I have seasonal data from which I create forecasts. The steps I perform are: deseasonalizing the data, finding the linear regression for the deseasonalized points, predicting a few points from the linear regression and adding seasonality to the predicted values to get forecast data. My input is quite sinusoidal so all works well.
The problem is that the more in the future you predict, the more prediction errors increase. I'd like to show that on a chart, but I am not sure how to calculate these errors. I was thinking something like prediction interval bands for forecast data (whatever they are called). These bands would increase the further you predict in the future.
Here are some images that show what I'm trying to do: sample bands image1 sample bands image2
My question is what is the name for these bands? (then I can do a google search for it) I'd also appreciate the formulas needed for the band calculations. I'm guessing there is a standard deviation in there somewhere.
I've looked at confidence interval, but that seems to be for the data already present, not for the forecast data.