[jeramey]

Persistence and linear regression are very common methods used to extend forecasts out in computationally cheap ways. Most forecast models have really awful validation statistics after about 48-60 hours out—depending on initial conditions, location, and a few other factors—so in some sense the forecast after about 3 days out isn't ever going to be very good so it's perfectly valid to use those methods. I would not be at all surprised if that's what Weather Underground does.

Another method that's occasionally used is to just fill in with TMY (Typical Meteorological Year) data. Lots of those data sets are freely available, or if not, are very inexpensive to calculate if station data is available.

If you're looking for a minimally spammy, information dense forecast and you're in the US, it's pretty hard to beat weather.gov. (And make sure to occasionally read the zone and regional forecast discussion texts, too. They're really interesting and often educational!)