ARMA and the need for log()

[Nadine]

hi everybody

i´m trying to understand an ARMA model which was used to describe the production of solar energy in Germany.
basis is the date of 2011 and 2012. lets call the series “input_pv”. here is the graph to visualize the data: http://imgur.com/n4B1HSh
as you can see the range is from 0 to 16,000 MW.
now there is a model with a few arma terms and some dummy variables (month and hour). if i use input_pv as dependent variable i get this result: http://imgur.com/hjmuUIl
if I try doing a forecast I will get negative data which is not possible in reality. of course the high values of the coefficients are responsible.
BUT if I use log(input_pv) as dependent variable i get this result: http://imgur.com/Y2p91D8
this one leads to realistic results.
Now my question is why. Why am I only getting a realistic result if I use the log. What is line of thought behind that step?
Thanks for your help

edit: thx for moving

[trubador]

In the first case, the model is: y = a + bX + u, which does not guarantee a positive result.
In the second case, it is: y = exp(a + bX + u), which ensures a positive outcome.