On 5/31/2011 5:12 AM, eddie smith wrote:
> Hi Guys,
>
> I had a monthly time series's data of land temperature from 1980 to 2008.
> After plotting a scatter diagram, it seems that annually, there is a semi
> sinusoidal cycle. How do I run Fourier's series to the data so that I can
> fit model on it?

       There are several methods.


             1.  The simplest would be to select the number of terms you 
want, put the data into a data.frame, and use lm(y ~ sin(t/period) + 
cos(t/period) + sin(2*t/period) + cos(2*t/period) + ..., data), 
including as many terms as you want in the series.  This is not 
recommended, because it ignores the time series effects and does not 
apply a smoothness penalty to the Fourier approximation.


             2.  A second is to use the 'fda' package.  Examples are 
provided (even indexed) in Ramsay, Hooker and Graves (2009) Functional 
Data Analysis with R and Matlab (Springer).  This is probably what 
Ramsay and Hooker would do, but I wouldn't, because it doesn't treat the 
time series as a time series.  It also requires more work on your part.


             3.  A third general class of approaches uses Kalman 
filtering, also called dynamic linear models or state space models.  
This would allow you to estimate a differential equation model, whose 
solution could be a damped sinusoid.  It would also allow you to 
estimate regression coefficients of a finite Fourier series but without 
the smoothness penalty you would get with 'fda'.  For this, I recommend 
the 'dlm' package with its vignette and companion book, Petris, Petrone 
and Campagnoli (2009) Dynamic Linear Models with R (Springer).


       If you want something quick and dirty, you might want option 1.  
For that, I might use option 2, because I know and understand it 
moderately well (being third author on the book).  However, if you 
really want to understand time series, I recommend option 3.  That has 
the additional advantage that I think it would have the greatest chances 
of acceptance in a refereed academic journal of the three approaches.


> I am really sorry for my question sound stupid, but I just don't know where
> to start.

       There also are specialized email lists that you might consider 
for a future post.  Go to www.r-project.org <http://www.r-project.org/> 
-> "Mailing Lists".  In particular, you might be most interested in 
R-sig-ecology.


       Hope this helps.
       Spencer Graves

> I am desperately looking for help from you guys.
>
> Thanks in advance.
>
> Eddie
>
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>
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-- 
Spencer Graves, PE, PhD
President and Chief Operating Officer
Structure Inspection and Monitoring, Inc.
751 Emerson Ct.
San José, CA 95126
ph:  408-655-4567


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