Relating the power to weather variables Could you please help me in this problem?
I have 3 independent variables, (T,H,t) , as inputs and one output P  ( I have all data for these inputs and the output, done experimentally measured every hour during one year).
I want to find a formula of this form: P=f(T,H,t)  where t  is the time in hours and it is always in the x -axis (index), T  is temperature, H  is humidity, and P  is power.
I have all the data, and when I draw them in the same graph during one year, meaning that P , T , and H  vs. hours. I found that the behavior of P  is oscillating, making a sinusoidal shape over the entire year:

So, if I make a zoom view to this figure, for example from the 2000 th hour of the year to the 3000 th hour, it is clear that it almost has the same shape but it is oscillating.
So, it keeps oscillating and increasing up to the peak point and then it starts decreasing till the end of the year.
So, how can I predict the structure of the formula that relates P  with T , H , and t ?
What is the effect of T,H and t on P .
Is there any approach that you advise me to follow?
Sorry for this long question and any help from you is highly appreciated. I read many papers but I could not know how to solve the problem.
 A: *

*You can train some Neural Networks with your data and then use them for predictions afterwards.

*You can use interpolation techniques to arrive at approximate formula from your data.

*One cool idea is to try applying models used in Algorithmic Trading for prediction from data.


EDIT:
From the graph it looks like
$P \propto T$ 
$P \propto \frac{1}{H}$
It can also be noted that power is not very sensitive to changes in humidity but is highly correlated with changes in temperature. 
A: Yes. I think we are missing something here. It might help if we knew what he means by power. If it is power consumption for heating and cooling a city, we can make some gueses as to plausible parameterizations. I'm assuming his hours are hours of the year (8760 hours/year), but then humidity doesn't seem right to me, it should rise at night and be at a minimum during the afternoon (but maybe these are a 24hour averages?). If is is heating and cooling, then t is a proxy for the amount of sunlight available, but it would be much better to have that as an independent variable as it is probably quite important (and quite variable depending upon cloud cover). 
