*Appendix A.2 Model 2. Model Description*

The purpose is to find a model that can approximate a target function by navigating the space of possible hypotheses (e.g., for ANN models, the space of hypotheses includes the network topology and hyperparameters) to predict the price changes for one day ahead. The target function can be written as:

$$
\Delta \hat{p}\_{i+1} = f(\Delta X\_{i1\prime} \,\Delta X\_{i2\prime} \,\Delta X\_{i3\prime} \dots \,\_\prime \Delta X\_{in}) \tag{A2}
$$

where <sup>Δ</sup>ˆ*pi*<sup>+</sup><sup>1</sup> are the BTC price changes at day *<sup>i</sup>* + 1. <sup>Δ</sup>*Xi*<sup>1</sup> *to* <sup>Δ</sup>*Xin* are attributes at day *<sup>i</sup>* that might affect the price changes, which are described as follows:

*Xi*<sup>1</sup> : Trade-weighted US dollar index or broad index (TWEXB) on day *i* is a measure of the value of the United States dollar relative to other world currencies.

*Xi*<sup>2</sup> : Gold-fixing price on day *i* is the setting of the price of gold that takes place via a dedicated conference line. The price continues to be set twice daily at 10:30 and 15:00 London GMT in US dollars.

*Xi*<sup>3</sup> : Dow Jones Industrial Average (DJIA) index on the day *i* is a stock market index that measures the stock performance of 30 large companies listed on stock exchanges in the United States.

*Xi*<sup>4</sup> : Brent Crude oil price on day *i* is a primary trading classification of sweet light crude oil from the North Sea that is an important benchmark that defines the prices for oil worldwide.

*Xi*<sup>5</sup> : West Texas Intermediate crude oil (WTI) prices or Texas light sweet, on day *i* is a benchmark in oil pricing, refined mainly in the Midwest and Gulf Coast regions in the United States.

*Xi*<sup>6</sup> : Trades per minute on the day *i* is the number of BTCs traded in a minute.

*Xi*<sup>7</sup> : Ask sum (5%) on day *i*, calculated as the amount of BTC on the order books waiting to be sold within a 5% range from the BTC price.

*Xi*<sup>8</sup> : Bid sum (5%) on day *i*, calculated as the amount of USD on the order books waiting to buy BTC within a 5% range from the BTC price.

*Xi*<sup>9</sup> : Bid–ask spread (10BTC) on day *i* is spread with 10 BTC slippage, i.e., with 10 BTC worth of orders removed from bids and from asks, which is calculated as *askmin*−*bidmax askmin* × 100.

*Xi*<sup>10</sup> : Bid–ask spread (100BTC) on day *i*, i.e., with 10 BTC worth of orders removed from bids and from asks, which is calculated as

$$\frac{ask\_{\min} - bid\_{\max}}{ask\_{\min}} \times 100.$$

*Xi*<sup>11</sup> : Buy0BTC on day *i*, defined as buy orders with an amount of less than 1 BTC.

*Xi*<sup>12</sup> : Sell0BTC on day *i*, defined as sell orders with an amount of less than 1 BTC.

*Xi*<sup>13</sup> : Buy1BTC on day *i*, defined as buy orders with an amount of 1 BTC.

*Xi*<sup>14</sup> : Sell1BTC on day *i*, defined as sell orders with an amount of 1 BTC.

*Xi*<sup>15</sup> : Buy5BTC on day *i*, defined as buy orders with an amount of 5 BTC.

*Xi*<sup>16</sup> : Sell5BTC on day *i*, defined as sell orders with an amount of 5 BTC.

*Xi*<sup>17</sup> : Buy10BTC on day *i*, defined as buy orders with an amount of 10 BTC.

*Xi*<sup>18</sup> : Sell10BTC on day *i*, defined as sell orders with an amount of 10 BTC.

*Xi*<sup>19</sup> : Momentum (MTM) (10 days) on day *i* is the difference between the price of BTC on day *i* and the BTC price on *i* − *N*th day which is *N* = 10 in this model.

*Xi*<sup>20</sup> : Commodity Channel Index (CCI), on day *i*, compares the price of BTC against its simple moving average and mean deviation of the price.

*Xi*<sup>21</sup> : Volume on day *i* is the number of BTCs traded during a given period, which is one day in our model.

*Xi*<sup>22</sup> : Simple moving average (SMA) on day *i*, calculated by adding recent prices and then dividing that by the number of periods, is five days for this model.


**Table A4.** Descriptive statistics.

**Table A5.** Chosen attributes by different feature selection techniques.

