Table 8 Summary of estimation results... | Emerald Publishing

Table 8

Summary of estimation results for Beijing air pollution dataset

Parameter	Value
Estimated A Matrix	$[\begin{matrix} 0.0824 & - 0.0681 & - 0.0355 & - 0.0599 & - 0.0263 \\ - 0.0266 & 0.1785 & - 0.0452 & - 0.0328 & - 0.0217 \\ 0.0103 & - 0.0118 & 0.0994 & - 0.0372 & 0.0618 \\ - 0.0137 & - 0.0356 & - 0.0749 & 0.2092 & - 0.0255 \\ 0.0021 & - 0.0034 & - 0.0367 & 0.0165 & 0.0208 \end{matrix}]$
Estimated B Matrix	$[\begin{matrix} 0.0019 & 0.0053 & - 0.0068 & - 0.0049 \\ - 0.0041 & 0.0138 & 0.0002 & - 0.0008 \\ 0.0016 & - 0.0011 & - 0.0016 & - 0.0107 \\ 0.0047 & - 0.0020 & 0.0002 & - 0.0134 \\ - 0.0061 & 0.0034 & 0.0077 & 0.0022 \end{matrix}]$
Eigenvalues of A	0.0434, 0.0565 ± 0.0339i, 0.1969, 0.2369
System Stability	Stable (all eigenvalues within the unit circle)
Mean Cross-Validation Estimation Error	0.0339 (Frobenius norm)
99% Confidence Interval for Estimation Error	Lower Bound: 0.0321, Upper Bound: 0.1168
Theoretical Upper Bound for Estimation Error	2.2927
Theoretical Lower Bound for MSE Risk	0.0857
Empirical MSE Risk	0.2131
Controllability Matrix Rank	5 (Full Rank)
Condition Number of Controllability Matrix	11.92
Smallest Singular Value of Controllability Matrix	0.0017

Parameter	Value
Estimated A Matrix	$[\begin{matrix} 0.0824 & - 0.0681 & - 0.0355 & - 0.0599 & - 0.0263 \\ - 0.0266 & 0.1785 & - 0.0452 & - 0.0328 & - 0.0217 \\ 0.0103 & - 0.0118 & 0.0994 & - 0.0372 & 0.0618 \\ - 0.0137 & - 0.0356 & - 0.0749 & 0.2092 & - 0.0255 \\ 0.0021 & - 0.0034 & - 0.0367 & 0.0165 & 0.0208 \end{matrix}]$
Estimated B Matrix	$[\begin{matrix} 0.0019 & 0.0053 & - 0.0068 & - 0.0049 \\ - 0.0041 & 0.0138 & 0.0002 & - 0.0008 \\ 0.0016 & - 0.0011 & - 0.0016 & - 0.0107 \\ 0.0047 & - 0.0020 & 0.0002 & - 0.0134 \\ - 0.0061 & 0.0034 & 0.0077 & 0.0022 \end{matrix}]$
Eigenvalues of A	0.0434, 0.0565 ± 0.0339i, 0.1969, 0.2369
System Stability	Stable (all eigenvalues within the unit circle)
Mean Cross-Validation Estimation Error	0.0339 (Frobenius norm)
99% Confidence Interval for Estimation Error	Lower Bound: 0.0321, Upper Bound: 0.1168
Theoretical Upper Bound for Estimation Error	2.2927
Theoretical Lower Bound for MSE Risk	0.0857
Empirical MSE Risk	0.2131
Controllability Matrix Rank	5 (Full Rank)
Condition Number of Controllability Matrix	11.92
Smallest Singular Value of Controllability Matrix	0.0017

Source(s): Table by authors