How to calculate that a value falls within a range given another value historically I have a forecasts for a specific variable and historical actual and forecast values for the same variable.
Let's say that my forecast for the next time period is X, what method can I use to calculate the probability that the actual value will fall within a range of 10% of X given historic performance?

If you have the probability distribution of $x_t$ given past observations, i.e. $p(x_t|x_{t-1}...x_0)$ you can calculate the probability that $x_t$ is between $0.9X$ and $1.1X$, i.e. within %10 of $X$. In most situations, this isn't readily available, and we estimate it along with some assumptions. There is no single method to do this, and the method of choice doesn't give any guarantees because your data is unique and nobody really knows its underlying distribution unless it's been artificially generated. Markov chains of some order is one simple method to achieve this. But, your forecast method may (not always) also give confidence intervals for your estimates.
