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Is it ever better to use ordinary least squares (OLS) over weighted least squares (WLS)? If a model is fit well by OLS, will I get worse results if I use WLS instead?

Obviously, OLS is faster, but who cares if it takes an extra 5 minutes.

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If the variance of the errors from a sarmax model evident a determinstic change at one or more points, this can't be easily ignored and needs to be rectified thus Weighted Least Squares a particular form of GLS is in order..as was discussed in Is this method to make data approximatly stationary valid?

Worst in what sense ? hypothesis testing ? prediction limits ? mape computation for a specific # of withheld values ? It would all depend !

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  • $\begingroup$ I'm looking for an example of where the MAPE of OLS < MAPE of WLS. $\endgroup$ – Frank Jun 19 '19 at 23:19
  • $\begingroup$ based upon the fitted values or some out-of-sample values ? $\endgroup$ – IrishStat Jun 20 '19 at 0:40
  • $\begingroup$ out of sample values $\endgroup$ – Frank Jun 20 '19 at 0:43
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    $\begingroup$ out of sample mape doesn't change because the modelparametrs don;t change because the values that are under-varianced so to speak simply get adjusted proportionally . The signal remains the same ... what does change is the test of significance for each parameters a a result of normalizaton suggested by TSAY $\endgroup$ – IrishStat Jun 20 '19 at 15:05
  • $\begingroup$ So, are you saying weighted least squares never performs worse than ordinary least squares, when it comes to mape of out of sample data? Would least squares fit data better than weighted least squares in any metric that you know of? Because, I think this would mean I should fit weighted least squares over ordinary least squares in every case (When not concerned about speed). $\endgroup$ – Frank Jun 20 '19 at 16:53

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