time series regression

noetsi

Fortran must die
#1
I have many questions, which gets few takers - I cycle around to these every year or so, :p This is a comment by a well known time series author. I don't understand the point being made in honesty [what comes before this in the link below does not explain it to me]. Note that my interest is not primarily in forecasting when I run regression [I prefer univariate models for that because many argue they generate better results than multivariate results and in any case I have little theory to work from]. I am asked how one variable influences another over time, this is the only reason I run time series regression.

"We do not discuss statistical inference of the predictors in this book (e.g., looking at p'>p-values associated with each predictor). If you do wish to look at the statistical significance of the predictors, beware that any procedure involving selecting predictors first will invalidate the assumptions behind the p'>p-values."

That makes no sense to me, how can you not select predictors first? the quote is from the bottom of this link

https://otexts.com/fpp2/selecting-predictors.html
 

noetsi

Fortran must die
#2
Might as well ask my second question now. If you want to know how a variable influences another over time what is the best form of time series regression to use? I want to balance simplicity, robustness of method, and what you learn here as many time series models [VAR and Garch come to mind] are far to complex IMVHO :( I would use them only without another legitimate alternative.
 

Dason

Ambassador to the humans
#3
To respond to your first post - the point being made was that if you're doing something like stepwise selection it is dubious to look at the raw p-value for the predictors in the final model that you select.
 

noetsi

Fortran must die
#4
Thanks dason. The author suggests, admittedly in a text focused exclusively on predicting not the relationship between variables, that you don't drop variables out of your model even if not significant. Do you agree?
 

noetsi

Fortran must die
#11
Say you have a time series that is non-stationary. You want to know how X influences Y (effectively you have two variables over time). One possibility is to conduct ARIMA on both series (aka transfer functions) but that is very time consuming and requires the judgement that always is part of ARIMA (times two in this case one for each series). Judgement I am not confident I have.

Is there a simpler way to determine how X influences Y over time (possibly lags of X influencing Y) for non-stationary data that does not involve ARIMA? If so I really need to find it...quickly.