# Detecting cycle maxima (peaks) in noisy time series (In R?)

This question is about an algorithm for determining the number and location of maxima in a sequence of numbers. Thus, there is a statistical flavor to the question, but it is more leaning towards programming, because I am not interested in the specific statistical properties, and the solution needs to be in R. The use of statistics to answer this question is OK, but not a requirement.

I want to extract maxima of cycles in time series data (i.e., an ordered sequence of numbers). An example of such data is the solar flare time series (~11 year cycle, between 9 & 14 years). The cycles don't repeat at a perfect interval, and the peaks aren't always the same height.

I found a recent paper describing an algorithm for this, and the paper actually uses solar flares as an example (Figure 5, Scholkmann et al. 2012, Algorithms). I was hoping that this algorithm, or an equally effective algorithm, was available as an R package.

Link to Scholkmann paper on "automatic multiscale-based peak detection" http://www.mdpi.com/1999-4893/5/4/588

I've tried the "turningpoints" function in the "pastecs" package but it seemed to be too sensitive (i.e., detected too many peaks). I thought of trying to smooth the time series first, but I'm not sure if this is the best approach (I'm no expert).

Thanks for any pointers.

If the peaks are almost periodic (with a slowly fluctuating period), as in the sunspot example, you can use the Hilbert transform or the empirical mode decomposition to smooth the time series.

```library(EMD)
x <- as.vector(sunspots)
r <- emd(x)
# Keep 5 components -- you may need more, or less.
y <- apply( r\$imf[,5:10], 1, sum ) + mean(r\$residue)
plot(x, type="l", col="grey")
lines( y, type="l", lwd=2)
n <- length(y)
i <- y[2:(n-1)] > y[1:(n-2)] & y[2:(n-1)] > y[3:n]
points( which(i), y[i], pch=15 )
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