Table 11 Song test results for the risk measure \(\tau ^{s}\) computed on Apple real data, considering \(M=30\%\), \(M=40\%\), \(M=80\%\). \(Z_0\) is the statistic test value under the null hypothesis
From: Drawdown-based risk indicators for high-frequency financial volumes
\(\tau ^{s}\) - APPLE | ||||
|---|---|---|---|---|
\(M=30\%\) | \(\alpha =0.10\) | \(\alpha =0.05\) | \(\alpha =0.01\) | \(Z_0\) |
\(s=3\) vs \(s=5\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 2.8595 |
\(s=3\) vs \(s=50\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 4.2746 |
\(s=3\) vs \(s=100\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 4.4523 |
\(M=40\%\) | \(\alpha =0.10\) | \(\alpha =0.05\) | \(\alpha =0.01\) | \(Z_0\) |
|---|---|---|---|---|
\(s=3\) vs \(s=5\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Accept \(H_{0}\) | 2.1057 |
\(s=3\) vs \(s=50\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 4.1383 |
\(s=3\) vs \(s=100\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 5.2446 |
\(M=80\%\) | \(\alpha =0.10\) | \(\alpha =0.05\) | \(\alpha =0.01\) | \(Z_0\) |
|---|---|---|---|---|
\(s=3\) vs \(s=5\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 5.7759 |
\(s=3\) vs \(s=50\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 6.3895 |
\(s=3\) vs \(s=100\) | Reject \(H_{0}\) | Reject \(H_{0}\) | Reject \(H_{0}\) | 6.9665 |