the acceptance of the Bitcoin is still debatable due to its frictionless nature, lack of intrinsic value, and unclear issuing authority (Ciaian et al. 2016). The price volatility of Bitcoin makes it one of the most speculative digital currency, and a poor form of "holder of value". Investors can lose their capital due to high volatility and uncertainty of Bitcoin price.

Media coverage about Bitcoin drew in amateur investors leading to a gambling mentality (Roberts 2017). However, Bitcoin is coming into the mainstream with large institutional investors eyeing its potential. Despite its limitations, Bitcoin is the most valuable and popular cryptocurrency to date (Corbet et al. 2019).

Bitcoin price has been extremely volatile since the inception of the cryptocurrency (Dwyer 2015). Due to concerns with speculative trading, in January 2018, Facebook banned all ads for Bitcoin and other cryptocurrencies (Robertson 2018). Additionally, experts foresee another financial crisis in the near future caused by the cryptocurrency boom (Lam et al. 2018). A major crash of the Bitcoin price can be triggered by a cyber hack and a governmen<sup>t</sup> crackdown, and can take weeks or months to bounce back (Roberts 2017). Typically, investors predict future Bitcoin price based on past trends. But it is not easy to predict future Bitcoin price with a high level of accuracy. The price of Bitcoin follows a

boom-bust pattern due to its speculative nature (Cheah and Fry 2015). Additionally, Bitcoin investors are speculative and short term oriented (Salisu et al. 2019).

Due to the progressive price change and increase in the market cap, the popularity of investment in Bitcoin has been increasing dramatically. Meanwhile, Urquhart (2016) found that Bitcoin is an ine fficient market. Caporale et al. (2018) also observe ine fficiency in the cryptocurrency market. In the same vein, due to high price volatility, speculators have a generic question of whether the price of Bitcoin can be forecasted in advance.

Thus far, there have been limited attempts in the literature to forecast the price of Bitcoin. Katsiampa (2017) scrutinised the in-sample goodness-of-fit of GARCH models for Bitcoin price but did not perform out-sample forecast. Kristjanpoller and Minutolo (2018) proposed a hybrid-forecasting model to predict Bitcoin price volatility, integrating artificial neural network (ANN), generalised autoregressive conditional heteroscedasticity (GARCH) and principal components analysis (PCA). They found that the accuracy of the hybrid model increases after incorporation of PCA pre-processing. Similar to Katsiampa (2017), Kristjanpoller and Minutolo (2018) also only examined in-sample forecast performance. Meanwhile, Aalborg et al. (2018) found that Bitcoin returns cannot be predicted (R<sup>2</sup> ≤ 0.01) using explanatory variables (i.e., google trend, trading volume, transaction volume, VIX index, and unique user addresses).

Given that Bitcoin is becoming more popular, ye<sup>t</sup> still volatile and not well explained, a need exists to study methods to better understand its price fluctuations. Accurately forecasting the daily movements can increase the returns of day traders and consequently make the market more e fficient. The choice of forecasting models can have a significant e ffect on performance (Chen et al. 2019). We contribute to the Bitcoin forecasting literature by testing autoregressive integrated moving average (ARIMA) and neural network autoregression (NNAR). ARIMA is one of the traditional forecasting methods, and NNAR is a rather sophisticated and more modern approach to forecasting (Hyndman and Athanasopoulos 2018). To ensure validation and implementation, as suggested by Adya and Collopy (1998), we use ex-ante Bitcoin forecast performance using a relatively large sample, and multiple training and testing samples to demonstrate the stability of the forecast results. By following this procedure, we di fferentiate the results of this study with the ones mentioned earlier.

In the next section, we discuss existing literature on Bitcoin price modelling. Section 3 presents daily Bitcoin price data used in this study. Section 4 presents the adopted forecast methodologies and performance measures. The analysis and findings are presented in Section 5, and final remarks are made in Section 6.
