Timing the market: the economic value of price extremes

Financial Innovation

Table 5 Granger Causality Tests on PMG and PML. Decomposition with High Price Extremes

	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 MG^F /→ P ML^F	0.493	0.794	0.869	0.014	0.007	0.029
P ML^F /→ P MG^F	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 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
\( {\displaystyle \begin{array}{l}{r}_t=\kern0.5em \left[\mathit{\log}\left({H}_t\right)\hbox{-} \mathit{\log}\left({O}_t\right)\right]\hbox{-} \left[\mathit{\log}\left({H}_t\right)\hbox{-} \mathit{\log}\left({C}_t\right)\right]\\ {}\kern1em =P\ {MG}_t\hbox{-} P\ {ML}_t\end{array}} \)