Detecting cycle maxima (peaks) in noisy time series (In R?) [closed]

Answer 1

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 )

Answer 2

Here is a solution involving the wmtsa package in R. I added my own little function to facilitate the searching of maxima once the wmtsa::wavCWTPeaks got it close.

PeakCycle <- function(Data=as.vector(sunspots), SearchFrac=0.02){
    # using package "wmtsa"
    #the SearchFrac parameter just controls how much to look to either side 
    #of wavCWTPeaks()'s estimated maxima for a bigger value
    #see dRange
    Wave <- wavCWT(Data)
    WaveTree <- wavCWTTree(Wave)
    WavePeaks <- wavCWTPeaks(WaveTree, snr.min=5)
    WavePeaks_Times <- attr(WavePeaks, which="peaks")[,"iendtime"]

    NewPeakTimes <- c()
    dRange <- round(SearchFrac*length(Data))
    for(i in 1:length(WavePeaks_Times)){
        NewRange <- max(c(WavePeaks_Times[i]-dRange, 1)):min(c(WavePeaks_Times[i]+dRange, length(Data)))
        NewPeakTimes[i] <- which.max(Data[NewRange])+NewRange[1]-1
    }

    return(matrix(c(NewPeakTimes, Data[NewPeakTimes]), ncol=2, dimnames=list(NULL, c("PeakIndices", "Peaks"))))
}

dev.new(width=6, height=4)
par(mar=c(4,4,0.5,0.5))
plot(seq_along(as.vector(sunspots)), as.vector(sunspots), type="l")
Sunspot_Ext <- PeakCycle()
points(Sunspot_Ext, col="blue", pch=20)