Journal of Probability and Statistics / 2023 / Article / Tab 1 / Research Article
Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails Table 1 Summary statistics for the MM estimator for different parameter values
, using an exponential kernel (representing short-range dependence) at different sample lengths of the series
for a Poisson-inverse Gaussian Lévy-based process.
N True value 1.9 5.5 0.03 2 9 0.04 9 0.8 6.7 30 Mean 1.8666 5.4666 0.0288 1.9666 8.9666 0.0388 8.9666 0.7666 6.6988 Bias 0.0022 −0.0004 −0.0000 0.0055 −0.0011 −0.0153 −0.0011 −0.1744 0.2066 MSE 0.0001 0.0000 0.0000 0.0009 0.0000 0.0070 0.0000 0.9129 1.2808 100 Mean 1.8900 5.4900 0.0299 1.9900 8.9900 0.0399 8.9900 0.7900 6.6999 Bias 0.0009 −0.0001 −0.0000 0.0019 −0.0001 −0.0046 −0.0001 −0.0521 0.0619 MSE 0.0000 0.0000 0.0000 0.0003 0.0000 0.0021 0.0000 0.2714 0.3843 400 Mean 1.8975 5.4975 0.0300 1.9975 8.9975 0.0399 8.9975 0.7975 6.6999 Bias 0.0002 −0.0000 0.0000 0.0004 −0.0000 −0.0011 −0.0000 −0.0130 0.0154 MSE 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0000 0.0676 0.0960 N True value 7 0.4 0.05 10 0.7 3 3 6 9 100 Mean 6.9900 0.3900 0.0499 9.9900 0.6900 2.9999 2.9900 5.9900 8.9999 Bias 0.0519 −0.0561 −0.0045 0.0819 −0.0531 0.0249 0.0119 −0.0001 0.0849 MSE 0.2693 0.3147 0.0020 0.6707 0.2819 0.0624 0.0141 0.0000 0.7224 200 Mean 6.9950 0.3950 0.0499 9.9950 0.6950 2.9999 2.9950 5.9950 8.9999 Bias 0.0259 −0.0280 −0.0022 0.0409 −0.0265 0.0124 0.0059 −0.0000 0.0424 MSE 0.1349 0.1570 0.0010 0.3357 0.1407 0.0312 0.0071 0.0000 0.3612 400 Mean 6.9975 0.3975 0.0499 9.9975 0.6975 2.9999 2.9975 5.9975 8.9999 Bias 0.0129 −0.0140 −0.0011 0.0204 −0.0132 0.0062 0.0029 −0.0000 0.0212 MSE 0.0675 0.0784 0.0005 0.1679 0.0702 0.0156 0.0035 0.0000 0.1806