While parked up the speed trend vector is showing on the speed tape? But both throttles are closed.

I would guess it's likely to be wind gusts registering on the ASI.

I was thinking that too

According to http://www.b737.org.uk the "EADI speed tape trend arrow tip depicts the predicted airspeed with the next 10 seconds based on present airspeed and acceleration". 

So most probably the speed tape trend arrow is calculated through a combination of G/S (logic) and IAS (value) measurement.

 

The NGX shows a 5 kts speed "arrowhead" from 45 kts (lowest freezed value) to 50 kts as long as the head wind component is between 5 and 31 kts. (I just tested it while being lined up (position and hold) on a RWY): at or below 4 kts and at or above 32 kts the green arrow just disappears. IAS speeds above 45 kts are shown without a trend even in gusts...

I don't know if this arrow behaviour inside the NGX is correct and if it corresponds to the RW model.

 

Does anyone here know if this logic is correct? :blink:

I've never seen this in NGX or the real 737. I don't know the inputs for sure but I would assume there would be some inertial input for the trend vector. With no actual motion I would guess the vector should not appear.