# Table 6 Granger Causality Tests on PMG and PML. Decomposition with Low Price Extremes

Panel A. Monthly Data Observations Panel B. Quarterly Data Observations
Lags 2 4 6 2 4 6
PMG /→ PML 0.390 0.851 0.622 0.594 0.566 0.436
PML /→ PMG 0.000 0.000 0.000 0.000 0.000 0.000
P MGF /→ P MLF 0.967 0.952 0.908 0.852 0.792 0.390
P MLF /→ P MGF 0.000 0.000 0.000 0.002 0.004 0.014
1. Note. X /→ Y means the null hypothesis that X does not Granger-causes Y. P MGF and P MLF mean filtered PMG and PML respectively. This table reports the p-values of the F -statistics. When performing Granger causality test, we set m = n in Equation (5) for the sake of being convenient. Di erent lags are used for being robust since the Granger causality tests are sensitive to the lag selection. Panels A and B report respectively the results for monthly and quarterly data observations. Decomposing stock returns with high price extremes are presented as
2. $${\displaystyle \begin{array}{l}{r}_t=\left[\mathit{\log}\left({\mathrm{C}}_t\right)-\mathit{\log}\left({\mathrm{L}}_t\right)\right]-\left[\mathit{\log}\left({\mathrm{L}}_t\right)-\mathit{\log}\left({\mathrm{O}}_t\right)\right]\\ {}\kern1.5em =P\ {MG}_t-P\ {ML}_t\end{array}}$$