Dear Professor Mean, I have two time series of data, one actual and one predicted. Since I'm quite new to statistical methods, I would like to know what methods are used to evaluate the different between the two time series. I would like to able to say something like "the predicted values were 70% accurate."
See what others in your area are doing and emulate them, as there is no one measure that is used uniformly. Most formulas are based on the residual.
To compute the residual, subtract the predicted value from the actual value. The residual is used in many statistical models, not just time series. Then there are several statistics that you can compute on the residuals. The simplest is the standard deviation of the residuals. Another possibility is the average absolute residual. The closer that these values are to zero, the better your prediction.
If you are interested summaries that represent a percentage, you might want to consider a relative measures such as the absolute residual divided by the actual time series, as long as the actual time series is never zero or negative. This would give you a percentage error.
Another possibility is to compare the residuals from your prediction to a much simpler prediction (for example, a prediction that uses the mean for every single value). Then the ratio of the variances (the squared standard deviation) of the two predictions is a measure of how well your predictions are doing. Place the variance of the simpler prediction in the denominator. In linear regression, this is known as R-squared or multiple R-squared depending on the context, but it should also work for time series data.