Example

The $\chi ^2$-test on transitional matrices for the BFAM, BEMOT and BSTRE configuration is applied for lags 1 to 10. Table 8.4 shows the results (in bold are significance dependences).

Table 8.4: Testing order of BFAM-BEMOT-BSTRE configuration using chi-square statistic

Lag	$\chi ^2$	d.f.	p-value
1	82.09	36	0.00
2	59.03	36	0.01
3	74.57	36	0.00
4	37.34	36	0.41
5	34.86	36	0.52
6	40.70	36	0.27
7	55.35	36	0.02
8	39.12	36	0.33
9	42.80	36	0.2
10	37.41	36	0.4

Interestingly results show that the three first lags are significant, as well as the seventh lag. It means that configurations are best predicted by using knowledge from the last three states and the seventh the subject was in. The fact that the seventh order emerges is no surprise: observations were taken 7 times a day. Therefore the dynamics of this subject is surely governed by certain daily patterns.