334 H. Shi et al. Fig. 41.3 Residual series obtained using the conventional cointegration method, the red dashed line indicates where damage occurs Fig. 41.4 Mutual relationship between natural frequency series 4. With the estimated best breakpoint and cointegrating vectors correspondingly, one can have the following regimeswitching cointegration relationship which is indexed by the value of temperature: "t D 147:90 y1t 107:29 y2t 122:96 y3t C10:69 y4t 3:54; if T 0:4767 4:51 y1t 84:87 y2t 127:87 y3t 165:07 y4t 24:19; if T >0:4767 (41.9) Figure 41.7 shows the residual series from (41.9), the red horizontal lines are the three times standard error bars which show the confidence interval of the health state.
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