Re: [R] Fourier Analysis and Curve Fitting in R
Rolf Turner wrote: On 26/01/2008, at 10:54 AM, Carson Farmer wrote: Dear List, I am attempting to perform a harmonic analysis on a time series of snow depth, in which the annual curve is essentially asymmetric (i.e. snow accumulates slowly over time, and the subsequent melt occurs relatively rapidly). I am trying to fit a curve to the data, however, the actual frequency is unknown. In general the actual frequency of the curve will indeed be close to 1/(1 year). However, because I intend to perform this analysis on many regions, this will not always be the case. This is perhaps an acceptable assumption however... Obviously there is something I am not understanding here. I would have thought that the ``actual frequency'' would be 1/(1 year) (period = 1 year) --- modulo the fact that the length of the year is constantly changing a tiny bit. (But I would've thought that this would have no practical impact in respect of any observed series.) My sampling interval is daily. What is your sampling interval, BTW? Day? Week? Month? I have been trying to follow the methods in Peter Bloomfields text Fourier Analysis of Time Series, but am having trouble implementing this in R. Yes it certainly would. Note that even though the ``actual frequency'' is (???) 1/(1 year), the representation of the mean function in terms of sinusoids will involve in theory infinitely many terms/frequencies since the mean function is clearly (!) not a sinusoid. Does anyone have any suggestions, or perhaps directions on how this might be done properly? Am I using the right methods for fitting an asymmetric curve? What I am really trying to do is fit a relatively smooth line to my data which will preferentially weight the larger values. This method needs to be able to fit through data gaps however, which is why I was originally looking to fit sinusoids. A jpg of a single year of the data is available here: http://www.geog.uvic.ca/spar/carson/snowDepth.jpg to give you an idea of the shape of my curve. Thank you again for your help, Carson I would have to know more about what you are *really* trying to do, and what the data are like, before I could make any useful suggestions. Many modelling issues could come into play, and many modelling strategies are potentially applicable. cheers, Rolf Turner __ R-help@r-project.org 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.
Re: [R] Fourier Analysis and Curve Fitting in R
well if you want to find the spectral density aka what frequencies explain most of the variance then I would suggest the spectral density. This can be implemented with spec.pgram(). This is conducted with the fast fourier transform algorithm. a-ts(data, frequency = 1) #make the time series with 365readings/365days ?spec.pgram and you should be able to take it from here This will give you the raw periodogram and the dominant frequencies after you smooth the periodogram. If your intention is to just fit a curve to your data there are many types of cuve fitting options moving average etc. What are you trying to do find the dominant periodicy? make a prediction equation? fit a smooth line? or... give us some more information and maybe we can help On 1/28/08, Carson Farmer [EMAIL PROTECTED] wrote: Rolf Turner wrote: On 26/01/2008, at 10:54 AM, Carson Farmer wrote: Dear List, I am attempting to perform a harmonic analysis on a time series of snow depth, in which the annual curve is essentially asymmetric (i.e. snow accumulates slowly over time, and the subsequent melt occurs relatively rapidly). I am trying to fit a curve to the data, however, the actual frequency is unknown. In general the actual frequency of the curve will indeed be close to 1/(1 year). However, because I intend to perform this analysis on many regions, this will not always be the case. This is perhaps an acceptable assumption however... Obviously there is something I am not understanding here. I would have thought that the ``actual frequency'' would be 1/(1 year) (period = 1 year) --- modulo the fact that the length of the year is constantly changing a tiny bit. (But I would've thought that this would have no practical impact in respect of any observed series.) My sampling interval is daily. What is your sampling interval, BTW? Day? Week? Month? I have been trying to follow the methods in Peter Bloomfields text Fourier Analysis of Time Series, but am having trouble implementing this in R. Yes it certainly would. Note that even though the ``actual frequency'' is (???) 1/(1 year), the representation of the mean function in terms of sinusoids will involve in theory infinitely many terms/frequencies since the mean function is clearly (!) not a sinusoid. Does anyone have any suggestions, or perhaps directions on how this might be done properly? Am I using the right methods for fitting an asymmetric curve? What I am really trying to do is fit a relatively smooth line to my data which will preferentially weight the larger values. This method needs to be able to fit through data gaps however, which is why I was originally looking to fit sinusoids. A jpg of a single year of the data is available here: http://www.geog.uvic.ca/spar/carson/snowDepth.jpg to give you an idea of the shape of my curve. Thank you again for your help, Carson I would have to know more about what you are *really* trying to do, and what the data are like, before I could make any useful suggestions. Many modelling issues could come into play, and many modelling strategies are potentially applicable. cheers, Rolf Turner __ R-help@r-project.org 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. -- Let's not spend our time and resources thinking about things that are so little or so large that all they really do for us is puff us up and make us feel like gods. We are mammals, and have not exhausted the annoying little problems of being mammals. -K. Mullis __ R-help@r-project.org 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.
Re: [R] Fourier Analysis and Curve Fitting in R
On 26/01/2008, at 10:54 AM, Carson Farmer wrote:
Dear List,
I am attempting to perform a harmonic analysis on a time series of
snow
depth, in which the annual curve is essentially asymmetric (i.e. snow
accumulates slowly over time, and the subsequent melt occurs
relatively
rapidly). I am trying to fit a curve to the data, however, the actual
frequency is unknown.
Obviously there is something I am not understanding here.
I would have thought that the ``actual frequency'' would
be 1/(1 year) (period = 1 year) --- modulo the fact that
the length of the year is constantly changing a tiny bit.
(But I would've thought that this would have no practical
impact in respect of any observed series.)
What is your sampling interval, BTW? Day? Week? Month?
I have been trying to follow the methods in Peter
Bloomfields text Fourier Analysis of Time Series, but am having
trouble implementing this in R.
Note that even though the ``actual frequency'' is (???) 1/(1 year),
the representation of the mean function in terms of sinusoids
will involve in theory infinitely many terms/frequencies since
the mean function is clearly (!) not a sinusoid.
Does anyone have any suggestions, or perhaps directions on how this
might be done properly? Am I using the right methods for fitting an
asymmetric curve?
I would have to know more about what you are *really* trying
to do, and what the data are like, before I could make any
useful suggestions. Many modelling issues could come into
play, and many modelling strategies are potentially applicable.
cheers,
Rolf Turner
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and provide commented, minimal, self-contained, reproducible code.
[R] Fourier Analysis and Curve Fitting in R
Dear List, I am attempting to perform a harmonic analysis on a time series of snow depth, in which the annual curve is essentially asymmetric (i.e. snow accumulates slowly over time, and the subsequent melt occurs relatively rapidly). I am trying to fit a curve to the data, however, the actual frequency is unknown. I have been trying to follow the methods in Peter Bloomfields text Fourier Analysis of Time Series, but am having trouble implementing this in R. Does anyone have any suggestions, or perhaps directions on how this might be done properly? Am I using the right methods for fitting an asymmetric curve? Any help is greatly appreciated, Sincerely, Carson __ R-help@r-project.org 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.
