Table 1 Model performance measures (average absolute bias, average interval length and average coverage) summary based on a simulation study
From: Estimated Covid-19 burden in Spain: ARCH underreported non-stationary time series
Structure | Parameter | Bias | AIL | Coverage (%) |
|---|---|---|---|---|
ARCH(1) | \(\widehat{{\phi }_{0}}\) | -0.377 | 3.586 | 68.77% |
\(\widehat{{\phi }_{1}}\) | 0.122 | 0.525 | 66.08% | |
\(\widehat{{\alpha }_{0}}\) | -0.296 | 1.351 | 74.72% | |
\(\widehat{{\alpha }_{1}}\) | -0.085 | 0.920 | 77.34% | |
\(\widehat{\omega }\) | -0.020 | 0.234 | 83.71% | |
\(\widehat{q}\) | -0.022 | 0.167 | 85.06% | |
\(\widehat{m}\) | -0.226 | 0.783 | 79.17% | |
\(\widehat{\beta }\) | -0.734 | 3.581 | 76.83% | |
\(\widehat{{\sigma }_{\epsilon }}\) | -1.540 | 3.323 | 63.65% | |
AR(1) | \(\widehat{{\phi }_{0}}\) | -0.983 | 5.189 | 70.10% |
\(\widehat{\alpha }\) | 0.043 | 0.814 | 92.46% | |
\(\widehat{\omega }\) | -0.003 | 0.111 | 94.10% | |
\(\widehat{q}\) | -0.001 | 0.014 | 89.03% | |
\(\widehat{m}\) | 0.001 | 0.190 | 75.17% | |
\(\widehat{\beta }\) | 0.007 | 0.192 | 74.49% | |
\(\widehat{{\sigma }_{\epsilon }}\) | -1.689 | 4.718 | 81.07% | |
MA(1) | \(\widehat{{\phi }_{0}}\) | -1.241 | 5.171 | 68.31% |
\(\widehat{\theta }\) | 0.051 | 0.818 | 90.40% | |
\(\widehat{\omega }\) | -0.005 | 0.108 | 95.06% | |
\(\widehat{q}\) | -0.001 | 0.014 | 87.24% | |
\(\widehat{m}\) | -0.002 | 0.187 | 76.95% | |
\(\widehat{\beta }\) | 0.004 | 0.190 | 80.38% | |
\(\widehat{{\sigma }_{\epsilon }}\) | -1.619 | 4.679 | 83.95% | |
ARMA(1,1) | \(\widehat{{\phi }_{0}}\) | -1.834 | 5.107 | 61.01% |
\(\widehat{\alpha }\) | 0.062 | 0.799 | 89.39% | |
\(\widehat{\theta }\) | 0.011 | 0.873 | 96.86% | |
\(\widehat{\omega }\) | -0.001 | 0.014 | 88.32% | |
\(\widehat{q}\) | -0.005 | 0.109 | 94.97% | |
\(\widehat{m}\) | 0.002 | 0.184 | 78.49% | |
\(\widehat{\beta }\) | 0.004 | 0.183 | 78.01% | |
\(\widehat{{\sigma }_{\epsilon }}\) | -1.828 | 4.631 | 74.74% |