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I am trying to normalize prices based on the (median, MAD) transformation. I attach a image below describing it in comparison to the (mean, std) normalization.

I have trouble underatanding if b should be based on the whole sample, or just on the calibration window. In the (mean, std) it says that both a and b are calculated by the window, but for the (median, MAD) it is more unclear.

Throwing this out there to see if someone knows this or if they know how to interpret the text.

Thanks. enter image description here

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    $\begingroup$ What is the reason for normalization? $\endgroup$ Dec 9, 2022 at 14:33
  • $\begingroup$ @FrankHarrell To decrease the severity of positive and negative price spikes. Transforming values far from a in logarithmic way while values close to a are transformed close to linearly. $\endgroup$ Dec 10, 2022 at 13:21
  • $\begingroup$ A robust analysis is a better approach than that in my opinion. And for those rare occasions where pre-transformation is recommended, consider transformations such as the cube root which allows zeros and negative values. $\endgroup$ Dec 10, 2022 at 14:26
  • $\begingroup$ Thank you for that information. This is not a question whether or not this transformation is recommended, it is only a question on how to interpret a and b, given this information. I am following the recommendations of leading research within my field, and this (medan, MAD) transformations is used together with the "area inverse hyperbolic sine" (asinh) transformation. $\endgroup$ Dec 11, 2022 at 10:43

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