[R] how to smooth timeseries without the lagging?

[stephen sefick]

Have you thought about fourier filtering?

here is some code that may help.

library(StreamMetabolism)
library(mFilter)
data(DOTemp)
#this makes it the same everytime

set.seed(100)

#making a time series with the frequency = 96
#reading in one unit in other words this is 15min data
#so there are 96 readings in one day this will make it
#easier to interpret, but feel free to put it on any scale that you would like

#this makes a time series with random noise added and this is what we
will remove starting at zero

x <- ts(rep(coredata(DOTemp[,"DO"]), 24)+rnorm(2304), frequency=96, start=0)

#fourier filtering

short.fft <- fft(x)

#so look at this plot and you can see that most of the power is one
day and below

plot(Re(short.fft), xlim=c(0,10), ylim=c(-1000, 1000))

#so now you know that you need to chunk out the higher
#frequencies to look at only the daily and longer signals,
#but just to be safe lets include 0-3 where most of the power seems to be
#the index values come from 3*96=288 and since the fourier transform
#is symetrical then you have to leave 288 observations on the
#other side also. So:

#first index
3*69

#to the second index (see above)
length(x)-288

short.fft[288:2016] = 0+0i

short.ifft = fft(short.fft, inverse = TRUE)/length(short.fft)

#so lets look at why we did this
par(mfrow=c(2,1))
plot(x)
plot(Re(short.ifft))

#and look at the spectrum
#most of the high noise garbage is gone.  If you want to
#get rid of more then please help yourself.

spectrum(short.ifft)

hth

Stephen Sefick


On Fri, Jul 24, 2009 at 10:44 PM, Michael<comtech.usa at gmail.com> wrote:
> Hi all,
>
> If I use a moving average, it will smooth the choppy time series, but
> it will lead to lagging...
>
> How do I smooth timeseries without the lagging effect?
>
> Thanks!
>
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-- 
Stephen Sefick

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