R help - Mar 2007 - Linear model and time series

Dear all,

I have three timeseries Uts, Vts, Wts. The relation between the time
series can be expressed as

Uts = x Vts + y Wts + residuals

How would I feed this to lm() to evaluate the unknowns x and y?

Thanks,
andre

On Sat, 31 Mar 2007, Andre Jung wrote:
> Dear all,
>
> I have three timeseries Uts, Vts, Wts. The relation between the time
> series can be expressed as
>
> Uts = x Vts + y Wts + residuals
>
> How would I feed this to lm() to evaluate the unknowns x and y?
If the time series are aligned (and univariate) you can just do
  lm(Uts ~ Vts + Wts)
If not, have a look at the "dynlm" and/or "dyn" packages.
Z
> Thanks,
> andre
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>

This question is not as simple as might appear.  As the data are time
series one should be very concerned about the distribution of the
residuals,   Are the series stationary and if not are they integrated
of the same order and cointegrated.  The danger of spurious results is
a very live issue. As an example the attached data file contains two
series.   The file cpi.csv contains data on the log of the Irish CPI
for the period 1957 Quarter 1 to 2006 Quarter 2.  It also contains
data on a variable c which has been proposed as an indicator of the
level of the CPI.  If you complete the regression using lm() you will
get an apparently good answer.  In effect the variable c is cumulative
rainfall in Armagh from 1857 Quarter 1 to 1906 Quarter 2.  Despite the
favourable regression results there is obviously no relationship
between the variables.

My recommendation to Andre would be to study a good book on
time-series analysis.  One is not doing him a favour by recommending a
procedure to him that may lead to spurious results when not applied
properly.

Best Regards

John Frain

On 31/03/07, Achim Zeileis <Achim.Zeileis at wu-wien.ac.at>
wrote:
> On Sat, 31 Mar 2007, Andre Jung wrote:
>
> > Dear all,
> >
> > I have three timeseries Uts, Vts, Wts. The relation between the time
> > series can be expressed as
> >
> > Uts = x Vts + y Wts + residuals
> >
> > How would I feed this to lm() to evaluate the unknowns x and y?
>
> If the time series are aligned (and univariate) you can just do
> lm(Uts ~ Vts + Wts)
> If not, have a look at the "dynlm" and/or "dyn"
packages.
> Z
>
> > Thanks,
> > andre
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
> >
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 
John C Frain
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.html
mailto:frainj at tcd.ie
mailto:frainj at gmail.com

On Sun, 1 Apr 2007, John C Frain wrote:
> This question is not as simple as might appear.
But it might as well be - I try to answer the questions people ask instead
of guessing what they wanted to ask but did not.
> As the data are time
> series one should be very concerned about the distribution of the
> residuals,   Are the series stationary and if not are they integrated
> of the same order and cointegrated.
<snip>
> My recommendation to Andre would be to study a good book on
> time-series analysis.  One is not doing him a favour by recommending a
> procedure to him that may lead to spurious results when not applied
> properly.
All the points you raise above are valid, of course, but note that I did
not "recommend" a procedure. The original poster wrote down a linear
model
that he wanted to estimate by OLS (aka lm()) and I just told him how he
can do that conveniently in R.

Whether or not the linear model is appropriate in this situation (and
there are time-series relationships where it is) I cannot say - but,
contrary to you, I assume that the poster knows what he is doing.

Z