[R] Simple spectral analysis

[Earl F. Glynn]

"Georg Hoermann" <georg.hoermann at gmx.de> wrote in message 
news:45A33EBC.3050503 at gmx.de...
> Peter Dalgaard wrote:
>> Earl F. Glynn wrote:

> Thanks a lot for the help. I will post the script when its ready
> (an introduction for our biology students to time series, just 8 hours)

I've been working with one of our labs here to find "cyclic" genes from 
microarray data.  The supplement for the paper we published is here (I 
haven't bothered making the code general enough for a package yet):

http://research.stowers-institute.org/efg/2005/LombScargle/index.htm



Normally we only have about 20 to 50 points in our time series for each 
gene.  With missing data a problem, I used a "Lomb-Scargle" approach to find 
the periodicity.  With Fourier analysis, one must impute any missing data 
points, but with Lomb-Scargle you just process the data you have without any 
imputation.



Perhaps you or your students would be interested in the "Numerical 
Experiments" on this page 
http://research.stowers-institute.org/efg/2005/LombScargle/supplement/NumericalExperiments/index.htm



I was curious how well the Lomb-Scargle technique would work with your 
data -- see the R code below.   Normally the Lomb-Scargle periodogram shows 
a single peak when there is a single dominant frequency.  The Peak 
Significance curve for all your data is a difficult to interpret, and I'm 
not sure the statistical tests are valid (without some tweaks) for your size 
dataset.



I took a random sample of 50 of your ~3000 data points and analyzed those --  
see the second code block below.  [For 50 data points I know all the 
assumptions are "good enough" for the statistics being computed.]  The 
periodogram here shows a single peak for period 365.6 days, which has good 
statistical significance.  Other subset samples can show harmonic 
frequencies, sometimes.





# efg, 9 Jan 2007

air = read.csv("http://www.hydrology.uni-kiel.de/~schorsch/air_temp.csv")
#air <- read.csv("air_temp.csv")

TempAirC <- air$T_air
Time     <- as.Date(air$Date, "%d.%m.%Y")
N <- length(Time)

# Lomb-Scargle code
source("http://research.stowers-institute.org/efg/2005/LombScargle/R/LombScargle.R")
MAXSPD <<- 1500
unit <<- "day"
M <- N    # Usually use factor of 2 or 4, but with large N use 1 instead

# Look at test frequencies corresponding to periods of 200 days to 500 days: 
f = 1/T
TestFrequencies <- (1/500) + (1/200 - 1/500) * (1:M / M)

# Use Horne & Baliunas' estimate of independent frequencies
Nindependent <- NHorneBaliunas(length(Time))  # valid for this size?

# Fairly slow with this large dataset

ComputeAndPlotLombScargle(as.numeric(Time), TempAirC,
  TestFrequencies, Nindependent,
  "Air Temperature [C]")





# Could get good results with fewer points too, say 50 chosen at random

MAXSPD <<- 25
TempAirC <- air$T_air
Time     <- as.Date(air$Date, "%d.%m.%Y")

set.seed(19)  # For reproducible results
RandomSet <- sample(1:length(Time), 50)
TempAirC <- TempAirC[RandomSet]
Time <-Time[RandomSet]

N <- length(Time)
M <- 4 * N    # Usually use factor of 2 or 4

# Look at test frequencies corresponding to periods of 200 days to 500 days: 
f = 1/T
TestFrequencies <- (1/500) + (1/200 - 1/500) * (1:M / M)

# Use Horne & Baliunas' estimate of independent frequencies
Nindependent <- NHorneBaliunas(length(Time))

# Very fast to compute for only 50 points

ComputeAndPlotLombScargle(as.numeric(Time), TempAirC,
  TestFrequencies, Nindependent,
  "Air Temperature [C]")





efg



Earl F. Glynn

Scientific Programmer

Stowers Institute