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I have access to forecasts produced using the methodology outlined in the following document, essentially to produce a forecast a linear regression against noon effective temperature (0.57 * noon temperature today + 0.28 * noon temperature yesterday + 0.15 * noon temperature day before that) and day of week. The regression is applied with regression coefficients varying according to season, day type etc. After the regression various transformations are made according to industry data, so the forecasts are no longer straight regressions. Therefore the independent and dependent variables are not available.

Upon analysing the forecasts, the errors are clearly autocorrelated, with the Durbin-Watson test coming out at 0.2 for one month's data.

My question is, since the forecasts are not produced using a straight regression (and I have no access to the code producing the forecasts), is it possible to remove autocorrelation using only the forecasted values, the actuals and the errors? I'm sure it is possible, but most of the textbooks deal with the idealised cases where all data is available and it's a pure linear regression.

https://www.elexon.co.uk/documents/training-guidance/bsc-guidance-notes/load-profiles/

Thanks for any help you can offer on this issue.

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I will try to go wild on this but i will based my "thing" on what is done with boosted methodology.

You just use your errors as explanatory variables for the predictions made, for example a model like this yt = b1*error in t + b2*error in t-1 and it could work to correct autocorrelation in your residuals of this new regression.

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