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The BSM process is the same as FSM except starting to constrain the parameters that show the strongest temporal behaviour (i.e. the smallest p-value) instead of constraining the parameter that does not show any trend along time. Table 3 represents the calibration setting and optimisation results for the BSM for the summer period from 1961 to 1990. For this nonstationary model, two parameters are set as a fixed value and six parameters are set to have trends along time.

Table 3

Parameter settings for the calibration and optimisation result for the BSM for summer period from 1961 to 1990

 Calibration setting
Optimisation result
Constant (fix)Trend (fix)FreeNo trendTrend
Calibration     c, τw, f, αs, αq, βq, l, p c, τw, βq, l, p f, αs, αq 
Step 1  αs c, τw, f, αq, βq, l, p c, τw, βq, l f, αq, p 
Step 2  αs, f c, τw, αq, βq, l, p c, τw, βq, l, p αq 
Step 3  αs, f, αq c, τw, βq, l, p c, τw, βq  l, p 
Step 4  αs, f, αq, l c, τw, βq, p c, τw, βq, p  
Step 5 c αs, f, αq, l τw, βq, p τw, βq p 
Step 6 c αs, f, αq, l, p τw, βq βq τw 
Step 7 c αs, f, αq, l, p, τw βq βq   
 Calibration setting
Optimisation result
Constant (fix)Trend (fix)FreeNo trendTrend
Calibration     c, τw, f, αs, αq, βq, l, p c, τw, βq, l, p f, αs, αq 
Step 1  αs c, τw, f, αq, βq, l, p c, τw, βq, l f, αq, p 
Step 2  αs, f c, τw, αq, βq, l, p c, τw, βq, l, p αq 
Step 3  αs, f, αq c, τw, βq, l, p c, τw, βq  l, p 
Step 4  αs, f, αq, l c, τw, βq, p c, τw, βq, p  
Step 5 c αs, f, αq, l τw, βq, p τw, βq p 
Step 6 c αs, f, αq, l, p τw, βq βq τw 
Step 7 c αs, f, αq, l, p, τw βq βq   

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