I'm looking to use a multivariate regression for prediction, but making use of (possibly) superior estimates of variance for both the independent and extraneous variables.
My approach is to standardize the dependent and extraneous variables (by dividing their respective standard deviations derived from the full data history). Once I have the standardized regression coefficients, I use these, together with my separately sourced variance estimates, to get back to an equation that will be used for generating the predictions. Do I simply multiply each coefficient by my separately sourced variance estimate? But what about the dependent variable variance estimate?
As background info, my separate sourcing of variances estimates is because I believe I have better (more up-to-date) estimates than available from the full data history (let's say, because the variances aren't stable through time, I can estimate a more timely measure of variance using higher frequency data over a shorter, recent period).
- Is this approach a sensible standard practice?
- How to go from the standardized betas, to un-standardized ones using the high frequency variance estimates?
I read here (http://stats.stackexchange.com/questions/29781/when-should-you-center-your-data-when-should-you-standardize) about WHEN to standardize, but not clear to me if this covers the case of standardizing both dependent and extraneous variables.