*4.2. Forecast Accuracy Measures*

Forecasting models are evaluated based on their accuracy of the forecast. Typical forecast accuracy measures such as RMSE (root mean square error) and MAPE (mean absolute percent error) are criticised for their instability with varying number of test-sample forecast periods. Thus, we adopt three indices to measure the accuracy of forecast results: RMSE, MAPE, and MASE (mean absolute scaled error). MASE was proposed by Hyndman and Koehler (2006) as a remedy to overcome the drawbacks of RMSE and MAPE when dealing with a varying number of test-sample periods. The three adopted accuracy measures can be expressed as follows:

$$RMSE = \sqrt{\frac{1}{n} \sum\_{t=1}^{n} (d\_t - z\_t)^2} \tag{4}$$

$$MAPE = \frac{100}{n} \sum\_{t=1}^{n} \left| \frac{(d\_t - z\_t)}{d\_t} \right| \tag{5}$$

$$MSE = \left. \begin{array}{c} emm \left| \frac{c\_t}{\frac{1}{n-1} \sum\_{t=2}^{n} |z\_t - z\_{t-1}|} \right| \right| \tag{6}$$

Here, *et* is the forecast error calculated as (*dt* − *zt*), *dt* is the actual Bitcoin price at time *t*, *zt* is the forecasted price at time *t*, *n* is the total number of observations and *zt* − *zt*−1 is the forecast error of the naïve forecast.
