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The main steps of forecasting are:
Formulate the problem or question. Also decide what is the degree of accuracy needed? For example, do you want to land the Apollo 11 on the dark side of the moon or land it on a 8x8 foot piece of a titanium rock inside a specific crater. What does success look like?
Obtain information. It could be judgmental (ie. doctor opinions) or statistical (ie. data based) etc.
Select the best method of forecasting based on what you get in number 2 in the CGM case it is the Auto-regressive model.
Implement the method.
Evaluate the method (does it hold true? and under what conditions/thresholds), then test it or model it and also calculate the maximum likelihood.
Test the forecasts in the real world and then share the forecasts
Extrapolation in math is the process of finding a value beyond a set of given values. You most often have to use extrapolation when you have to find the relationship of values or next values in a sequence. Extrapolation techniques have a higher probability of success in short time horizons and in a stable model. We thus are limited to how far into the future we can predict blood glucose values. Also the better you manage your carb counting and insulin the better the predictions will be as this creates a less volatile system. One key to extrapolation is to know your error rate and adjust accordingly. Data smoothing and filtering can also be used:
Here is a link to a great article on the principals for forecasting http://repository.upenn.edu/cgi/viewcontent.cgi?article=1146&context=marketing_papers