Timeline for Does a prediction interval have to contain the mean?
Current License: CC BY-SA 3.0
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| Mar 17, 2015 at 21:27 | comment | added | whuber♦ | Anotherdream, your reference to "start" suggests you have in mind a particular formula (which you have not disclosed), such as that for a prediction interval for a Normal distribution, which is constructed as an estimated mean plus or minus some multiple of an estimated standard deviation. When the distribution is highly skewed, then such a formula is altogether inapplicable. | |
| Mar 17, 2015 at 13:27 | comment | added | Anotherdream | Stephan. Your comment helps a BUNCH. I think this is what needs to happen in the future of these estimates. Really I think the problem is the mean was the wrong place to start with using such skewed distributions... But since they DID start here, I was confused with what I could do... Is it commonly 'acceptable' to use a median as a 'forecast point estimate' and give it bounds? I am very new to forecasting and am not sure if that is commonly done with skewed distributions.. | |
| Mar 17, 2015 at 7:28 | comment | added | Stephan Kolassa | +1, very nice point about a possible confusion about prediction intervals and confidence intervals. Incidentally, if you want to minimize the expected absolute error, you use the median of the predictive distribution as your point forecast (see here). This will of course always be included in a (central) prediction interval. | |
| Mar 17, 2015 at 2:06 | comment | added | jlimahaverford | I'm still having trouble interpreting the question. Let me be clear about what I'm looking for. I have a random variable X, and data {x1, x2,... xN}. I assume this 6 month rolling average is something along the lines of \sum_{j=i}^{i+180} x_i / 180. Something along these lines. As for what I meant about minimizing the absolute residuals, it's simply another objective function. While the mean minimizes the sum of the squared residuals, this does not necessarily minimize the absolute residuals, but some value (not necessarily unique) does. | |
| Mar 16, 2015 at 21:48 | comment | added | Anotherdream | To clarify my question a bit further. If someone took a 6 month moving average forecast, but had non-normal residuals in this estimate... Is it correct to create the forecast distribution by sampling from the residual distribution and adding the value to the Mean forecast point estimate, and then calculating the 95% prediction interval from the percentiles of this resulting distribution? Also, can you specify what else you might go with besides the "mean" if I wanted to minimize the absolute error in a given prediction for highly skewed data? Again I truly appreciate your help! | |
| Mar 16, 2015 at 21:39 | comment | added | Anotherdream | Thanks for the time jlimahaverfold. So if I understand you correctly is the following a true statement (I think I do, it just 'feels wrong' haha). If I had a variable where I was given a "point" estimate (using the mean), but the residuals were extremely non-normal (exponential for example) I could get the 'forecast distribution' by basically randomly sampling from the residual distribution 10k times (monte carlo) and then the newly created distribution would the forecast interval? I think this is how this should be done, but wwant to confirm i'm understanding correctly | |
| Mar 16, 2015 at 20:49 | history | answered | jlimahaverford | CC BY-SA 3.0 |