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# Re: st: How to find the best transformation for each variable in 120 periods

 From "JVerkuilen (Gmail)" To statalist@hsphsun2.harvard.edu Subject Re: st: How to find the best transformation for each variable in 120 periods Date Fri, 22 Feb 2013 12:28:39 -0500

```On Fri, Feb 22, 2013 at 10:40 AM, Xixi Lin <winnielxx@gmail.com> wrote:
> Hi JVerkuilen,
>
> You are right that the key assumption is Gaussian errors, but my data
> does not have Gaussian errors, and I wanna use t statistics, so I
> wanna to fix the non-normal residuals by transforming the variables (I
> don't know what else to do to fix the Gaussian errors). Is there any
> better way to deal with it? Or Is there any papers that I can read
> about it?

Well as I said, the Atkinson book is excellent. What's the nature of
the non-normality? Outliers? Are they symmetric? You can't really
decide this without thinking of what the likely problems are.

The inverse hyperbolic sine is an under-used transformation for
long-tailed data with zero or negative values. It was originally part
of the Johnson system of distributions, which are based on
transformations of the Gaussian. It behaves like the log for large
magnitudes and like the square root for smaller ones.

Burbidge, John B., Lonnie Magee and A. Leslie Robb. 1988 "Alternative
Transformations to Handle Extreme Values of the Dependent Variable."
Journal of the American Statistical Association, vol. 83, 123-127.

http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/07/a-rant-on-inverse-hyperbolic-sine-transformations.html
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