**2. Data**

The study is based on the S&P 500 index components' daily time series in the interval from 2016.01.04 to 2021.03.26. There are a total of 1315 data points in each of the time series. The S&P500 index consists of the largest stocks of the New York Stock Exchange and NAS-DAQ (National Association of Securities Dealers Automated Quotations). Considering the importance of stock indices for the assessment of the state of the economy, we can conclude that the entities on which the S&P 500 index is based constitute a representative group that allows the observation of important processes taking place in the economy. Furthermore, this index is based on a broad range of companies of different sectors; therefore, it can be considered representative for the USA economy. The time interval is chosen such that it contains a period before the COVID-19 pandemic. It is worth noticing that the pandemic period is before the broad availability of vaccination, so the observed changes are the effects of the institutional response to the pandemic situation. The inclusion of different periods is particularly important because the algorithm of the study is new and has never been tested.

The time series were downloaded from the web page Available online: https://stooq. pl (accessed on 28 March 2021). Although the index is based on 500 quotes, after inspection of the data, 432 time series were chosen for the analysis due to missing data. The list of quotations used for the analysis is presented in Appendix A.

The time series were converted into logarithmic daily return time series (so-called log-returns) according to Equation (1),

$$\log \mathcal{R}(A)\_i = \log \frac{a\_i}{a\_{i-1}} \,\prime \tag{1}$$

where *A* represents the time series, and *ai* represents the i-th element of the time series *A*.

The evolution of the mean value of stocks included in the study is presented in Figure 1. By analysing the evolution of the mean quote in Figure 1, it should be noticed that it has the form of a visible growing trend with periods of significant fluctuations. The fluctuations correspond to periods of rapid growth followed by a significant drop in value—price bubbles or crises resulting from external factors. The major fluctuations which should be pointed out are the beginning of 2016 (which is the result of two shocks, the Chinese stock market and USA stock market selloffs), the third quarter of 2017, the first quarter of 2018, the second half of 2018 (the cryptocurrency crash), minor fluctuations in the middle of 2019 and a dramatic drop at the beginning of 2020 related to the COVID-19 pandemic. In general, the fluctuations seen in the mean value of quotes are also present in the averaged log-returns evolution graph seen in Figure 1, particularly in the left and right plots, respectively. It is worth noting that the range of fluctuations at the beginning of 2020 was ≈ 0.2, while the others observed in the period 2016–2019 did not exceed 0.07; therefore, the fluctuations resulting from the pandemic shock were approximately 3 times bigger than the other shocks. Within the analysed period, COVID-19 is the dominating factor in financial markets.

**Figure 1.** (**Left**) Evolution of the mean value of 432 quotes included in the study. (**Right**) Evolution of the averaged log-returns of 432 quotes included in the study.
