## 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:

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

- Compute the average ($\bar x$) and the standard deviation ($s$)of each series.
- Multiply the forecast value (in the standardized form) by the standard deviation (step 1).
- 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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