Dynamics and co-movements between the COVID-19 outbreak and Polish stock market: A dynamic conditional correlation modeling and wavelet coherence analysis

DCC models are estimated in two steps.

Let r t {r}_{t} be an n × 1 n\times 1 vector of the asset returns and ARMA(1,1) a process in the mean equation for R t {R}_{t} . r t = μ + A R 1 r t − 1 + M A 1 ε t − 1 + ε t . {r}_{t}=\mu +AR1{r}_{t-1}+MA1{\varepsilon }_{t-1}+{\varepsilon }_{t}.

The equation for residuals is as follows: ε t = H t 1 / 2 z t {\varepsilon }_{t}={H}_{t}^{1/2}{z}_{t} , where H t {H}_{t} is the conditional covariance matrix of R t {R}_{t} and z t {z}_{t} is an identical and independently distributed vector of random errors.

In the first step, GARCH parameters are estimated and then the DCCs in the second step. Proposed by Engle (2002) the dynamic correlation model, comparing to Bollerslev’s (1990) constant condition correlation, differs only in allowing R R to be time varying: H t = D t R t D t {H}_{t}={D}_{t}{R}_{t}{D}_{t} . H t {H}_{t} is the conditional covariance matrix, n × n, and R t {R}_{t} is the conditional correlation matrix. D t {D}_{t} is a diagonal matrix with time-varying standard deviations on the diagonal.

Parameters of H t {H}_{t} matrix from the GARCH(1,1) are as follows: h i t = ω i + α i ε i t − 1 2 + β i h i t − 1 . {h}_{it}={\omega }_{i}+{\alpha }_{i}{\varepsilon }_{it-1}^{2}+{\beta }_{i}{h}_{it-1}.

Q t {Q}_{t} is a symmetric positive definite matrix: Q t = ( 1 − a − b ) Q ¯ + a z t − 1 z t − 1 ′ + b Q t − 1 . {Q}_{t}=(1-a-b)\bar{Q}+a{z}_{t-1}{z}_{t-1}^{^{\prime} }+b{Q}_{t-1}.

Q t {Q}_{t} is the n × n n\times n unconditional correlation matrix of the standardized residuals z i t = ε i t h i t {z}_{it}=\frac{{\varepsilon }_{it}}{\sqrt{{h}_{it}}} . Parameters a a and b b are associated with the smoothing process. The DCC model means return to equilibrium if sum of a a and b b is less than 1 and positive. The correlation is estimated as follows: ρ i . j . t = q i , j , t q i , i , t q j , j , t {\rho }_{i.j.t}=\frac{{q}_{i,j,t}}{\sqrt{{q}_{i,i,t}{q}_{j,j,t}}} .

Second model that was applied is the ADDC model as the DCC model fails to capture asymmetry effects. The formula for h h is given by the following equation: h i , t = ω i + α i ε i , t − 1 2 + β i h i , t − 1 + λ i ε i , t − 1 2 I ( ε i , t − 1 ) , {h}_{i,t}={\omega }_{i}+{\alpha }_{i}{\varepsilon }_{i,t-1}^{2}+{\beta }_{i}{h}_{i,t-1}+{\lambda }_{i}{\varepsilon }_{i,t-1}^{2}I({\varepsilon }_{i,t-1}), where I ( ε i , t − 1 ) I({\varepsilon }_{i,t-1}) = 1, if ε i , t − 1 {\varepsilon }_{i,t-1} < 0 and 0 in other cases.

Finally, the Q t {Q}_{t} in the ADCC model is as follows: Q t = ( Q ¯ A ′ Q ¯ A − B ′ Q ¯ B − G ′ Q ¯ − G ) + A ′ z t − 1 z t − 1 ′ A + B ′ Q t − 1 B + G ′ z t − z t ′ − G , \begin{array}{c}{Q}_{t}=(\bar{Q}{A}^{^{\prime} \bar{Q}}A-B^{\prime} \bar{Q}B-G^{\prime} {\bar{Q}}^{-}G)+A^{\prime} {z}_{t-1}{z}_{t-1}^{^{\prime} }A\\ \hspace{2em}+B^{\prime} {Q}_{t-1}B+G^{\prime} {z}_{t}^{-}{z}_{t}^{^{\prime} -}G,\end{array} where A A , B B , and G G are parameter matrices of size n × n n\times n , z t − {z}_{t}^{-} is a vector of standardized errors. Q ¯ \bar{Q} and Q ¯ − {\bar{Q}}^{-} are the unconditional matrices of z t {z}_{t} and z t − {z}_{t}^{-} .

In the second stage of the analysis, the wavelet coherence method was used. It provides insightful information on dynamic market behavior over time. Wavelet coherence is based on the frequency of a given phenomenon, which allows to capture long-run and short-run market linkages. The wavelet analysis involves a transform from a one-dimensional time series (or frequency spectrum) to a diffuse two-dimensional time-frequency image.

To be a wavelet, function must have zero mean and be localized in both time and frequency space (Farge, 1992) ∅ t , s ( t ) = 1 s ∅ t − τ s , {\varnothing }_{t,s}(t)=\frac{1}{\sqrt{s}}\varnothing \left(\frac{t-\tau }{s}\right), where 1 s \frac{1}{\sqrt{s}} is responsible for the variance stabilizing normalization, t t is the time parameter, τ refers to the location, and s s represents the scale.

In the next step, the continuous wavelet transformation is applied. This transformation represents one analysis tool for extracting local-frequency information from a signal W x ( τ , s ) = 1 s ∫ − ∞ + ∞ x ( t ) ∅ t − τ s d t . {W}_{x}(\tau ,s)=\frac{1}{\sqrt{s}}\underset{-\infty }{\overset{+\infty }{\int }}x(t)\varnothing \left(\frac{t-\tau }{s}\right)\text{d}t.

We utilize the wavelet coherence technique, a method characterized by localization in both time and frequency domains, which in turn allows to measure the strength of association between two time-series over sample period across different time frequencies. We define the cross-wavelet between the two series x(t) and y(t) as follows: W x y ( τ , s ) = W x ( τ , s ) W y ( τ , s ) . {W}_{xy}(\tau ,s)={W}_{x}(\tau ,s){W}_{y}(\tau ,s).

To capture the co-movement between the two series, we define the wavelet coherence as R 2 ( τ , s ) = ∣ S ( S − 1 W x y ( τ , s ) ∣ 2 S ( S − 1 ∣ W x ( τ , s ) ∣ 2 ) S ( S − 1 ( ∣ W y ( τ , s ) ∣ 2 ) , {R}^{2}(\tau ,s)=\frac{{| S({S}^{-1}{W}_{xy}(\tau ,s)| }^{2}}{S({S}^{-1}{| {W}_{x}(\tau ,s)| }^{2})S({S}^{-1}({| {W}_{y}(\tau ,s)| }^{2})}, where S S is the smoothing operator and 0 ≤ R 2 ( τ , s ) ≤ 1 0\le \hspace{.25em}{R}^{2}(\tau ,s)\le 1 .

The coefficient R 2 ( τ , s ) {R}^{2}(\tau ,s) reflects the degree of correlation between the examined series. Values closer to 1 indicate the presence of strong (weak) correlation between the two time series and values closer to 0 indicate the presence of weak correlation between the two time series.

This study focuses on the analysis of graphs showing the estimated wavelet with arrows plotted, which indicate the correlations between the studied series A black outline indicates the significance of relations at the 5% significance level. Warm colors indicate areas with a strong relationship, while cold colors indicate the occurrence of weak dependence. On the wavelet coherence plots, the red colors represent strong co-movement, whereas the blue colors correspond to weak co-movement. The direction of the arrows is the direction of the relation. Arrows pointing to the right mean that two series are in phase or moving in a similar way. If arrows point to the left, then two series are negatively correlated. Furthermore, the phase difference shows the lead/lag relationship between two series. Arrows pointing to the right and up suggest that first variable is leading and the two variables are positively correlated. If arrows are pointing to the right and down, then the second variable is leading. On the other hand, arrows pointing to the left and up signify that the first series is lagging and the correlation is negative, while arrows facing the left and down indicate that the first series is leading but with a negative correlation.

To perform empirical investigations, we used daily data from Poland WIG20 index, which measures the stock performance of 20 companies with the largest capitalization traded on the Warsaw Stock Exchange and daily data from the US S&P500 index, which measures the stock performance of the 500 large companies traded on the New York Stock Exchange. The choice of the US stock exchange was motivated by the fact that it affects European markets. For comparative purposes, an analysis was also performed for the FTSE 250 (United Kingdom), BUX (Hungary), and PX index (Czech Republic). The selection of such countries provides a broad comparison of the relationship between European stock markets and the US market, and also analyzes the impact of the pandemic on several markets. Great Britain was selected for the study as the stock market with the largest capitalization in Europe and, additionally, a country outside the European Union. However, Poland, Hungary, and the Czech Republic are countries with much lower capitalization than the United Kingdom, and they all belong to the European Union. This gives some diversity in the analyzed countries, which may influence the result. We collected daily data from January 2, 2019 to April 4, 2022. Further, we assembled another dataset on daily cumulative cases of infection, deaths, first-dose COVID-19 vaccinations, second-dose COVID-19 vaccinations and booster COVID-19 vaccinations. Here the data were collected starting from March 3, 2020, the date is associated with the appearance of the first case of infection by an unknown virus. WIG20 index and S&P500 index data were taken from the Stooq website, whereas the data concerning the pandemic were taken from the Our World in Data website.

For the purpose of capturing the behavior of the stock market along with the progress of the pandemic, the dataset was divided into sub-samples: I wave 04.03.2020 – 31.07.2020, II wave 01.09.2020 – 01.02.2021, III wave 01.02.2021 – 30.06.2021, and IV wave 15.10.2021 – 04.04.2022.

Based on Figure 1, it can be seen that with the beginning of the pandemic, both the US and Polish stock markets experienced a significant decline. However, after a few days, both increased. The graphs also show declines in the index values related to the rapid increase in infections in given waves. On this basis, the above-described subsets were distinguished. The decreases with every next wave of infections were smaller than with the first wave. This could be due to investors getting used to the situation. The graphical analysis indicates a strong link between the pandemic situation and the situation on the stock market, as with the increase in infections, the decrease in index values is observed.

Figure 1

Closing prices of WIG20 index and S&P500 index.

The values were then transformed into logarithmic rate of returns multiplied by 100. Table 1 presents descriptive statistics concerning the WIG20 and S&P500 returns. Significantly higher volatility reflected by higher value of variance and standard deviation during the COVID-19 period was observed for both indices. The WIG20 and S&P500 exhibit positive returns during the COVID-19 period, which highlights the capacity of these stock markets to perform during crisis period.

When analyzing summary statistics of variables for all four waves of infections, the highest decline in the WIG20 index was observed during the first and fourth waves. But it should also be noted that negative average return on Warsaw stock during the fourth wave can be linked more to the beginning of the war in Ukraine than to COVID-19 pandemic. Thus, we conclude that the highest effect on stock market was observed at the beginning, during the first wave. With the subsequent waves, the shock was lower as investors got used to the situation prevailing on the market.

We estimated several versions of DCC and ADCC models for WIG20 and S&P500 indices. A constant term was included in the mean equation. The ARMA(1,1) term was then added to some of them, modification concerning the error term distribution was considered (normal distribution vs Student’s t-distribution, and GARCH and EGARCH for modeling volatility were proposed. For the purpose of comparison, we extended the analysis to include Hungary, the United Kingdom, and the Czech Republic. These are countries similar to Poland, due to their location in Europe and economic cooperation.

Information criteria were used in the model selection process: the Akaike criterion, Bayesian criterion, Shibata criterion, and the Hannan−Quinn criterion. Models with the Student’s t-distribution turned out to be better. Finally, ARMA(1,1)-DCC-GARCH(1,1) and ARMA(1,1)-ADCC-GARCH(1,1) were chosen for Poland and Hungary and DCC-GARCH(1,1) and ADCC-GARCH(1,1) appeared to be the best for United Kingdom and Czech Republic.

Table 2 reports the results of modeling the DCC and ADCC process between the stock markets of the analyzed countries and the US stock market (S&P500).

Table 2

	Poland	Hungary	UK	Czech Republic	Poland	Hungary	UK	Czech Republic
	ARMA(1,1)-DCC-GARCH(1,1)		DCC-GARCH(1,1)		ARMA(1,1)-ADCC-GARCH(1,1)		ADCC-GARCH(1,1)
μ country {\mu }_{\text{country}}	0.0110	0.0623*	0.0701***	0.084***	0.0110	0.0623*	0.0701***	0.0840***
	(0.0374)	(0.0361)	(0.0279)	(0.0242)	(0.0376)	(0.0360)	(0.0279)	(0.0242)
A R ( 1 ) country AR{(1)}_{\text{country}}	0.3929***	−0.8023*			0.3929***	−0.8023*
	(0.1240)	(0.4848)			(0.1241)	(0.4850)
M A ( 1 ) country MA{(1)}_{\text{country}}	−0.4476***	0.8348*			−0.4476***	0.8348*
	(0.1205)	(0.4457)			(0.1204)	(04459)
ω country {\omega }_{\text{country}}	0.0761**	0.0926**	0.0523***	0.0532***	0.0761*	0.0926**	0.0523***	0.0532***
	(0.0401)	(0.0470)	(0.0202)	(0.0199)	(0.0401)	(0.0470)	(0.0202)	(0.0199)
α country {\alpha }_{\text{country}}	0.0974***	0.1486***	0.1495***	0.1977***	0.0974***	0.1486***	0.1495***	0.1977***
	(0.0380)	(0.0425)	(0.0448)	(0.0504)	(0.0380)	(0.0425)	(0.0445)	(0.0503)
β country {\beta }_{\text{country}}	0.8726***	0.7944***	0.8124***	0.7579***	0.8726***	0.7944***	0.8124***	0.7580***
	(0.0477)	(0.0653)	(0.0485)	(0.0555)	(0.0477)	(0.0652)	(0.0483)	(0.0556)
shape \text{shape}	4.4122***	6.7275***	5.4617***	5.1220***	4.4122***	6.7275***	5.4617***	5.1220***
	(0.5929)	(1.5729)	(0.8774)	(0.8574)	(0.6118)	(1.5808)	(0.8878)	(0.8627)
μ S&P500 {\mu }_{\text{S\&P500}}	0.1419**	0.1419**	0.1434***	0.1434***	0.1419**	0.1419**	0.1434***	0.1434***
	(0.0598)	(0.0599)	(0.0251)	(0.0251)	(0.0598)	(0.0600)	(0.0250)	(0.0251)
A R ( 1 ) S&P 500 AR{(1)}_{\text{S\&P}500}	0.8719**	0.8719**			0.8719**	0.8719**
	(0.3624)	(0.3627)			(0.3622)	(0.3630)
M A ( 1 ) S&P 500 MA{(1)}_{\text{S\&P}500}	−0.9276***	−0.9276***			−0.9276***	−0.9276***
	(0.2795)	(0.2797)			(0.2794)	(0.2800)
ω S&P 500 {\omega }_{\text{S\&P}500}	0.0518***	0.0518***	0.0545***	0.0545***	0.0518***	0.0518***	0.0545***	0.0545***
	(0.0159)	(0.0160)	(0.0165)	(0.0165)	(0.0159)	(0.0159)	(0.0164)	(0.0165)
α S&P 500 {\alpha }_{\text{S\&P}500}	0.2403***	0.2403***	0.2428***	0.2428***	0.2403***	0.2403***	0.2428***	0.2428***
	(0.0522)	(0.0522)	(0.0520)	(0.0519)	(0.0516)	(0.0517)	(0.0512)	(0.0517)
β S&P 500 {\beta }_{\text{S\&P}500}	0.7416***	0.7416***	0.7354***	0.7354***	0.7416***	0.7416***	0.7354***	0.7354***
	(0.0434)	(0.0433)	(0.0438)	(0.0438)	(0.0431)	(0.0432)	(0.0436)	(0.0437)
shape \text{shape}	5.6651***	5.6651***	6.0295***	6.0295***	5.6651***	5.6651***	6.0295***	6.0295***
	(1.0134)	(1.0318)	(1.0559)	(1.0471)	(1.0155)	(1.0334)	(1.0563)	(1.0473)
a a	0.0057	0.0118**	0.0030	0.0136**	0.0057	0.0099	0.0011	0.0131**
	(0.0054)	(0.0055)	(0.0058)	(0.0067)	(0.0071)	(0.0063)	(0.0150)	(0.0069)
b b	0.9751***	0.9760***	0.98***	0.9750***	0.9751***	0.9739***	0.9708***	0.9746***
	(0.0113)	(0.0095)	(0.0266)	(0.0146)	(0.0459)	(0.0124)	(0.0422)	(0.0152)
c c	—				0.0000	0.0043	0.0027	0.0011
					(0.0181)	(0.0087)	(0.0159)	(0.0069)
m shape m\text{shape}	5.7024***	6.2533***	5.9472***	5.6219***	5.7024***	6.3229***	5.9864***	5.6353***
	(0.6054)	(0.7427)	(0.0595)	(0.5705)	(0.6664)	(0.7838)	(0.6372)	(0.5802)
Models with exogenous variables
a a	0.0162	0.0217***	0.0000	0.0245***	0.0255***	0.0217***	0.0395***	0.0447***
	(0.1287)	(0.0030)	(0.0000)	(0.0017)	(0.0074)	(0.0035)	(0.0131)	(0.0056)
b b	0.9409***	0.9248***	0.8833***	0.9147***	0.9036***	0.9248***	0.9131***	0.9491***
	(0.1477)	(0.0126)	(0.0875)	(0.0209)	(0.0410)	(0.0149)	(0.0149)	(0.0310)
c c					0.0000	0.0000	0.0068**	0.0070***
					(0.0032)	(0.0024)	(0.0033)	(0.0022)

Notes: Standard errors are in parentheses; ***p < 0.01, **p < 0.05, *p < 0.1.

Source: own elaboration.

Assuming a 10% significance level, all coefficients –except for μ for WIG20 – are significant. Based on these estimates, short-term persistence and long-term persistence can be analyzed. The short-term persistence ( α \alpha ) is statistically significant for both variables under all the models. The estimated coefficient on long-term persistence ( β \beta ) is statistically significant for each country and S&P500 series, thus indicating the importance of long-term persistence. In addition, in both models, DCC and ADCC, sum of the coefficients for short-term persistence ( α \alpha ) and long-term persistence ( β ) (\beta ) for each country index and S&P500 is less than 1, and in each case, β \beta exceeded α \alpha , which indicates that long-term volatility is more intense compared to short-term volatility. The statistical significance of short-term persistence and long-term persistence provides evidence of volatility clustering.

At the end of Table 2, the DCC coefficients are presented. The positive and significant coefficients of b b indicate that there exists a long-term relationship between the variables (Yousfi et al., 2021). The sum of the coefficients of a a and b b is also less than 1, thus ensuring the return to equilibrium of DCCs and model stability. Moreover, after adding exogenous variables, the DCC coefficient a turned out to be statistically significant for all countries in the case of the ADCC model. In the model without exogenous variables, it was significant only for the Czech Republic. This indicates that correlations between variables are also influenced by current (short-term) information. However, the impact of coefficient b is greater for all countries analyzed because its estimates are much higher than those for coefficient a.

Following Bilgili et al. (2023) results, that dynamics of stock exchange markets can be explained by some other parameters, we tested the robustness of our results by adding exogenous variables. We thus used a DCC model that allows us to measure the effect of exogenous variables on time-varying correlations (Horra et al., 2024). Based on the literature, we proposed an extension of DCC model with the following additional exogenous variables: the price of a barrel of crude oil (Gunay, 2020), the price of gold (Mensi et al., 2022), the VIX, the EPU index, and the GEPU index (Thai Hung, 2024). The VIX is a popular measure of stock market expectations regarding volatility, which is based on options on the S&P 500 index. The EPU and GEPU indices are indicators that measure the level of economic uncertainty, based on the analysis of articles, expert statements, and available reports. This extended analysis confirmed the conclusions formulated above.

Based on Figure 2 presenting the DCC for WIG20 index and S&P500 index, we can see the rapid increase in coefficients in March 2020, so just at the beginning of COVID-19 pandemic in Poland. This means that the two stock markets are strongly linked at the beginning of the pandemic. Over time, the strength of the relation began to decline, until around 2021, the correlation fell below the pre-COVID-19 value.

Figure 2

DCC for WIG20 index and S&P500 index.

In the next step, we focused on the dynamic correlations between WIG20 index and daily cases of infection and deaths caused by COVID-19 in Poland for four waves of infections. Further, the effect of the vaccination program on Polish stock market was also checked. The first-dose COVID-19 vaccinations, second-dose COVID-19 vaccinations, and booster COVID-19 vaccinations were investigated. The modeling process was based on ARMA(1,1)-DCC-GARCH(1,1) model with Student’s t-distribution. For comparative purposes, an analogous analysis was carried out for Hungary, the United Kingdom, and the Czech Republic.

Results reported in Table 3 indicate that the strongest relation between WIG20 index and cases of infections was observed during the first wave of pandemic in Poland, as only for this period, both coefficients, a and b, are statistically significant. For the second wave, only b coefficient occurred to be statistically significant and close to unity which indicates long-term persistence. In contrast, for next waves, the DCC parameters were found to be insignificant. When analyzing the results for WIG20 and deaths caused by COVID-19, it can be noted that a coefficient is not significant for all waves and b parameter is insignificant for the third wave.

Summing up, the obtained results indicate that a higher correlation occurred in the case of the number of infections and WIG20 than in the case of the number of deaths and WIG20. This could be due to the fact that the increase in the number of deaths is naturally related to the increase in the number of infections and occurs a few weeks after it. For this reason, investors reacted more strongly when information about the increase in infections appeared. Not significant results for the third and fourth waves may be related to lower investors’ uncertainty due to a certain familiarity of functioning during the pandemic. In addition, from 2021, vaccines were present and mass vaccinations started, which also gave hope for a possible end to the pandemic.

The results most similar to those in Poland were obtained for the United Kingdom. In this case, a strong relationship was also observed between the number of infections and the FTSE250 index during the first wave. However, during subsequent waves, only the b coefficient was statistically significant. The results for Hungary were somewhat surprising, as during the first wave, both DCC coefficients were insignificant for the number of infections. This suggests that the number of infections had no impact on the BUX index at that time. This changed in the second wave as the b coefficient became statistically significant. At this stage, it should be emphasized that the conclusions change when controlling for additional exogenous variables, and the patterns are different for the countries studied, which is worth further detailed analysis.

In order to extend the research, wavelet coherence analysis was performed. Correlations between the WIG20 index and variables related to pandemics and vaccinations were examined. The analysis was conducted both on the full sample and for four waves of infections.

The graphs show the estimated wavelets and behavior of the studied pairs of series. On the wavelet coherence plots, the warm colors represent strong co-movement, whereas the cold colors correspond to weak co-movement. Significance at the 5% level is marked with black outlines. There are also arrows on the graphs representing the phase (lead/lag) relations between two series. A right arrow indicates that time series are in phase, i.e., moving in the same direction (positive correlation). The left arrow suggests that the series are in antiphase, and so move in opposite directions (negative correlation). There are also right-down and left-up arrows, which means that the second variable leads the first, while the right-up or left-down arrows show that the first variable leads the second. On the other hand, arrows pointing up or down suggest that the variable leads or lags, respectively.

Figure 3 presents the wavelet coherence analysis results. In case of full sample, many significant areas indicating a strong relationship, in particular around the end of 2020 and the beginning of 2021, and then at the end of 2021, can be found. These periods are related to the intensification of COVID-19 infection waves. Figures for both COVID-19 infections – WIG20 index relation and COVID-19 deaths – WIG20 index relation seem to be similar. A slight shift in areas with a strong correlation to a later period in case of COVID-19 deaths – WIG20 index relation can be noticed, which may be associated with a delay in increase in deaths relative to increase in infections. In both cases, at the end of 2020, the arrows are pointing to the right and up, which indicates a positive correlation with WIG20 and signifies that the first series (the number of infections/deaths) is leading. It changes in the case of the number of infections around March 2021, a positive correlation with WIG20 remains, but the first variable is lagging now. This change may be related to the decrease in infections during this period.

Figure 3

Wavelet coherence analysis. (a) The full sample. (b) The first wave. (c) The second wave. (d) The third wave. (e) The fourth wave.

In case of the first wave, the areas indicating the strong significant relation in the case of the number of infections and WIG20 index are not detected. Although throughout the period, the variables were weakly positively correlated, as indicated by arrows pointing to the right. The situation is different for the number of deaths. At the beginning and during the first wave, there are areas with a strong relation with the WIG20 index. The positive correlation was observed and the first variable was leading. The results of the wavelet coherence for the second wave are similar for number of infections and number of deaths. Attention is drawn to one area of significant relation. In both cases, number of infections – WIG20 index relation and number of deaths – WIG20 index relation, arrows are pointing to the right and up. It indicates that the first series is leading with a positive correlation. The wavelet coherence results for the third wave highlight some change. For number of infections, the arrows are now pointing right and down, meaning that the correlation with WIG20 index is positive but the first variable is now lagging. In the case of the number of deaths, similar conclusion can be drawn for April, while around June, the correlation with WIG20 that is found is negative. For the fourth wave, the negative correlation between pandemic variables and WIG20 index was confirmed here. In case of number of infections, the second variable was leading.

In summary, the strongest relations between pandemic variables and WIG20 index occurred during the first and second waves, the correlation was positive and the first variable was leading. However, the behavior of variables during the third and fourth waves was slightly different, because the correlation was mostly negative and the second variable was leading.

4.3.1

Wavelet coherence analysis – vaccination program

In the last stage, a wavelet coherence analysis was carried out for the WIG20 index and given vaccination doses. As can be seen on the graphs (Figure 4), areas with a strong relationship emerged throughout the duration of the vaccination program. The correlation between the variables changed over time as there are arrows indicating both, positive and negative relations. However, it is worth emphasizing that most of the time, there was a negative correlation between WIG20 and vaccinations. In the meantime, there were also changes in the leading of the variables.

Figure 4

Wavelet coherence analysis for vaccinations.

The analysis in every aspect confirms the conclusions of the study of dynamic correlations. The pandemic has had a huge effect on the stock market in Poland. Presented figures might be compared to those given by Karamti and Belhassine (2022) for the Nikkei225 (Japan), SSE (China), CAC40 (France), DAX (Germany), and FTSE (United Kingdom). For each country, some differences can be detected.