*Appendix A.3 Model 3. Model Description*

The purpose is to find a model that can approximate a target function, which can be written as:

$$
\hat{\Delta p}\_{i+1} = f(\Delta X\_{i1}, \Delta X\_{i2}, \Delta X\_{i3}, \dots, \Delta X\_{\text{int}}) \tag{A3}
$$

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> : S&P500 stock market index on day *i* is a stock market index that measures the stock performance of 500 large companies listed on stock exchanges in the United States.

*Xi*<sup>2</sup> : Dow Jones Industrial Average (DJIA) index on 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>3</sup> : CAC 40 stock market index on day *i* is a stock market index representing a capitalization-weighted measure of the 40 most significant stocks among the 100 most oversized market caps on the Euronext Paris.

*Xi*<sup>4</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>5</sup> : Nasdaq Composite on day *i* is a stock market index of the common stocks and similar securities listed on the Nasdaq stock market.

*Xi*<sup>6</sup> : Gold-fixing price on day *i* is the setting of the gold price 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>7</sup> : Bid–ask spread (10BTC), on day *i* is spread with 10 BTC slippage, that is with 10 BTC worth of orders removed from bids and from asks, which is calculated as *askmin*−*bidmax askmin* × 100.

*Xi*<sup>8</sup> : Ask sum (10%) on day *i*, calculated as the amount of BTC on the order books waiting to be sold within a 10% range from the BTC price.

*Xi*<sup>9</sup> : Bid sum (10%) on day *i*, calculated as the amount of USD on the order books waiting to buy BTC within a 10% range from the BTC price.

*Xi*<sup>10</sup> : Trades per minute on day *i* are the number of BTCs traded in a minute.

*Xi*<sup>11</sup> : Volatility on day *i* is the changes in market prices over a specified period. The faster prices change, the higher the volatility. It can be measured and calculated based on historical prices and can be used for trend identification.

*Xi*<sup>12</sup> : Volume on day *i* is the number of BTCs traded during a given period, which is one day in our model.

*Xi*<sup>13</sup> : Simple moving average (SMA) on day *i*, calculated by adding recent prices and then dividing that by the number of periods, which is five days for this model.

*Xi*<sup>14</sup> : Hash rate on day *i* is the speed at which computational operations are completed to mine a BTC block.

*Xi*<sup>15</sup> : Mining difficulty on day *i* is a measure of how difficult it is to mine a BTC block, or in more technical terms, to find a hash below a given target.

*Xi*<sup>16</sup> : Number of transactions per block on day *i* are the transactions that happen in a block, and as soon as a block is solved, it is not possible to extend the block by adding in more transactions.

*Xi*<sup>17</sup> : Block time on day *i* is an average time to mine a block in minutes.


**Table A6.** Descriptive statistics.

**Table A7.** Attributes selected by different feature selection methods.

