| Panel A. Monthly Data Observations | Panel B. Quarterly Data Observations |
---|
Lags | 2 | 4 | 6 | 2 | 4 | 6 |
---|
PMG /→ PML | 0.009 | 0.712 | 0.878 | 0.036 | 0.049 | 0.107 |
PML /→ PMG | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
P MGF /→ P MLF | 0.493 | 0.794 | 0.869 | 0.014 | 0.007 | 0.029 |
P MLF /→ P MGF | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
- 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
-
\( {\displaystyle \begin{array}{l}{r}_t=\kern0.5em \left[\mathit{\log}\left({H}_t\right)\hbox{-} \mathit{\log}\left({O}_t\right)\right]\hbox{-} \left[\mathit{\log}\left({H}_t\right)\hbox{-} \mathit{\log}\left({C}_t\right)\right]\\ {}\kern1em =P\ {MG}_t\hbox{-} P\ {ML}_t\end{array}} \)