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:
- using the PC values time series, I modeled and created a forecast for each one separately.
- Next, 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.
Comments
Please sign in to leave a comment.