I used holt winters in excel to forecast 12 moths ahead based on 40 months of historic data. Then I ran a monte carlo simulation to create 1000 scenarios and computed upper and lower bounds to create a 95% interval for each of the forecasted 12 months. The problem is that, when graphed, the forecast is above 95% confidence interval for 10 out of 12 forecasted moths, which doenst make sense to me.
A thing to note is, when data are de-seasonalised, I could observe a steady downward trend with sudden and rapid increase in month 40. I believe, due to holt model nature, the higher weight given to preceeding month made the forecasted values go up in months 41-52.
To be more precise about what I did:
- estimated the model up to month 40 using holt winters.
- generated forecast errors for months 41-52 using =NORMINV(RAND(); 0; st dev of errors) formula, where 0 is the mean error)
- added the simulated error to my one-step forecast for months 41-52 to get simulated actuals.
- ran the macros to generate a 1000 new sets of simulated actuals for months 41-52
- used =PERCENTILE function to select 0,975 and 0,025 bounds
- ploted the area chart
My question is, why did a simulated confidence interval did not follow the forecasted values? Was it influenced by "inertia" of the overall historic trend? Thank you!