Table 29 Selection of the best parametric model as a function of s, M and \(M'\) for the measure \(R_t^{s}\) computed on Apple real data
From: Drawdown-based risk indicators for high-frequency financial volumes
Model selection for \(R_t^{s}\)-APPLE | ||||||||
|---|---|---|---|---|---|---|---|---|
M=80% | Lognormal | Exponential | Weibull | Gamma | ||||
\(M' \mid s=0\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
\(30\%\) | 1.0024e+03 | 1.0081e+03 | 1.3678e+03 | 1.3706e+03 | 1.0518e+03 | 1.0574e+03 | 1.2893e+03 | 1.2949e+03 |
\(40\%\) | 995.3318 | 1.0010e+03 | 1.3678e+03 | 1.3706e+03 | 1.0466e+03 | 1.0523e+03 | 1.2712e+03 | 1.2768e+03 |
\(50\%\) | 977.2639 | 982.9365 | 1.3621e+03 | 1.3649e+03 | 1.0309e+03 | 1.0366e+03 | 1.2577e+03 | 1.2634e+03 |
\(M' \mid s=5\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
|---|---|---|---|---|---|---|---|---|
\(30\%\) | 1.0632e+03 | 1.0688e+03 | 1.2149e+03 | 1.2177e+03 | 1.1092e+03 | 1.1149e+03 | 1.1487e+03 | 1.1544e+03 |
\(40\%\) | 907.9526 | 913.6251 | 1.0962e+03 | 1.0991e+03 | 972.3222 | 977.9948 | 1.1255e+03 | 1.0312e+03 |
\(50\%\) | 736.9171 | 742.5897 | 964.0400 | 966.8763 | 825.9198 | 831.5924 | 896.9408 | 902.6134 |
\(M' \mid s=50\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
|---|---|---|---|---|---|---|---|---|
\(30\%\) | 966.2662 | 971.9387 | 1.0456e+03 | 1.0485e+03 | 1.0023e+03 | 1.0079e+03 | 1.0194+03 | 1.0251e+03 |
\(40\%\) | 888.8694 | 894.5419 | 974.2439 | 977.0802 | 931.9785 | 937.6511 | 951.6929 | 957.3654 |
\(50\%\) | 763.3344 | 769.0069 | 818.7865 | 821.6228 | 804.0412 | 809.7137 | 814.9187 | 820.5912 |
\(M' \mid s=100\) | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC |
|---|---|---|---|---|---|---|---|---|
\(30\%\) | 1.0526e+03 | 1.0583e+03 | 1.1999e+03 | 1.2028e+03 | 1.0952e+03 | 1.1008e+03 | 1.1468e+03 | 1.1525e+03 |
\(40\%\) | 946.6623 | 952.3348 | 1.1337e+03 | 1.1365e+03 | 1.0009e+03 | 1.0066e+03 | 1.0645e+03 | 1.0702e+03 |
\(50\%\) | 864.3296 | 870.0021 | 1.0934e+03 | 1.0963e+03 | 928.3033 | 933.9758 | 1.0019e+03 | 1.0076e+03 |