Hmm, thanks Paul, yes that's a good point. I do indeed hope to quantify relative influence, rather than simply successfully predict (or hindcast) measured values. Ultimately I hope to estimate what conditions would have been like, had driver values been different.
I had come across the ARIMA method in my reading around, but I hadn't even been sure that it could handle an independent variable distinct from its dependent variable. I need things really dumbed down before I can take them in.
I'm thinking probably econometrics is going to include methods pretty close to what I want to achieve, but wondered whether there might be anything in climate modelling that was statistical rather than numerical (mechanistic, PDE whatever you want to call it) in nature.
Further complexity is that the integration period for an independent variable I1 may vary over time, and may be dependent on the value of another independent variable I2. There may by lags between independent variables and the dependent variable, these lags might be different for different IVs, and they may vary over time, dependent on values of IVs.
As a first stab I divided the data in several contrasting sets, with driver values greater or less than an arbitrary threshold, and tested for a difference between the dependent values of those two sets.
It's such a comprehensive dataset, I really feel like I owe it a thorough investigation!
On Jan 27, 11:33 am, Paul <parubi...@gmail.com> wrote: > There are a variety of potential issues with this sort of decomposition. The first that comes to mind is that by "detrending" the response variables, you may be washing out some of the effect of the predictors. If X (predictor) has a trend and Y (response) depends on X, then is the trend you see in Y a response to the trend in X, is it an intrinsic trend in Y, or a mix? (I suspect this is more of a problem if you are trying to prove significance of X as a predictor of Y, or estimate regression coefficients, than if you are just trying to forecast Y.) > > For a single predictor (simple regression), I'd be tempted to use an ARIMA transfer function model. I'm not sure if transfer functions generalize to multiple predictors (it's been years since I looked at time series methods). > > Paul