I was hoping for some advice. I use SAS for automatic forecasting (I have a large number of forecasts to complete in a limited timeframe).
As part of the forecast output from SAS, I get a mid-point (median or mean), and an upper and lower confidence limit for each forecast. This is determined at a pre-specified level (i.e. 95%). Evidently, the confidence limits are derived statistically. I appreciate that within the upper and lower limits there is a range of potential forecasting results that could occur.
Based on my interpretation, values close to the upper and lower limits of the forecasts will be less likely because they depart a fair way from the mean/median and are close to the tails in terms of the distribution of possible forecasted values.
In a number of potential forecasting scenarios I face each month, I have a target the business needs to achieve by the end of the next financial year (june 30, 2012). I also have a forecast of the likely future value + upper and lower forecast limits for end of year (june 30, 2012) derived using moderate to long term historical performance. I need to quantify the probability of reaching a target given a forecasted result, using the point where the target is located relative to the mean/median and also the upper and lower forecast limits. For example, if the series has a mean forecast of 50, a LCL of 0 and UCL of 100 and the target is 75, I need to quantify the probability this target will be met at June 30, 2012.
It seems to me I can use the fact the target of 75 falls on the 75th percentile relative to the forecast upper and lower forecast limits.
- Is it fair to say that there is a 25% chance of hitting the target under an assumed uniform distribution?
- Or is it more appropriate to assume the forecast series within the upper and lower limits is normally distributed with a greater concentration of values in the CDF closer to the mean?
- Or is this model dependent (i.e. different for arima and esm models)
Also, as a rule of thumb how many holdouts do people use for
- a series with 12 months (I am using 10% or 1)
- a series with 24 months (I am using 10% or 2)