1 Introduction

Markets’ reaction to the pandemic was a test of their efficiency. Efficient markets should react to the new information not only immediately but also accurate to the weight of the news. During the beginning phase of the Covid-19 pandemic reactions of markets were unexpected but later, despite the fact that investors calmed down, the results of research confirmed the shortcomings related to market efficiency that could be related to the methods of reporting the Covid-19 cases and their manipulations.

The method of measuring and reporting Covid-19 cases is a key factor of the analysis related to the relationship between the pandemic and investors’ behavior. Different factors can affect the rates of return and in this paper the data manipulation issues are analyzed to recognize the impact of Covid-19 on rates of return of markets in the USA, Turkey and Poland. Covid-19 data gathering, and its announcements may not be objective because the manipulation can appear in the information chain from the hospitals to the institutions directly responsible for reporting.

The aim of this paper is to present the reaction patterns of the S&P500 Index in the USA, BIST100 Index in Turkey and WIG Index in Poland to exemplify the process of Covid-19 new cases reporting and investors’ reaction. These three examples of markets with data reporting issues can reflect the importance of a transparent system of informing the public about the situation related to the pandemic. The hypothesis that the change in the principles of Covid-19 data reporting influenced the ways the surveyed markets reacted to the information about new cases is tested. Different methods of Covid-19 cases presentation is applied such as weekly average and moving average to equalize the periods of reporting and trading. Moreover, the traditional correlation analysis based on Pearson, Spearman, Kendall, and dichotomous methods based on Point biserial, Matthews and Tetrachoric with the delays of markets’ reaction including the differences between the correlations in the periods before and after the breakthrough date are analyzed.

Considering the USA case, where on September 12, 2020, the news in press appeared with the information that the reports about the number of cases were manipulated by White House Administration. Political appointees repeatedly pressured Centers for Disease Control and Prevention officials to manipulate reports, to make them more closely align with President Donald Trump’s public statements about the pandemic. The politically appointed Health and Human Services spokesperson and his team demanded and received the right to review CDC’s scientific reports to health professionals. The data from hospitals was redirected to HHS instead of National Healthcare Safety Network. All those methods essentially bypassed the Centers for Disease Control and Prevention and National Healthcare Safety Network, which had long been the nation’s healthcare-associated infection tracking system. Despite the protests of CDC employees Donald Trump did not agree with their point of view and decided to shut them up. The change in the presidency bringing Joe Biden on a chair as a president influenced the situation of data reporting in USA and the incident could influence the market and its reaction to the number of cases announced.

The second case presented in this paper comes from Turkey. Turkish health authorities divided the Covid-19 groups for patients with symptoms and without symptoms but with positive tests, and the former group was not reported to the public at first. WHO criticized the government authorities since the data released by the official authorities did not match the data released by the local authorities. The official Covid-19 data created both confusion, controversy, and criticism. As a result of the increased pressure both at home and abroad, the Ministry of Health in Turkey had to release the real data regarding Covid-19 infections from December 10, 2020, and that day number of cases reported was higher 4 times comparing to the previous day. Starting from December 10 total cases reported by Turkish Government represented total number of all people who were tested positive regardless of clinical signs and symptoms. That day can be regarded as the beginning of the fair reporting that could influence the behavior of the investors on the Exchange in Istanbul.

The information about the cases is collected, and published by official institutions but sometimes, as it was in Poland it had been also provided by regional Health Departments to the public. The numbers presented by the local institutions and Polish Ministry of Health had not matched and the discrepancy between announcements was realized by a private person in November 2020. It was on November 24, 2020, when the government forbidden public announcements regarding the Covid-19 cases by regional Health Departments and from that time started providing the data through the only one channel, the official Twitter account of Ministry of Health. Centralizing the data, according to ombudsman, is contrary to the constitutional right to public information, which presupposes the broadest and easiest access to the public data. Investors at first could be confused with different data coming from different sources but after centralizing the reporting system there has been no control on the information. It can be a reason of luck of trust and weak influence of Covid-19 cases reporting on rates of return in Poland.

The paper is structured as follows. First the literature related to the impact of pandemic on market is analyzed, followed by the data and methods description, with results presentation, discussion and conclusions presented in the end.

2 Literature Review

In this part of the article the results of research related to the market reaction to new information, also in the light of the COVID-19 pandemic are presented. The efficient market hypothesis states that stock prices should react immediately to all available information. Covid-19 announcements are made publicly every day and should influence the reaction of investors, however the behavioral finance states that investors are not always rational and they over- or underreact to information due to different biases (Tversky & Kahneman, 2013). The reaction on the available information may be related to the quality of the news if they are trustful. Haroon and Rizvi (2020) stated that in times of common access to news and information, investors find it difficult to accurately assess and include it in the prices of financial instruments. Dias et al. (2020) after testing random walks on US, Chinese and European capital markets presented findings that prices did not fully reflect the information available and changes in prices were not independent and identically distributed resulting in opportunities for arbitrage and for abnormal returns. When information distribution methods are considered, Smales (2021) found that Global GSV (Google search volume) was negatively associated with stock index returns across G7 and G20 countries. Earlier studies revealed weak or moderate relationship between quantum of news and volume, volatility, rates of returns in financial markets (e.g.,Berry & Howe, 1994; Mitchell & Mulherin, 1994). On the other hand, Ederington and Lee (1994) observed that scheduled macroeconomic news announcements explained a significant portion of the volatility in financial markets. Covid-19 announcements were scheduled information and therefore it can be expected that markets reacted accurately to data about new cases. Klibanoff et al. (1998) found evidence of market overreaction in closed end mutual funds, and not only individuals, but also collective investment institutions did not react properly to news, although they employ professionals. Harjoto et al. (2021) found that the impact of Covid-19 during the rising infection period (pre-April) was different from its impact during the stabilizing period (post-April). The market tended to overreact about COVID-19 and then resettled itself as it learned more about the pandemic. Considering different time intervals could support the statement about the change in market reaction.

Recent emerging literature reports that stock markets around the world have reacted to Covid-19 pandemic with strong negative returns (Al-Awadhi et al., 2020; Ashraf, 2020a; Baker et al., 2020). However, this reaction was not uniform across countries. National-level uncertainty avoidance, which determines how sensitive members of a nation are to uncertainty, moderated the stock markets’ reaction to the pandemic. Focusing on stock market returns, Alfaro et al. (2020) used data from the US exchange and found that equity market value declined in response to pandemics. Likewise, Al-Awadhi et al. (2020) found overall share prices declined in China due to the expected adverse economic outcomes of Covid-19. Yilmazkuday (2021) found that increase in the cumulative daily Covid-19 cases in the US resulted in a negative daily return in the S&P 500 index. Albulescu (2021) examined the impact of Covid-19 on the stock market volatility in the US and found that the global new cases and fatality ratio increased the volatility. Considering the difference related to the religion Salisu and Sikiru (2021) demonstrated that although Islamic stocks’ effectiveness had declined, they provided superior performance relative to the conventional stocks during the Covid-19.

Recent studies that examined the impact of Covid-19 on stock markets across distinct phases of infections documented a time-varying impact of Covid-19 on capital markets. Ramelli and Wagner (2020) found that the stock markets' reactions to Covid-19 changed during different periods of pandemic. Phan and Narayan (2020) examined the impact of Covid-19 across 25 countries and argued that the stock markets tend to overreact as the number of deaths and cases increased and were more likely to self-correct as the time lapses. For instance, Alfaro et al. (2020) found that US stock market returns declined in response to local Covid-19 outbreaks. Xu (2021) found that there was a negative effect of an increase in the Covid-19 cases on the stock returns in Canada and USA. Finally, Harjoto et al. (2021) found different investment behaviors between emerging and developed markets, such as risk and return framework.

A lot of factors can affect rates of return. Ashraf (2020b) showed that higher national-level uncertainty avoidance significantly strengthened the negative stock markets’ reaction to the growth in Covid-19 confirmed cases. Rahman et al. (2021) analyzed Australian market and found that the reaction was positively related to the government package of job keeper. Markets’ reaction varied across countries not only because of different levels of expected future economic losses (Gormsen & Koijen, 2020) but also due to investors’ sentiment (Zhang et. al 2020). Schmeling (2009) showed that the cross-country differences in cultural values influenced investors’ sentiment, which in turn determined investors’ reaction to news.

Dominant national culture which determines how sensitive individuals are to uncertainty and news is an important sentimental factor due to which investors in different countries responded heterogeneously to the Covid-19 crisis. National culture can be defined as the collective programming of the mind distinguishing the members of one nation from others (Hofstede, 2001; Hofstede et al., 2005). Cultural psychologists found that uncertainty avoidance varies across countries (Hofstede 1980; House et al., 2004). Uncertainty avoidance dimension is the most important aspect of national culture for financial sector outcomes (Kwok & Tadesse, 2006) and a missing link in finance (Aggarwal & Goodell, 2014; Nadler & Breuer, 2019). Comparing different markets can help to understand the differences in the investment process. The use of dedicated software and artificial intelligence for making financial decisions based on news became a viable trading strategy recently (Groß-Klußmann & Hautsch, 2011) and can avoid culture as the determinant of market reaction.

Covid-19 is a rare event and entails enormous uncertainty, where probabilities of different outcomes are unknown. Ashraf (2020b) postulated that stock market investors in countries with higher level of uncertainty aversion are more likely to involve in panic selling to avoid uncertainty leading to higher negative market returns as compared to the investors in countries with lower levels of uncertainty aversion who remain calm and tolerant to risk even in the crisis. Ohan and Narayan (2020) showed how the stock prices reacted in real time to different stages in Covid-19’s evolution and they found that with any unexpected news, markets overreacted, and as more information became available and people understanded the situation more broadly, as a result the market corrected itself.

3 Data and Methods

The data in the presented research includes daily closing prices of the USA S&P Index, BIST100 Index quoted on Istanbul Stock Exchange in Turkey and WIG Index quoted on Warsaw Stock Exchange in Poland. Stock data was collected from Stooq.com service, the number of covid cases were reported by WHO.

Two methods of data transformation are implemented in this paper. In the first approach daily data of Covid-19 cases and closing prices of stock market indices were cumulated for weekly values to equalize the periods of Covid-19 cases reporting schedule and stock exchanges working days and weekly average was calculated. The second method is based on the data of Covid-19 cases and stock prices moving averages.

Relative change of average closing stock index price (Rp) is calculated according to the formula (1):

$$R_{{p_{k} }} = \frac{{p_{k} - p_{k - 1} }}{{p_{k - 1} }}$$
(1)

where pk denotes average close price in k week counted since the beginning of analysis.

Relative change of average number of cases (Rc) is calculated according to the formula (2):

$$R_{{c_{k} }} = \frac{{\mathop \sum \nolimits_{i = 0}^{N} c_{k - i} - \mathop \sum \nolimits_{i = 0}^{N} c_{k - i - 1} }}{{\mathop \sum \nolimits_{i = 0}^{N} c_{k - i - 1} }}$$
(2)

where ck denote number of Covid-19 cases registered in k day counted since the beginning of analysis.

The delays in reaction of the markets are analyzed with 1, 2, 3 and 4 weeks or 20 days delay when moving average was applied.

US market is represented by 65 weekly observations, 23 weeks before and 41 weeks after the day of revealing the manipulation, with a breakthrough week omitted. With the moving average as a measure the number of observations in a total sample is equal to 319, 117 before the revealing the manipulation date and 198 after the breakthrough date. The research covers the period from March 23, 2020, up to June 27, 2021, with a critical day on September 12, 2020.

Turkish market is represented by 64 weekly observations, 33 weeks before and 30 weeks after the day of introducing the real cases reporting, with a breakthrough week omitted. When the moving average is applied the number of observations in a total sample is equal to 311, 171 before the breakthrough date and 135 after this date. The research covers the period from March 3, 2020, up to June 27, 2021, with a critical day on December 10, 2020.

Polish market is represented by 65 weekly observations, 34 weeks before and 30 weeks after the day the data reporting on Covid-19 was constrained, with a breakthrough week omitted. When the moving average is applied the number of observations in a total sample is equal to 316, 170 before the breakthrough date and 141 after the breakthrough date. The research covers the period from March 23, 2020, up to June 27, 2021, with a critical day on November 24, 2020.

Data distribution analysis is presented in Table 1. Skewness, Kurtosis, and tests for the null hypothesis that a sample is characterized by a normal distribution is based on D'Agostino and Pearson's test.

Table 1 Data distribution analysis
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In USA normality of data can be observed in the period after the date of publication about the Covid-19 data manipulation only for weekly cumulative data. In case of Turkey the normality is observed in case of Relative change of cases for weekly cumulated data after the breakthough date. Observations in Poland are characterized by normal distribution in every period for weekly cumulated data and it is the only market where normal distribution appears for moving average when relative change of cases is taken into consideration after the Covid-19 reporting system was monopolized.

Since the corresponding data corresponding to the same periods is of different character of the distributions for different countries, to unify and synthesize the results, a targeted analysis was used based on variables having the character of a normal distribution (Pearson's coefficient) as they are not characterized by such a distribution (Spearman and Kendall measures). Additional dichotomous measures enabled a qualitative analysis of the relationships between the studied phenomena.

The methods applied for the research are based on various correlation coefficients. First, the most common correlation ratios: Pearson, Spearman and Kendall are calculated. Moreover, the dichotomous correlations are taken into consideration: Matthews, Tetrachoric and point biserial. Pearson correlation is applied when dependence is proportional and the normality of the distribution of variables is tested. Kendall correlation on the other hand, should be applied when the dependence does not have to be proportional, because ranks are created considering the monotonic dependence. Ranking is the ordering of data, but the data is treated as continuous. Spearman correlation is characterized by no normal distribution of variables and no linear relationship. Matthews for discrete data is a simple ups and downs relationship. Tetrachoric coefficient determines the level of dependence between two dichotomous and ordinal variables. We assume that both variables are continuous and normally distributed, while they have been reduced to a dichotomous scale to simplify them. The point biserial correlation coefficient is used when one variable is dichotomous. Especially in the case of Covid-19 data, they may be ambiguous.

The inequality of the correlation coefficients between periods are tested in the next step. To verify the significance of the difference between two Pearson correlation coefficients deriving from two independent populations, the t-test based on the Fisher transformation is applied. The null hypothesis states that these correlation coefficients are equal.

The t-statistic is given by the formula (3):

$$t = \frac{{z_{A} - z_{B} }}{{\sqrt {\frac{1}{{n_{A} - 3}} + \frac{1}{{n_{B} - 3}}} }}$$
(3)

where \({z}_{GPW}=\frac{1}{2}\mathit{ln}\left(\frac{1+{r}_{A}}{1-{r}_{A}}\right)\), \({z}_{NC}=\frac{1}{2}\mathit{ln}\left(\frac{1+{r}_{B}}{1-{r}_{B}}\right)\), \({r}_{A}\), \({r}_{B}\) denote the estimated correlation coefficients in the two samples of companies and \({n}_{A},{n}_{B}>3\) are the numbers of companies in each sample. The test statistic has a t-Student distribution with \({n}_{periodA}+{n}_{periodB}-4\) degrees of freedom.

The results of the research are presented in the next section.

4 Results

The results of the research on the correlation analysis between Covid-19 cases and the reaction as measured by rates of return on exchange markets in the USA, Turkey and Poland are presented below.

4.1 USA

4.1.1 Weekly Averages of S&P500 Closing Prices and Covid-19 Cases Relative Changes

In the first step the analysis of weekly average relative changes in number of cases and close prices of S&P500 Index are taken into consideration for the whole period and sub-periods related to the possible breakthrough day, when the publication describing the manipulation on Covid-19 data was delivered to the market on September 12, 2020. The behavior of variables is presented on Fig. 1.

Fig. 1
figure 1

Weekly average relative changes in number of Covid-19 cases and close prices of S&P500 Index

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In the next step the analysis of the correlations as calculated by different methods is presented, with the delays of reaction in three periods– the whole period, the period before the breakthrough date and after. The results of correlation analysis with Pearson, Spearman and Kendall coefficients are presented in Table 2.

Table 2 Relative changes of weekly average Covid-19 cases and closing prices of S&P500 correlations with delays
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The results indicate that when the whole period is taken into consideration the positive correlation as measured by Pearson, Spearman and Kendall coefficients appeared within 2 weeks and after one week only with Pearson coefficient. When the division for subperiods is applied it is found that until the breakthrough date only Pearson correlation for one week delay in market reaction is significant but relatively strong. After the breakthrough date the significant correlation between weekly average Covid-19 relative changes and rates of return of S&P 500 Index as measured by Spearman and Kendall coefficients is recognized with 2 weeks delay. It can be concluded that before the critical day markets reacted faster and stronger to the Covid-19 number of cases announcements when weekly average data relative changes are taken into consideration. The correlation is positive.

In the next step the dichotomous correlations as measured by Matthews, Tetrachoric and point biserial coefficients between relative changes of weekly average Covid-19 cases and S&P500 closing prices with weekly delays are tested and the results are presented in Table 3.

Table 3 Relative changes of weekly average Covid-19 cases and S&P500 dichotomous correlations with delays
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The results presented in Table 3 indicate that the dichotomous correlation analysis does not confirm the results obtained earlier with classical correlation coefficients and no significant correlation between data presented as weekly relative changes is found.

In the next step the difference between Pearson correlation coefficients in two subperiods for relative changes of variables is analyzed. The results are presented in Table 4.

Table 4 Difference between Pearson coefficients for weekly average data in USA
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All difference tests are significant and indicate the Pearson correlation coefficients in the two analyzed periods, before and after the breakthrough day differ and it can be concluded that after the publication of the report related to the possible manipulation of Covid-19 data in the USA, market reaction changed its strength and was weaker.

4.1.2 Relative Changes of Covid-19 Cases and S&P 500 Closing Prices Variables Calculated as Moving Averages

Moving average can reflect market reaction in a continuous manner. The changes of variables as measured by Covid-19 cases and A&P500 closing price influenced the observations making them smoother as it is presented on Fig. 2.

Fig. 2
figure 2

Moving average relative changes in number of Covid-19 cases and close prices of S&P500 Index

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Weekly average relative changes of Covid-19 cases and delayed up to 20 days S&P500 prices are analyzed in the next step with Pearson, Spearman, and Kendall correlation. The results are visualized on Figs. 3 and 4. Significant results are darker.

Fig. 3
figure 3

Classical correlation coefficients of moving average data with delays for S&P500—evidence before the breakthrough date

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Fig. 4
figure 4

Classical correlation coefficients of moving average data with delays for S&P500—evidence after the breakthrough date

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The results presented on Figs. 3 and 4 indicate that in the period before the breakthrough the correlation is significant only with Pearson coefficient and this correlation is stronger comparing to the period after the breakthrough date where the correlation is weaker but significant with all three correlation coefficients.

In the next step the dichotomous correlation as measured by Matthews, Tetrachoric and point biserial coefficients are calculated for relative changes of variables calculated as moving averages with delays of market reaction up to 20 days. The results are presented on Figs. 5 and 6.

Fig. 5
figure 5

Dichotomous correlation coefficients of moving average data with delays for S&P500—evidence before the breakthrough date

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Fig. 6
figure 6

Dichotomous correlation coefficients of moving average data with delays for S&P500—evidence after the breakthrough date

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The conclusions deriving from Figs. 5 and 6 indicate that there is a negative correlation observed before the breakthrough date and the reaction changes to mostly positive after this date.

The Pearson correlation coefficients difference between two periods, one until the breakthrough and one after is analyzed in the next step for the moving average data and delayed reaction of the market. The results are presented in Table 5.

Table 5 Difference between Pearson coefficients for moving average data in USA
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The results presented in Table 5 indicate that there is no difference between Pearson correlation coefficients for moving average data when 2, 3, 4 and 11 days of delay are taken into consideration. In other cases, the difference is significant, and it can be concluded that the date of publication of the report describing the possible data manipulation affected the US market reaction.

4.2 Turkey

4.2.1 Weekly Averages of BIST 100 Closing Prices and Covid-19 Cases Relative Changes

In the first step the correlation between relative changes in number of cases and close price of BIST100 Index are analyzed for the whole period taken into consideration and subperiods related to the critical day. It was on December 10, 2020, when Turkish Government started reporting the correct data of Covid-19 cases. The graphical presentation of the variables is presented on Fig. 7.

Fig. 7
figure 7

Weekly average relative changes in number of Covid-19 cases and close prices of BIST 100 Index

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In the next step the analysis of the correlation as calculated by Pearson, Spearman and Kendall is presented, with the delays of data in three periods, before and after the breakthrough date. The results are presented in Table 6.

Table 6 Relative changes of weekly average Covid-19 cases and closing prices of BIST100 correlations with delays
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The results presented in Table 6 indicate that in the whole period and before the breakthrough date the significant negative correlation with one week of BIST100 rate of return delay is observed with Pearson coefficient. After the breakthrough date the significant negative correlation is observed with all three coefficients, and it must be indicated that the reaction of the market to the change of data reporting was immediate and negative.

In the next step the dichotomous correlation as measured by Matthews, Tetrachoric and point biserial coefficients between relative changes of Covid-19 cases and BIST100 rates of return with weekly delays is tested and the results are presented in Table 7.

Table 7 Relative changes of weekly average Covid-19 cases and BIST100 dichotomous correlations with delays
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The results presented in Table 9 do not confirm the significant correlation between variables.

In the next step the difference between Pearson correlation ratios in two sub-periods for relative changes of variables is presented in Table 8.

Table 8 Difference between Pearson coefficients for weekly average data in Turkey
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The results indicate that there are significant differences between Pearson correlation coefficients for weekly average data in two periods taken into consideration in Turkey.

4.2.2 Relative Changes of Covid-19 Cases and BIST100 Closing Prices Variables Calculated as Moving Averages

Moving average of data taken into consideration can reflect reaction of the market in a continuous process. The changes in Covid-19 cases and BIST100 closing prices calculations influenced the observations making them smoother as it is presented on Fig. 8.

Fig. 8
figure 8

Moving average relative changes in number of Covid-19 cases and close prices of BIST100

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Relative changes of moving average of cases and prices are analyzed in the next step with Pearson, Spearman, and Kendall correlation coefficients as it is presented on Figs. 9 and 10. Darker color is related to the significant results.

Fig. 9
figure 9

Classical correlation coefficients of moving average data with delays for BIST100—evidence before the breakthrough date

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Fig. 10
figure 10

Classical correlation coefficients of moving average data with delays for BIST100—evidence after the breakthrough date

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The results presented on Figs. 9 and 10 indicate that in the period before the implementation of the correct reporting system date the correlation between relative changes of moving average variables is partially negative and positive and in the period after this day the correlation is stronger, negative, and more significant. In the period when data was manipulated the market could hesitate more comparing to the reaction in the period of more reliable data reporting.

In the next step the dichotomous correlation as measured by Matthews, Tetrachoric and point biserial is calculated for relative changes of variables calculated as moving averages. The results are presented on Figs. 11 and 12.

Fig. 11
figure 11

Dichotomous correlation coefficients of moving average data with delays for BIST100—evidence before the breakthrough date

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Fig. 12
figure 12

Dichotomous correlation coefficients of moving average data with delays for BIST100—evidence after the breakthrough date

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The results presented on Figs. 11 and 12 confirm findings related to the classical correlation coefficients. Before the breakthrough date market reacted in a more chaotic manner and the significant correlation between the announcements of Covid-19 cases and BIST100 rates of return is mostly not significant while after the breakthrough day the situation improved, and the reaction is negative and more significant.

The Pearson correlation coefficients difference between two periods, one until the breakthrough date and one after is analyzed in the next step (Table 9) for the moving average data and delayed reaction of the market.

Table 9 Difference between Pearson coefficients for moving average data in Turkey
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Table 10 Relative changes of Covid-19 cases and closing prices of WIG correlations with delays
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Table 11 Relative changes of Covid-19 cases and WIG dichotomous correlations with delays
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Table 12 Difference between Pearson coefficients for weekly average data in Poland
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The results presented in Table 13 indicate that there is no difference between Pearson correlation coefficients for moving average data when no delay, 7, 8 and 9 days of delay are taken into consideration. In other cases, the difference is significant, and it can be concluded that the introduction of reliable data reporting system could influence the behavior of Turkish market.

Table 13 Difference between Pearson coefficients for moving average data in Poland
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4.3 Poland

4.3.1 Weekly Averages of WIG Closing Prices and Covid-19 Cases Relative Changes

In the first step the correlation between relative changes in the number of Covid-19 cases and close price of WIG Index are analyzed for the whole period and subperiods related to the breakthrough day, when Polish Government decided to monopolize the Covid-19 data reporting to the public and it was on November 24, 2020. The graphical presentation of the variables is on Fig. 13.

Fig. 13
figure 13

Weekly average relative changes in number of Covid-19 cases and close prices of WIG Index

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In the next step the analysis of the correlation as measured by Pearson, Spearman and Kendall coefficients is presented, with weekly delays of data. The results are presented in Table 10.

There is no statistically significant correlation found in neither of the periods taken into consideration when weekly averages of data and classical correlation coefficients were applied. In the next step the dichotomous correlation as measured by Matthews, Tetrachoric and point biserial coefficients for weekly average data with weekly delays are calculated and the results are presented in Table 11.

The results presented in Table 11 indicate just one significant, positive correlation with 4 weeks delay of market reaction, as measured by Tetrachoric correlation. The methods of variables measurement as well as the correlation methods do not bring the satisfactory results.

In the next step the difference between Pearson correlation ratios in two sub-periods for relative changes of variables, one until the breakthrough date and one after is tested and the results are presented in Table 12.

The results presented in Table 12 indicate, that the Pearson correlation coefficients differ significantly for both periods taken into consideration.

4.3.2 Relative Changes of Covid-19 Cases and WIG Closing Prices Variables Calculated as Moving Averages

Moving average of data can reflect market reaction in a continuous manner. Moving averages of Covid-19 cases and WIG closing prices are influencing the presentation of data making them smoother as it is presented on Fig. 14.

Fig. 14
figure 14

Moving average relative changes in number of Covid-19 cases and close prices of WIG

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Relative changes of Covid-19 cases and prices moving averages are analyzed in the next step with Pearson, Spearman and Kendall correlation coefficients and the results are presented on the Figs. 15 and 16. Significant results are darker.

Fig. 15
figure 15

Classical correlation coefficients of moving average data with delays for WIG—evidence before the breakthrough date

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Fig. 16
figure 16

Classical correlation coefficients of moving average data with delays for WIG—evidence after the breakthrough date

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The results presented on Figs. 15 and 16 indicate that the correlation is changing from positive to negative and moreover is stronger after the breakthrough date.

In the next step the dichotomous correlation as measured by Matthews, Tetrachoric and point biserial coefficients are calculated and the results are presented on Figs. 17 and 18. Significant results are darker.

Fig. 17
figure 17

Dichotomous correlation coefficients of moving average data with delays for WIG—evidence before the breakthrough date

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Fig. 18
figure 18

Dichotomous correlation coefficients of moving average data with delays for WIG—evidence after the breakthrough date

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The results are opposite for those obtained for classical correlation coefficients and correlation in this case is stronger for the period before the breakthrough day. These results indicate stronger and more significant correlation when information channel was not monopolized by Polish Government.

The difference between Pearson correlation coefficients in two periods, one until the breakthrough date and one after is analyzed in the next step for the moving average data and delayed reaction of the market. The results are presented in Table 13.

The results presented in Table 13 indicate that there is no difference between Pearson correlation coefficients for moving average data when 5, 6, 8, 16, 17-, 18-, 19- and 20-days delays are taken into consideration. In other cases, the difference is significant, and it can be concluded that the date of monopolizing the Covid-19 data reporting could influence the behavior of Polish market, but the difference is not as obvious as in previous cases.

5 Discussion of the Results

The results indicate the existence of differences between markets and periods related to analyzed issues and stock exchanges in the USA, Turkey, and Poland. When US market is taken into consideration it can be concluded that before the critical day the market reacted faster and stronger to the Covid-19 number of cases when weekly average data relative changes are taken into consideration. The dichotomous correlation analysis does not confirm the results obtained with classical correlation coefficients and no significant correlation between data presented as weekly relative changes is found. Pearson correlation coefficients in the two periods, before and after the breakthrough day differ significantly and it can be concluded that after the publication of the report related to the possible manipulation of Covid-19 data, market reaction changed its pattern. When moving average of data is taken into consideration it can be realized that in the period before the breakthrough date the correlation is significant only with Pearson coefficient and this correlation is stronger comparing to the period after the breakthrough date, where the correlation is weaker but significant with all three coefficients taken into consideration. It can be concluded that there is a negative correlation observed before the breakthrough date and the reaction are changing to mostly positive after this date. There is no difference between Pearson correlation coefficients for moving average data in a few cases of delay. It can be concluded that the possible data manipulation could influence the behavior of the US market.

The results for Turkey indicate that in the whole period and before the breakthrough date, the significant negative correlation after one week is observed with Pearson coefficient when weekly average data relative changes are analyzed. After the breakthrough date the significant negative correlation is observed with all three coefficients and the reaction is immediate. When correlation is measured as dichotomous, there is no significant correlation between variables. There are significant differences between Pearson correlation coefficients for weekly average data. In the period before the breakthrough the correlation between relative changes of moving average of variables is partially negative and positive and in the period after the day of breakthrough the correlation is stronger, negative, and more significant. The results indicate that there is no difference between Pearson correlation coefficients for moving average data in a few cases. In other cases, the difference is significant, and it can be concluded that the date of publication of the report describing the possible data manipulation could influence the behavior of Turkish market.

When Polish market is taken into consideration, the results are reflecting just one significant, positive correlation with 4 weeks delay of market reaction to the Covid-19 cases as measured by Tetrachoric correlation. The Pearson correlation coefficients differed significantly for both periods taken into consideration when weekly average data is analyzed. For the moving average analysis, when classical correlation coefficients are taken into consideration the relationship is changing from positive to negative and moreover is stronger after the breakthrough date. The results for the dichotomous coefficients are opposite for the results obtained for classical correlation and the relationship between variables is stronger for the period before the breakthrough day. There is no difference between Pearson correlation coefficients for moving average data in many cases. The change in market reaction was not so obvious comparing to the US and Turkish markets.

6 Conclusions

Dichotomous correlation coefficients provide better results for moving averages and perform poor for the weekly averages of observations in USA and Turkey but not in Poland. Investors in Poland at first could be confused with different data coming from two distinguished sources but after centralizing the reporting system there is no control on the information provided to the public. It could be a reason of luck of trust and significant influence of Covid-19 cases on rates of return in Poland. In case of US before the day of presenting the manipulation of data, the market reacted faster and stronger to the Covid-19 number of cases as measured by weekly average data relative changes. In the period before the breakthrough date, Turkish investors hesitated more comparing to the reaction in the period representing more reliable data.

The announcement of the number of Covid-19 cases is strongly related to the reporting system applied in a specific country. Manipulations can influence the reaction of markets as it is presented in this paper. The results of presented research confirm the thesis that the moment when reporting issues were announced to the public influenced the way market started to react on the Covid-19 new cases announcements appearing in the following days. Moreover, it must be stressed that the way of calculating data is influencing the results as well as the correlation method application.

The future study can cover the issue of the differences between markets depending on the phases of pandemic.