Further to the above:

(i) The simulated fcast's not within the PI's are not visible using a fan chart (I did say however I would like a plot to have an idea of the area or size of the forecast probability distribution), but they are using the normal graph and listing the fcasts individually for NCount<<a very large number, although I could list them...

(ii) If the actual ur had been transformed to logs, lur, exp'ing trendmean would result in median forecasts rather than mean forecasts. Correct? If so why? And therefore how to calculate the mean forecasts after back-transformation?

(iii)

Also, I have noticed from an MC simulation:

The PI's (standard calculation, assuming normality)

- Code: Select all
`set res_M fstart fend = sum/NCount; * sum is calculated from fcast`

set res_SE fstart fend = sqrt(res_MSS-(res_M)^2)

set L95 fstart fend = res_M+%invnormal(.025)*res_SE; * 95%

set L80 fstart fend = res_M+%invnormal(.1)*res_SE; * 80%

set U80 fstart fend = res_M+%invnormal(.9)*res_SE; * 80%

set U95 fstart fend = res_M+%invnormal(.975)*res_SE; * 95%

are different to these PI's

- Code: Select all
`set fcast025 fstart fend = work=%xt(fcast,t),%fractiles(work,||.025||)(1); * 95%`

set fcast100 fstart fend = work=%xt(fcast,t),%fractiles(work,||.100||)(1); * 80%

set fcastmean fstart fend = work=%xt(fcast,t),%avg(work)

set fcast900 fstart fend = work=%xt(fcast,t),%fractiles(work,||.900||)(1); * 80%

set fcast975 fstart fend = work=%xt(fcast,t),%fractiles(work,||.975||)(1); * 95%

whilst the averages, res_M and fcastmean are the same.

Which method to use?

For the above calculations, the series is in logs, and I would like to back-transform.