The Impact of COVID-19 Crisis on Stock Markets’ Statistical Complexity

Figure 6

Wavelet coherence total number of cases (worldwide) and first principal component of Bayesian PCA analysis. Time is shown on the horizontal axis, while the vertical axis indicates the frequency (the lower the frequency, the higher the scale). Regions in time-frequency space where the two time series covary are located by the wavelet coherence. Warmer colours (red) represent regions with significant interrelation, while colder colours (blue) signify lower dependence between the series. Cold regions beyond the significant areas represent time and frequencies with no dependence in the series. White contour lines indicate significance (with respect to the null hypothesis of white noise processes) at the 10% level. An arrow in the wavelet coherence plots represents the examined series’ lead/lag phase relations. A zero phase difference means that the two time series move together on a particular scale. Arrows point to the right (left) when the time series are in phase (antiphase). When the two series are in phase, it indicates that they move in the same direction; antiphase means they move in the opposite direction. Arrows pointing to the right-down or left-up indicate that the first variable is leading, while arrows pointing to the right-up or left-down show that the second variable is leading. The arrows are plotted only within white contour lines, indicating significance (with respect to the null hypothesis of white noise processes) at the 10% level. Wavelet coherence is implemented in Roesch and Schmidbauer [54]. One thousand randomisations of the data set are used. Mother wavelet function is “Morlet” (“Gabor”). This is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). The cross-wavelet power estimation is rectified according to Veleda et al. [55] in order to avoid “biased” results in the sense that high-frequency (short-period) processes frequently tend to be underestimated by conventional approaches. The type of window for smoothing in both time and scale directions is Boxcar (rectangular, Dirichlet). This leads to fewer granularities in high-frequency areas.