How true is that Dave Giles? "Non-linear Functions of Non-Stationary Data Can be Stationary"

What will happen if you do a non linear transformation to non-stationary data? Dave Giles help us understand the obvious but important aspects of data transformation, in particular a Sin - Cos transformation. 

Nevertheless, besides the matematical and statistical usefulness of data transformations, the econometric foundations and analysis is often forgotten. There is no way you can explain economically those graphs to Kids, Mr. Giles. That why econometrics is a different from the others, where the "econ" prefix, must never be kept aside. 

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