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time series multiple regression
Posted:
Jan 25, 2012 9:02 PM
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Gday
Maybe you can comment on the validity of my approach.
I've got a multiyear timeseries data set, which I have reduced to
daily resolution by averaging. Data are environmental /
meteorological / oceanographic. I'm hoping to isolate the effects of
various meteorological drivers on oceanographic response(s).
Understanding that consecutive samples are not independent, I was
stumped for some time, avoiding standard linear regression. Is this
alternative approach better? Is it better enough to be acceptable?
I fitted an annual signal to each variable, using GAM from the mgcv
package in R. Where the gam fitted a smooth unimodal signal that
explained a decent amount of the total variation, I took forward the
residuals of that model to use as the "detrended" variable. Both for
the drivers, and the response(s).
I then use standard multiple linear regressions, with detrended
drivers (gam residuals) to predict detrended response (gam residuals).
I achieved R squared values for these detrended linear models of
roughly 0.5 for half a dozen models (predicting oceanographic
properties closest to the sea surface), down to 0.13 (for predictions
at greater depth in the sea). I can increase the R^2 from 0.13 to 0.2
if I allow lags in the time series.
If I then make predictions of the seasonal fluctuation using my gam,
and add these to predictions of the non-seasonal, detrended (residual)
values using the linear models, I get correlations of 0.95 to the
measured data. (Note I did not separate training and test data, and
n= 2191).
Thoughts?
Eric Goodwin
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