Transforming standardized values to non-standardized values

Question

I have a question related to a PCA. It involves the target or desired value and projected forecast:

  • The PCA gives excellent PC Values, but they are centered around zero since they are standardized.
  • All desired/target values are positive since the markets only have positive values.

What I did is: (1) using the PC values time series, I modeled and created a forecast for each one separately. Next, (2) Using the loadings (weights) and the PC forecast values, I computed each input variable's corresponding values, but the values are standardized. My question is how to transform standardized predicted values back to ordinary non-standardized forms? Maybe use Excel functions?

Answer

Standardization is done by subtracting the average and dividing the difference by the standard deviation.

$$y_i = \frac{x_i - \bar{x}}{s}$$

To reverse the effect:

$$ x_i = y_i \times s + \bar{x}$$

  1. Compute the average ($\bar x$) and the standard deviation ($s$)of each series.
  2. Multiply the forecast value (in the standardized form) by the standard deviation (step 1).
  3. Add the average (computed in step 1) to the product (computed in step 2).

This should take care of the scaling (de-standardization) issue. You can do this in Excel using STDEV(.) and AVERAGE(.) functions.

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