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Sensors 2021, 21, 6319 7 of 16 under the condition that the Lagrangian multipliers αk ≥ 1, for k = 1, . . . , p [35]. Note that the tolerance errors are again introduced, defining ξ as the value outside the error margins and ξ⋆ to limit the value to the dependent variable. Thus, the Lagrangian dual of the problem stated in (9) may be solved by minimizing the expression given by 1p 2||w||2 + c ∑(ξk − ξk⋆), (10) k=1 under the conditions (w⊤xk + b) − yk ≤ 1 + ξk and yk − (w⊤xk + b) ≤ 1 + ξk⋆. 4. Empirical Analysis with Real-World Data To conduct our study with real-world data, we employ the SVC algorithm proposed in [23]. We use the R software with the e1071 [36] and ggplot2 [37] packages to carry out the data analysis [38]. As mentioned, we perform our analysis using three type of data: (i) daily confirmed COVID-19 infections and deaths; (ii) daily gold price –in US dollars–; and (iii) daily closing price of major cryptocurrencies—in US dollar—. • Daily confirmed COVID-19 infections and deaths: First, we collect the daily confirmed COVID-19 infections and deaths from the online repository https://github.com/CSSEGISandData/COVID-19 (accessed on 29 August 2021). This web-hosting has been operated by the Johns Hopkins University Center for Systems Science and Engineering from 23 January 2020 until the present, and it is updated twice daily. We consider the period from 23 January 2020 to 14 July 2021. This period essentially accounts for all available data officially published [39] up to the date where we started this research. • Daily gold price in US dollars: Second, to compare the impact of the pre-COVID-19 period with the COVID-19 period on the classification of cryptocurrency returns according to the quantile values of the gold price (in US dollars), we collected the gold price data from the website https://www.gold.org/goldhub/data/gold-prices (accessed on 29 August 2021) over the period 04 December 2018 to 14 July 2021. In this article, the word return is used synonymously with log returns. The four graphs in the upper and middle of Figure 2 present the distribution and trend of the daily infections and deaths due to COVID-19. The graphs show that, for more than 100 days, the number of daily deaths ranged from 5000 to 7500 cases. The plots in Figure 2 show that the daily confirmed COVID-19 infections and deaths and the daily gold prices followed a similar trend during the period of the ongoing COVID-19 pandemic. The gold prices report high volatility clustering in the pandemic compared with the pre-COVID-19 period. For the entire period of study, the probability density function of the gold prices is slightly skewed to the left with a high excess kurtosis. Remark. Note that the shaded region in Figures 2–4 describes the period after the beginning of the pandemic for better visualization of the impact of COVID-19 on the gold price/cryptocurrency return. Also, in these figures and in Figures 5–7, the vertical dotted line represents the threshold between the pre-COVID-19 period and ongoing COVID-19 period. • Daily closing price of major cryptocurrencies in US dollars: Third, we collect the daily closing price and market capitalization for some major cryp- tocurrencies available from the online source https://coinmarketcap.com (accessed on 29 August 2021). For the current research, as mentioned, we study the six cryptocur- rency assets, that is, ADA, BNB, BTC, DOGE, ETH, and XRP, selected from the top 10 ranked currencies. Table 1 provides the main characteristics of the top-ranked cryptocurrencies and Figure 3 presents the market capitalization of used currencies over the study period. Again, the vertical dotted lines represent the threshold between the two periods of time (before and during the pandemic). The trends show an exponential increase inPDF Image | Predicting Cryptocurrency Returns Based on the Gold Prices
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