Variables of interest in regression are different manipulations of same time series data - is collinearity a problem?

by E. Wade   Last Updated September 10, 2018 19:19 PM

I am working with time series data and would like to test two different forms of operationalizing patterns in these data. I am specifically interested in a measure of instability (specifically mean squared successive difference, or MSSD) and a measure of inertia (specifically autocorrelation). I have theoretical reasons for thinking both of these metrics may be associated with a personality variable in my dataset (i.e., other literature in the field suggests these are related to similar outcomes). These metrics (MSSD and autocorrelation) are different but show both conceptual and mathematical overlap (i.e., higher MSSD is often associated with lower autocorrelation) but I don't expect them to be perfectly correlated in my data.

I want to see how my personality variable predicts both measures of instability (MSSD) and inertia (autocorrelation). I have theoretical reasons for wanting to test them both. I want to acknowledge/account for the fact that MSSD and autocorrelation are not independent (they are derived from the same time series data). I thought of using a covariate, but this is complicated because: 1) I expect the thing I would include as a covariate to be related to my outcome rather than my predictor (i.e., I would want to test if my personality trait predicts MSSD, controlling for autocorrelation), which seems backwards, because MSSD here is the outcome, and 2) regardless of #1, I don't know if it violates the no multi-collinearity assumption of regression to enter both MSSD and autocorrelation in the same regression equation.

Is there a model I'm missing that would allow me to test what I'm getting at here (i.e., understand how the non-independence of MSSD and autocorrelation affect my results, so as not to over-estimate the amount of variance accounted for)? Should I just run two separate regression models (#1: does personality trait predict MSSD; #2 does personality trait predict autocorrelation), without doing anything more?

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