\[ Y_{it} \sim N(\phi_{it} + \mu_{i}, \sigma^{2}_{yi}) \\ \phi_{it} \sim N(\nu_{it} + \gamma_{t}, \sigma^{2}_{\phi_{i}}) \\ \nu_{it} \sim N(2\nu_{it-1} + \nu_{it-2}, \sigma^{2}_{\nu_{i}}) \\ \gamma_{t} \sim N(2\gamma_{t-1} + \gamma_{t-2}, \sigma^{2}_{\gamma_{t}}) \\ \] (Where) \(\mu_{i}\): level; \(\nu_{it}\): trend; \(\gamma_{t}\): intrinsic growth
Age class | \(\mu_{i}\) | \(\nu_{it}\) | \(\gamma_{i}\) |
---|---|---|---|
10s’ | Least | lower & \(\downarrow\) | decreasing |
20s’ | 3rd. | lower & \(\downarrow\) | decreasing |
30s’ | 2nd. | lower & \(\downarrow\) | decreasing |
40s’ | Most | lower & \(\downarrow\) | decreasing |
50s’ | 4th. | highest & \(\uparrow\) | decreasing |
60s’ and over | 5th. | higher & \(\uparrow\) | decreasing |