Table 32 Selection of the best parametric model as a function of s, M and \(M'\) for the measure \(R_t^{s}\) computed on APPLE simulated data
From: Drawdown-based risk indicators for high-frequency financial volumes
Model selection for \(R_t^{s}\)-simulated data for APPLE | ||||||||
|---|---|---|---|---|---|---|---|---|
M=80% | Lognormal | Exponential | Weibull | Gamma | ||||
\(M' \mid s=0\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
\(30\%\) | 1.1635e+03 | 1.692e+03 | 1.3839e+03 | 1.3868e+03 | 1.2043e+03 | 1.2099e+03 | 1.3705e+03 | 1.3762e+03 |
\(40\%\) | 1.0663e+03 | 1.0719e+03 | 1.2982e+03 | 1.3010e+03 | 1.1181e+03 | 1.1237e+03 | 1.2279e+03 | 1.2336e+03 |
\(50\%\) | 952.0155 | 957.6881 | 1.0814e+03 | 1.0842e+03 | 996.7772 | 1.0024e+03 | 1.0383e+03 | 1.0440e+03 |
\(M' \mid s=5\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
|---|---|---|---|---|---|---|---|---|
\(30\%\) | 1.1715e+03 | 1.0682e+03 | 1.3693e+03 | 1.3722e+03 | 1.2146e+03 | 1.2203e+03 | 1.3535e+03 | 1.3592e+03 |
\(40\%\) | 1.0682e+03 | 1.0739e+03 | 1.2301e+03 | 1.2329e+03 | 1.1145e+03 | 1.1201e+03 | 993.4517 | 999.1242 |
\(50\%\) | 957.2985 | 962.9711 | 1.0039e+03 | 1.0067e+03 | 982.4105 | 988.0830 | 993.4517 | 999.1242 |
\(M' \mid s=50\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
|---|---|---|---|---|---|---|---|---|
\(30\%\) | 1.0515e+03 | 1.0572e+03 | 1.1927+03 | 1.1956+03 | 1.1000+03 | 1.1057e+03 | 1.1523e+03 | 1.1580e+03 |
\(40\%\) | 955.5430 | 961.2155 | 1.0827+03 | 1.0855+03 | 1.0091+03 | 1.0147+03 | 1.0509+03 | 1.0566+03 |
\(50\%\) | 852.3765 | 858.0491 | 933.0831 | 935.9094 | 901.2634 | 906.9360 | 920.7401 | 926.4127 |
\(M' \mid s=100\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
|---|---|---|---|---|---|---|---|---|
\(30\%\) | 1.0343e+03 | 1.0400e+03 | 1.1503e+03 | 1.1531e+03 | 1.0686e+03 | 1.0743e+03 | 1.1031e+03 | 1.1087e+03 |
\(40\%\) | 957.3771 | 963.0496 | 1.0217e+03 | 1.0245e+03 | 985.0520 | 990.7245 | 998.5607 | 1.0042e+03 |
\(50\%\) | 868.0799 | 873.7524 | 933.0373 | 935.9094 | 900.6337 | 906.3062 | 914.7511 | 920.4237 |