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Sensors 2021, 21, 6319 12 of 16 MAPE = 1∑Nyi−yˆi×100%, N yi i=1 1 N RMSE = N∑(yi−yˆi)2, i=1 N∑N (y−yˆ)2 NRMSE = i=1 i i , where N is the total number of observations, yˆi is the predictive value of yi, for i = 1, . . . , N, and yi − yˆi denotes the prediction error in yi. Second, we utilize the SVM optimization strategy as a dynamic model that involves all available data. In [41], it is showed that the dynamic model can achieve more accurate forecasting results compared with the one based on a fixed training set. Therefore, in this article, we adopt the dynamic SVM algorithm. The optimized estimation of the coefficient c stated in (10) and the parameters γ, d defined in (2) and (3), respectively, may be obtained based on the k-fold cross validation method, where the index expressed in (11) has the mimimum value. In this article, we con- sider a 10-fold cross validation and a set of tuning parameters c ∈ {0.001,0.01,1,2,2,4,8,16,32,64,128,256}, d ∈ {1,2,3}, and γ ∈ {0.3,0.4,0.5}. The estimated parameters of the linear, polynomial, and radial kernel models for the entire sample are shown in Table 4. Applying the optimized parameters in Table 4, the SVM models with each kernel are run on a daily series and the forecasting performance accuracy (in %) for each currency is calculated. The results are indicative of the SVM’s superior pre- dictive power when using a radial kernel (between 89.4% and 91.8% performance accuracy) compared with linear (between 71.8% and 74.5% performance accuracy) and polynomial (between 74.8% and 79.3% performance accuracy) kernels. To illustrate the SVM classification prediction capabilities, using the radial classifier, during both periods, pre- and during the COVID-19 outbreak, Figures 5–7 show the decision rules for a different set of patterns in the hyperplane. The four classes of gold price quartiles are represented by dotted points with four different colors. In the figures, we indicate the support vectors (patterns) with dotted points and double circles, and the errors (misclassifications) with dotted points and double circles but in different colors. Figures 5–7 display that the majority of the errors occurred during the COVID-19 period compared with the pre-period of COVID-19, where some of the cryptocurrencies returns from Q3 class of the gold price are misclassified as Q4. This is justifiable as the uncertainty about the COVID-19 has resulted in significant effects that continue to drive perceptions of risk and volatility in cryptocurrencies and gold prices. Table 4. Optimal parameters and performance accuracy (in %) for the indicated currency and kernel. (∑N y)2 i=1 i (11) Currency Binance Coin Bitcoin Cardano Dogecoin Ethereum Ripple Linear Kernel Accuracy c 73.2 64 74.5 256 72.6 256 71.8 256 73.0 64 72.3 128 Polynomial Kernel Accuracy c d 76.8 512 3 77.3 256 3 74.8 512 3 76.5 512 3 79.3 128 3 75.8 512 3 Radial Kernel Accuracy c γ 91.5 512 0.4 91.8 512 0.3 91.1 128 0.4 89.4 16 0.4 90.9 128 0.3 90.8 256 0.3 Where the parameter c is used for all kernels, d is the degree parameter of the polynomial kernel, and γ is the radial kernel parameter.PDF Image | Predicting Cryptocurrency Returns Based on the Gold Prices
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