Deterministic trend in VECM

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Dear friends,

I have a question that need your help. That's about Deterministic trend in VECM. I tested if there were unit roots in my data with constant only included in the tests and with both constant and trend. They have unit roots at level. For the first differenced data, however, they still have unit roots when tested with constant only, but did not have unit roots when tested with constant and trend. So I am thinking if this implies that I should apply a VECM model specifying 4) Intercept and trend in CE - no trend in VAR under the Cointegration tab, though the default and most commonly used is 3) Intercept (no trend) in CE and VAR.

The estimated VECM model specifying 4) is
D(CO2) = C(1)*( CO2(-1) - 0.028*CNG(-1) - 0.0229*@TREND(31) - 4.83) + C(2)*D(CO2(-1)) + C(3)*D(CO2(-2)) + C(4)*D(CNG(-1)) + C(5)*D(CNG(-2)) + C(6)
In this model, C(1) is significant.

The estimated VECM model specifying 3) is
D(CO2) = C(1)*( CO2(-1) - 0.679*CNG(-1) - 3.96) + C(2)*D(CO2(-1)) + C(3)*D(CO2(-2)) + C(4)*D(CNG(-1)) + C(5)*D(CNG(-2)) + C(6)
In this model, however, C(1) is not signifcant.

So the models results appear totally different. I am confused which model should I use? And if the first model with a signifcant C(1) is more appropriate, does that mean the long-run causality between CNG and CO2 is significant. I am asking this additional queastion because I am some unconfident about how to interpret the trend term "-0.0229*@TREND(31)" in the first model.

Thanks in advance!!

Van