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 >>
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