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Table 9 Song test results for the risk measure \(\tau ^{s}\) computed on Tesla 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

\(\tau ^{s}\) - TESLA

\(M=30\%\)

\(\alpha =0.10\)

\(\alpha =0.05\)

\(\alpha =0.01\)

\(Z_0\)

\(s=3\) vs \(s=5\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

2.9737

\(s=3\) vs \(s=50\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

6.3366

\(s=3\) vs \(s=100\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

7.1834

\(M=40\%\)

\(\alpha =0.10\)

\(\alpha =0.05\)

\(\alpha =0.01\)

\(Z_0\)

\(s=3\) vs \(s=5\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

2.4755

\(s=3\) vs \(s=50\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

5.5628

\(s=3\) vs \(s=100\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

7.1885

\(M=80\%\)

\(\alpha =0.10\)

\(\alpha =0.05\)

\(\alpha =0.01\)

\(Z_0\)

\(s=3\) vs \(s=5\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

4.8902

\(s=3\) vs \(s=50\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

5.8083

\(s=3\) vs \(s=100\)

Reject \(H_{0}\)

Reject \(H_{0}\)

Reject \(H_{0}\)

6.3683