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Testing the frequency of noisy biological data: the value of a periodogram?

I am trying to analyze some noisy time series data in R. The data are based on the CO2 emissions of animals, and they show some cyclic periodicity that I would like to characterize. I would like to test hypotheses:

H0: There is no cyclic release of CO2 (i.e. no more than random).

H1: There is a picture of CO2 emissions in a cycle or pulses.

So, to do this, I imported the data into R, converted it to a time series class, and built its periodogram.

t25a <- read.table("data.txt", header=TRUE, sep="\t")
t1 <- ts(t25a$Co2)
plot(t1)
spec.pgram(t1, spans=4, log="no")

Here's what it looks like, with raw data plotted on top and a periodogram below:

R periodogram of time series CO2 data

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 Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne,
 D.F and Wickham, H. (2009) Statistical Inference for exploratory
 data analysis and model diagnostics Phil. Trans. R. Soc. A 2009
 367, 4361-4383 doi: 10.1098/rsta.2009.0120

vis.test TeachingDemos R ( ).

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