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I am doing a regression on time series data. I have 60 lagged predictors which I will call x to predict a continuous variable y. I used the BoxCox function from the forecast package to transform y and then performed a linear regression of y on x. I did a one step ahead forecast over 5.5 months of data and found that the BoxCox function made the forecast error worse. I am using mae and rmse as critera for accuracy

It was better to simply perform no transformation. I am trying to reconcile this because I learned BoxCox in school and it was grilled into our heads that it is necessary to do but now it seems like it is a waste of time. Is my approach and conclusions about BoxCox right, or is simply that my data cannot benefit from BoxCox?

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  • $\begingroup$ Your comment "I learned BoxCox in school and it was grilled into our heads" probably means that you were probably trained as an econometrician whom generally start with a model before they see the data rather than vice-versa or somewhere in between. Transformations are like drugs ... some are good for you and some are not. Please review stats.stackexchange.com/questions/18844/… for discussion that I think is relevant. $\endgroup$
    – IrishStat
    Commented Jan 16, 2016 at 14:41
  • $\begingroup$ BoxCox is a wonderful transformation because it encompasses wide range of transformation such as log, reciprocal, square root, cube root and more importantly $ \textbf{no transformation}$. So if you user BoxCox transformation on the time series procedure correctly and if it doesn't require transformation, then box cox procedure should have recommended no transformation $\endgroup$
    – forecaster
    Commented Jan 16, 2016 at 15:50
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    $\begingroup$ Ahhh .. But the statistical requirements are on the errors from a model and not the original data.thus transforming the original series can easily lead to a false positive conclusion (other than a Box-Cox lambda of 1.0 ) as the original data has not been conditioned on a useful equation ( other than a simple mean model ) . What I am saying here is that you can easily get a false (Box-Cox coefficient reading by analyzing the original data. $\endgroup$
    – IrishStat
    Commented Jan 16, 2016 at 17:11
  • $\begingroup$ @forecaster ...thus it is not a placebo i.e. no downside effects as you are stating but a possibly (probably !) a rather dangerous (false) alternative to a useful model thus confounding/confusing the subsequent model identification phase $\endgroup$
    – IrishStat
    Commented Jan 16, 2016 at 17:28
  • $\begingroup$ .... see stats.stackexchange.com/questions/8955/… and review @probabilityislogic superb comments about when and why to transform . $\endgroup$
    – IrishStat
    Commented Jan 16, 2016 at 18:04

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  1. It's difficult to respond to whatever you were actually taught because you don't give us access to it. If you had a quote or a reference or something...

    I would be surprised if "Box-Cox is necessary" would have been presented as a general, unbending rule.

  2. You present nothing of the criteria by which you judge the forecasts, but if, for example you use MSPE on the original scale (i.e. you transform back then measure performance using square error loss in predictions), then even when the Box Cox leads to exactly the right model you might still on that basis conclude it was worse.

  3. Box Cox has parameters (at least 1, depending on what your model is and what you consider for transformation), so - as with adding parameters anywhere else - it may sometimes be advantageous and sometimes not -- even when it leads to the "correct" model it may lead to actually worse predictions, measured on either the original or the transformed scale.

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  • $\begingroup$ Sorry I forgot to add, I am using mae and rmse as critera for accuracy. $\endgroup$
    – Hidden Markov Model
    Commented Jan 13, 2016 at 1:14

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