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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.

enter image description here

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:

  1. estimated the model up to month 40 using holt winters.
  2. generated forecast errors for months 41-52 using =NORMINV(RAND(); 0; st dev of errors) formula, where 0 is the mean error)
  3. added the simulated error to my one-step forecast for months 41-52 to get simulated actuals.
  4. ran the macros to generate a 1000 new sets of simulated actuals for months 41-52
  5. used =PERCENTILE function to select 0,975 and 0,025 bounds
  6. 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!

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    $\begingroup$ One has to suspect either some coding error in the spreadsheet or a mismatch between the statistical models underlying the CI and the MC calculations. In the absence of any information about the details, though, how could we do more than speculate? Could you provide more explanation about precisely what you have done, or illustrate the results? Give your readers something to go on so they can help you. $\endgroup$ – whuber Jun 19 '15 at 13:02
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    $\begingroup$ The picture makes it obvious there is an error in the CI calculation. $\endgroup$ – whuber Jun 19 '15 at 13:43
  • $\begingroup$ @whuber thank you for your comment. I have attached a picture of my forecast. To be more precise about what I did: 1) estimated the model up to month 40 using holt winters. 2) generated forecast errors for months 41-52 using =NORMINV(RAND(); 0; st dev of errors) formula, where 0 is the mean error) 3) added the simulated error to my one-step forecast for months 41-52 to get simulated actuals. 4) ran the macros to generate a 1000 new sets of simulated actuals for months 41-52 5) used =PERCENTILE function to select 0,975 and 0,025 bounds 6) ploted the area chart $\endgroup$ – mkuser_23 Jun 19 '15 at 13:50
  • $\begingroup$ That is important information: could you please edit your post to include it prominently? $\endgroup$ – whuber Jun 19 '15 at 13:58
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You derive your confidence intervals from errors that you simulate from your optimized minimum error and by assuming the mean of erros to be zero. If your confidence interval is not conforming to your forecast line then this could either be due to non-zero mean or be due to non-normal distributions of errors in the past and hence in the future also. Check whether your past errors were normal or not. I believe if u are using Holt Winters' then you already would have been correctling for autocorrelation. So besides that, the only thing I can figure out is non-normal distribution of errors which may demand then to try non-linear base model than linear ones. In which case you would have to change your one step forecast formula from linear function to non-linear function.

P.S. I am assuming there are no coding errors, for which I am not an expert.

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