*5.2. Forecasting Results*

Both VAR and BVAR models were tested with three timeframes in two different experiments. Experiment A: For the 2016 timeframe, values of variables described in Sections 4.2.1 and 4.2.2 between 01-01-2016 and 30-09-2016 were imported as input to the two models. For the Post-boom timeframe, data from 10-12-2013 to 30-09-2016 were imported as input. Both models forecasted the Bitcoin price in USD for the period 01-10-2016 to 30-10-2016 and compared the forecasting results with the actual Bitcoin price. For the Full timeframe, the time period selected to forecast was the last 199 days [05/08/2016–11/22/2016] to evaluate the effectiveness of these two models. Experiment B: For the 2020 timeframe, input and output variables between 01-01-2020 and 01-08-2020 were used for both the VAR and BVAR models. For the Post-boom timeframe, data from 01-01-2017 to 01-08-2020 were used. For the Full timeframe, the time period selected for forecasting was the last six months [01-02-2020, 01-08-2020] to evaluate the effectiveness of these two models.

### 5.2.1. Results of the VAR Model: Experiment A

The model selects the most suitable coefficients, where the outcome minimizes FPE. Figures 4–6, respectively show the evaluation of the Full, Post-boom, and the Year of 2016 timeframes forecasting in comparison to the BTCUSD OHLC candle from Rbitcoincharts.com, where "fcst" is the forecasted closing price, "lower" is the lower bound (95% CI), and "upper" is the upper bound (95% CI). The endogenous variables were simulated from the estimated VAR, as shown in Figures 7–9 for three different timeframes. The simulated exogenous variables were the real datasets taken from Quandl for the aforementioned timeframe. Ultimately, by evaluating the results of different timeframes, the full timeframe using the VAR model showed the best forecasting performance. The Full timeframe represents the most data available and incorporates the relationships over different timeframes. Although the significance of the relationship between these variables may change over time, the 7-year timeframe surely aided in modeling the market behavior.

**Figure 4.** Forecasting Bitcoin closing price using Full timeframe. Data Vs. BTC OHLC.

**Figure 5.** Forecasting Bitcoin closing price using Post-boom timeframe. Data Vs. BTC OHLC.

**Figure 6.** Forecasting Bitcoin closing price using Year of 2016 timeframe. Data vs. BTC OHLC.

**Figure 7.** Forecasting the endogenous variables using Full timeframe data (VAR).

**Figure 8.** Forecasting the endogenous variables using Post-boom timeframe data (VAR).

**Figure 9.** Forecasting the endogenous variables using Year of 2016 timeframe data (VAR).

### 5.2.2. Results of the VAR Model: Experiment B

In this experiment, we evaluated the performance of the VAR model using the period [January 2011–August 2020] Full timeframe data, Post-boom timeframe data [January 2017–August 2020], and the Year of 2020 timeframe data [January 2020–August 2020]. We can observe that the VAR model could effectively predict the prices of the BTC using the three timeframes for the variables MKPRU, MWNUS, and TOTBC, as shown in Figures 10–13, with the best performance obtained for the Full timeframe period.

**Figure 10.** Forecasting the endogenous variables using Full timeframe data (VAR).

**Figure 11.** Forecasting the endogenous variables using Post-boom timeframe data (VAR).

**Figure 12.** Forecasting the endogenous variables using Year of 2020 timeframe data (VAR).

**Figure 13.** Forecasting Bitcoin closing price using Full timeframe data (BVAR).

### 5.2.3. Results of the BVAR Model: Experiment A

The forecasting results of Bitcoin price in USD for Full, Post-boom, and the Year of 2016 timeframes are shown in Figures 13–15, respectively. The red lines in each plot are from the BTC Market Price dataset (MKPRU) of Quandl. The mean absolute percentage error (MAPE) of each forecasting result was calculated to evaluate the model performance. The forecasting of Year of 2016 and Post-boom timeframes gave good performances, as the result of the Year of 2016 timeframe has a MAPE value of 2.38% and the MAPE value of the Post-boom timeframe result is 2.85%. However, forecasting price using the Full timeframe resulted in the largest MAPE value, 19.88%. The BVAR model provided high forecasting accuracy with fewer data available or shorter timeframe in the period of [January 2009–November 2016].

**Figure 14.** Forecasting Bitcoin closing price using Post-boom timeframe data (BVAR).

**Figure 15.** Forecasting Bitcoin closing price using Year of 2016 timeframe data (BVAR).

### 5.2.4. Results of the BVAR Model: Experiment B

In this experiment, we evaluated the performance of the VAR model using the period [January 2011–August 2020] Full timeframe data, Post-boom timeframe data [January 2017–August 2020], and the Year of 2020 timeframe data [January 2020–August 2020], as shown in Figures 16–18. We can observe that the BVAR model could predict the values of the two endogenous variables (MWNUS, and TOTBC) effectively for the Post-boom period and the Year of 2020 only, while the MKPRU variable had its best prediction for the Year of 2020 alone. This experiment confirms that the BVAR model achieves better forecasting performance for short time periods.

**Figure 16.** Forecasting the endogenous variables using Full timeframe data (BVAR).

**Figure 17.** Forecasting the endogenous variables using Post-boom timeframe data (BVAR).

**Figure 18.** Forecasting the endogenous variables using Year of 2020 timeframe data (BVAR).

### 5.2.5. Analysis and Discussion of Results

For the VAR model, the price of BTC was affected by short-term lag of itself as well as the number of MyWallet users. Surprisingly, it was not affected by the supply of BTC available on the market. One explanation for this could be that the supply of BTC is limited, and as such, this value is known by speculators beforehand as a market symmetric variable. The current BTC price was positively affected by 1, 2, 4, 5, 9, 11, 17, and 20 day lags of itself. It was negatively impacted by 7, 8, 10, 12, 16, and 18 day lags of itself, as shown in Table 1.



The effects of MyWallet users on BTC price were slightly positive overall. In terms of exogenous variables, the Miner's Revenue (+), Number of Transactions per Block (−), BTC Difficulty (+), the Change in the Number of unique addresses used (+), and Hash Rate (−) all played a significant part in estimating BTC. The R<sup>2</sup> of the model was above 99%, with F-Stats significant at a 99% confidence level, as shown in Table 2.


In addition to analyzing the individual factors of influence on Bitcoin price, the VAR model predicted a grea<sup>t</sup> pattern of fluctuating prices. Compared with the forecasting price curves from the VAR model, the BVAR model gave a more accurate prediction of Bitcoin price to the actual values in general. Additionally, the availability and completeness of the input data played a significant role in the performance of the VAR model, while the BVAR model achieved a grea<sup>t</sup> forecasting result with a low percentage error rate while using only data of the years 2016 and 2020. The results demonstrate that the BVAR model performed well for a fairly limited number of observations.
