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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