Timing the market: the economic value of price extremes

Financial Innovation

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 MG^F /→ P ML^F	0.967	0.952	0.908	0.852	0.792	0.390
P ML^F /→ P MG^F	0.000	0.000	0.000	0.002	0.004	0.014

Note. X /→ Y means the null hypothesis that X does not Granger-causes Y. P MG^F and P ML^F 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
\( {\displaystyle \begin{array}{l}{r}_t=\left[\mathit{\log}\left({\mathrm{C}}_t\right)-\mathit{\log}\left({\mathrm{L}}_t\right)\right]-\left[\mathit{\log}\left({\mathrm{L}}_t\right)-\mathit{\log}\left({\mathrm{O}}_t\right)\right]\\ {}\kern1.5em =P\ {MG}_t-P\ {ML}_t\end{array}} \)