Chow–denning joint variance ratio test results based on five-day returns
| Market | Dof | Homoscedasticity robust test statistics max |z| | Heteroscedasticity robust test statistics max |z| | ||
|---|---|---|---|---|---|
| Panel A | Panel B | Panel A | Panel B | ||
| Australia | 755 | 14.08 | 14.08 | 4.98 | 4.98 |
| Canada | 751 | 14.03 | 14.03 | 5.34 | 5.34 |
| France | 767 | 14.17 | 14.17 | 7.76 | 7.76 |
| Germany | 761 | 15.16 | 15.16 | 8.28 | 8.28 |
| Hong Kong | 738 | 13.77 | 13.77 | 8.37 | 8.37 |
| Israel | 720 | 13.16 | 13.16 | 7.11 | 7.11 |
| Japan | 734 | 14.97 | 14.97 | 5.34 | 5.34 |
| Sweden | 752 | 15.19 | 15.19 | 5.50 | 5.50 |
| UK | 756 | 14.23 | 14.23 | 8.39 | 8.39 |
| US | 753 | 16.90 | 16.90 | 5.44 | 5.44 |
| Brazil | 740 | 16.12 | 16.12 | 7.08 | 7.08 |
| Chile | 746 | 14.52 | 14.52 | 6.77 | 6.77 |
| China | 727 | 13.57 | 13.57 | 10.18 | 10.18 |
| Greece | 741 | 14.16 | 14.16 | 7.31 | 7.31 |
| India | 740 | 15.37 | 15.37 | 8.72 | 8.72 |
| Malaysia | 736 | 14.01 | 14.01 | 6.77 | 6.77 |
| Mexico | 750 | 15.77 | 15.77 | 6.18 | 6.18 |
| Poland | 745 | 14.30 | 14.30 | 7.22 | 7.22 |
| Russia | 743 | 14.60 | 14.60 | 6.85 | 6.85 |
| South Africa | 746 | 13.37 | 13.37 | 7.72 | 7.72 |
| Market | Dof | Homoscedasticity robust test statistics max | | Heteroscedasticity robust test statistics max | | ||
|---|---|---|---|---|---|
| Panel A | Panel B | Panel A | Panel B | ||
| Australia | 755 | 14.08 | 14.08 | 4.98 | 4.98 |
| Canada | 751 | 14.03 | 14.03 | 5.34 | 5.34 |
| France | 767 | 14.17 | 14.17 | 7.76 | 7.76 |
| Germany | 761 | 15.16 | 15.16 | 8.28 | 8.28 |
| Hong Kong | 738 | 13.77 | 13.77 | 8.37 | 8.37 |
| Israel | 720 | 13.16 | 13.16 | 7.11 | 7.11 |
| Japan | 734 | 14.97 | 14.97 | 5.34 | 5.34 |
| Sweden | 752 | 15.19 | 15.19 | 5.50 | 5.50 |
| UK | 756 | 14.23 | 14.23 | 8.39 | 8.39 |
| US | 753 | 16.90 | 16.90 | 5.44 | 5.44 |
| Brazil | 740 | 16.12 | 16.12 | 7.08 | 7.08 |
| Chile | 746 | 14.52 | 14.52 | 6.77 | 6.77 |
| China | 727 | 13.57 | 13.57 | 10.18 | 10.18 |
| Greece | 741 | 14.16 | 14.16 | 7.31 | 7.31 |
| India | 740 | 15.37 | 15.37 | 8.72 | 8.72 |
| Malaysia | 736 | 14.01 | 14.01 | 6.77 | 6.77 |
| Mexico | 750 | 15.77 | 15.77 | 6.18 | 6.18 |
| Poland | 745 | 14.30 | 14.30 | 7.22 | 7.22 |
| Russia | 743 | 14.60 | 14.60 | 6.85 | 6.85 |
| South Africa | 746 | 13.37 | 13.37 | 7.72 | 7.72 |
Note(s): 1. This table presents five-day return results of Chow–Denning tests (test of martingale hypothesis). The presented are Max |z| with probability approximation using studentized maximum modulus with parameter value 4 and infinite degrees of freedom
2. All the test statistics are statistically significant (different from 1), using a critical value of 2.49 (panel A) and using the confidence intervals calculated with the Wild Bootstrapping method (panel B)
3. The results strongly reject the null hypothesis of a martingale across all markets
4. We also ran the above tests in panel settings under the assumption that cross-sections are independent, with cross-section heterogeneity of the processes. The combined the p-values from cross-section results using the Fisher approach as in Maddala and Wu (1999) were all highly significant for both developed and emerging market panels
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