The cointegrating equation in VECM changed sign when I added a trend in the deterministic regressor

Question

I am studying the cointegration between retail prices of pork. In an economical theory this should have a positive relationship. However, when I tested for cointegration using Johansen in Eviews, it only appears to be cointegrated at Case 4 and 5 where there is a linear trend in the cointegrating equation. When I tried to estimate the VECM, it showed me that there is a negative relationship between the prices and a positive trend. What seems to be the problem with this and how can I fix it?

This is the results of the VECM when I use the Case 4 of Johansen, as it appears to be cointegrated with trend.

Cointegrating Eq:   CointEq1    
        
C_R(-1)  1.000000   
        
NCR_R(-1)    0.810135   
     (0.13148)  
    [ 6.16153]  
        
@TREND(1)   -1.212315   
     (0.08452)  
    [-14.3441]  
        
C   -401.4768   
        
Error Correction:   D(C_R)  D(NCR_R)
        
CointEq1    -0.318874   -0.043231
     (0.05565)   (0.01781)
    [-5.73006]  [-2.42791]
        
D(C_R(-1))   0.325381   -0.026421
     (0.08673)   (0.02775)
    [ 3.75181]  [-0.95211]
        
D(C_R(-2))   0.297387   -0.004909
     (0.09267)   (0.02965)
    [ 3.20902]  [-0.16555]
        
D(NCR_R(-1))     0.454352    0.282226
     (0.29558)   (0.09457)
    [ 1.53718]  [ 2.98416]
        
D(NCR_R(-2))    -0.910092    0.089290
     (0.29257)   (0.09361)
    [-3.11066]  [ 0.95381]
        
C    0.513729    0.286834
     (0.51764)   (0.16563)
    [ 0.99245]  [ 1.73181]

Notice how it has a negative relationship with a positive trend. On another note, this also happen when I use OLS in regression.

Dependent Variable: C_R             
Method: Least Squares                               
Sample: 1 120               
Included observations: 120              
                
Variable    Coefficient Std. Error  t-Statistic Prob.  
                
NCR_R   0.788551    0.101903    7.738264    0.0000
C   48.57702    27.27814    1.780804    0.0775
                
R-squared   0.336634        Mean dependent var      258.9932
Adjusted R-squared  0.331012        S.D. dependent var      29.07133
S.E. of regression  23.77792        Akaike info criterion       9.191918
Sum squared resid   66715.96        Schwarz criterion       9.238376
Log likelihood  -549.5151       Hannan-Quinn criter.        9.210785
F-statistic 59.88074        Durbin-Watson stat      0.066291
Prob(F-statistic)   0.000000            

There seems to be a positive relationship, however when I add a @trend in the regression equation it becomes a negative relationship with a positive trend, just like the results of Johansen cointegration, Case 4 with restricted trend.

Dependent Variable: C_R             
Method: Least Squares                           
Sample: 1 120               
Included observations: 120              
                
Variable    Coefficient Std. Error  t-Statistic Prob.  
                
NCR_R   -0.703379   0.079795    -8.814858   0.0000
C   381.0169    18.95859    20.09732    0.0000
@TREND  1.103617    0.049068    22.49174    0.0000
                
R-squared   0.875395        Mean dependent var      258.9932
Adjusted R-squared  0.873265        S.D. dependent var      29.07133
S.E. of regression  10.34936        Akaike info criterion       7.536408
Sum squared resid   12531.77        Schwarz criterion       7.606095
Log likelihood  -449.1845       Hannan-Quinn criter.        7.564708
F-statistic 410.9832        Durbin-Watson stat      0.417294
Prob(F-statistic)   0.000000            

What seems to be the problem?