Table 1.
Parameter Estimates for 3D Simulation Data. In each case, a time series consisting of 1 × 105 observations uniformly spaced by 4ms was simulated to create draws from the stationary distribution of a 3D model. Parameters were estimated by dividing the long stationary signal into windows using various schemes. Case 1: Computed average and standard deviation (reported in parenthesis) of 3D model estimated with 400 observations per window; Case 2: Results with 1D model estimated with 400 observations (interaction terms Bxy, Bxz, Byz are set to zero); Case 3 and 4: Correspond to Case 1 and 2 except using a window of size 1600 (resulting in a larger sample size for each parameter estimate).
| Case | 1 | 2 | 3 | 4 | Truth |
|---|---|---|---|---|---|
| Ax | −0.003 (0.008) | −0.000 (0.006) | 0.000 (0.003) | 0.001 (0.002) | 0 |
| Ay | 0.003 (0.015) | −0.000 (0.007) | 0.000 (0.009) | −0.000 (0.001) | 0 |
| Az | 0.003 (0.031) | −0.001 (0.004) | 0.009 (0.014) | −0.001 (0.004) | 0 |
| Bxx | −10.735 (3.236) | −3.896 (0.889) | −9.790 (1.138) | −3.586 (0.556) | −10 |
| Bxy | 10.542 (3.267) | - | 9.825 (1.442) | - | 10 |
| Bxz | −0.597 (3.080) | - | −0.140 (1.941) | - | 0 |
| Byy | −16.319 (4.071) | −5.879 (1.245) | −15.190 (2.005) | −5.397 (0.519) | −15 |
| Byz | 1.049 (2.959) | - | 0.351 (1.807) | - | 0 |
| Bzz | −45.543 (14.190) | −42.906 (11.842) | −43.790 (4.924) | −42.353 (4.107) | −40 |
| Cx | 0.209 (0.050) | 0.159 (0.025) | 0.209 (0.012) | 0.157 (0.007) | 0.2 |
| Cy | 0.148 (0.028) | 0.121 (0.016) | 0.143 (0.016) | 0.119 (0.009) | 0.15 |
| Cz | 0.103 (0.033) | 0.106 (0.042) | 0.095 (0.015) | 0.098 (0.015) | 0.10 |
| Rx | 0.020 (0.002) | 0.021 (0.001) | 0.020 (0.001) | 0.021 (0.001) | .020 |
| Ry | 0.015 (0.001) | 0.016 (0.001) | 0.015 (0.001) | 0.016 (0.001) | 0.015 |
| Rz | 0.010 (0.002) | 0.010 (0.002) | 0.010 (0.001) | 0.010 (0.001) | 0.010 |