correlation coefficient between weather data and power consumption I have power consumption and the corresponding temperature data for one year, that is, for several weeks (week1, week2,..., week48) as one month has 4 weeks. I want to forecast power consumption for a month.

Forecasting power consumption means forecasting 4 weeks(a month has 4 weeks). I am using Ms excel to obtain the pearson correlation coefficient. The power consumption data and temperature data have a strong correlation of 0.8 for week1 to week48, that is, they have a good correlation for one year. One year means over a large time interval.

But over a small time interval, for eg, correlation b/w power consump and temperature for 12 weeks (3 months) is weak (0.2). I want to use a neural network with window size of 3 to represent 12 weeks(3 months) to forecast the next 4 weeks(next month).

My question is: since the power data and temperature data has good correlation(0.8) for 48 weeks(1 year) but weak correlation(0.2) for 12 weeks(3 months), is it possible to use a neural network with window size of 3 as mentioned above to predict the power consumption for the next month with input variables power data and temperature data?
I am not very sure how effective NN would be for this problem. The way I see it is that you have 48 entries in a time series and now you are trying to predict the next 4. Keeping aside the correlations for a second, it seems like there is very little data to "learn" from. I mean the power consumption is a seasonal thing (much like temperature) but you have only 1 years data so it should be difficult for NN to capture this seasonality. 

I would like to raise another point about the way you are using correlations. If you are taking correlations using the actual temperature value then I do not think that to be a good idea. Think of it in this way, I would be using a lot of power at both very high and very low temperature. So instead of using the raw temperature values, I should normalize them with respect to some "comfortable" temperature value by taking the absolute difference between the actual temperature and the "comfortable" temperature. 

For instance, let us say that "comfortable" temperature is 25C, then both 5C and 45C would be normalized to 20 and this looks more plausible as my power consumption should be high in both the cases. This might also explain the poor correlation that you observe for 3 months of data. What should be the "comfortable" temperature is an entirely different story altogether. 

Do let me know if this line of thought makes sense.