Elevation display way off

I normally don't view the elevation display on my Garmin GPS, but I turned it on during a recent road trip that took us over the Rockies. The readings were reasonably close to what I saw on road side elevation signs, and most of the time the reading goes up on climbs and down on declines, but in some cases the readings were going up when we were obviously going down hill. Not just a little bit, but hundreds of feet. Does anyone know why?

 

Depending on what device it is, perhaps try setting the elevation data field to GPS Elevation if it has that option, instead of just Elevation or Altitude.
I always find that much more accurate on the Garmin devices I have, if not on GPS Elevation they seem to use barometric pressure to calculate the elevation, which unless calibrated regularly, is usually wrong.
Being in a vehicle with closed windows can affect the pressure reading accuracy etc..
If it's not a device that has a barometric sensor then it might have just been poor satellite communication at the time.
Sometimes when I turn my devices on they will show the elevation hundreds of metres wrong until they get a good satellite fix.