My first post so apologies for any mistakes.
I'm attempting to perform spectral analysis on a simulated circadian data set. I'm splitting the dataset into overlapping windows of say 72 hours, moving the window by 1 hour at a time then performing analysis on each window.
I've split the data into windows easy enough and the windows are analysed in MATLAB by spectrum resampling before importing back into R to perform the fit and forecast. The data is linearly detrended before analysing.
The problem I have is that sometimes, the fit is upside down and I have no idea why. It seems to be at different points for different simulations.
Data for one window that is guilty of flipping the harmonic fit:
[1] -2.9136538 0.0010000 34.5624105 22.4405751 30.9085542 52.0034490 79.5249172
119.5003560 131.3097901 161.3732205 151.1808213 151.3683942 137.2054086 129.6240755
119.3947248 104.8470942 109.6584816 92.4747798 64.1060229 47.8765937 38.5499292
27.9335235 29.4226107 27.2898893 19.2395761 6.7445437 5.5157589 0.6936448
8.1536902 2.7837173 18.8406092 38.0873956 34.7811886 34.8339832 77.8551701
96.4206791 59.8705545 69.8435641 84.0060386 86.8470648 75.5799761 95.7528280
104.4698246 109.9925047 111.0268326 114.4968343 92.4072921 82.8064504 87.8407758
82.2552400 58.5038630 45.4751850 44.4046889 42.6263098 34.6088522 36.9155973
32.8585151 19.1018107 7.7472503 13.6565334 9.6832063 2.3193501 8.2114646
8.9220096 15.9007696 24.4889114 38.9416853 44.6872649 66.7847050 88.5166601
123.3687771 135.0492302
For this particular window, the significant frequencies are as follows:
Period Amplitude Phase
32.508896 52.346609 0.840978
11.882840 17.036845 0.733279
8.650918 6.771955 -0.573897
3.600676 8.561309 0.863454
6.661385 7.278945 -0.823185
Now, the number of frequencies that are picked up differ by window. This is code I've written to produce the sum of the cosine curves and forecasts for each window and put them in a matrix with each column being the fit for that window:
no.freq72_3 <- tabulate(freq72_3$Window)
cusum72_3 <- cumsum(no.freq72_3)
length <- 28
forecast72_3 <- matrix(NA, nrow=(dim(window72_3)[1])+length,
ncol=length(no.freq72_3))
for(i in 2:length(no.freq72_3)){
tt72_3 <- matrix(NA, nrow=(dim(window72_3)[1])+length, ncol=no.freq72_3[i])
t72_3 <- c()
a72_3 <- c()
ph72_3 <- c()
for(j in 1:no.freq72_3[i]){
t72_3[j] <- freq72_3[j+cusum72_3[i-1],2]
a72_3[j] <- freq72_3[j+cusum72_3[i-1],3]
ph72_3[j] <- freq72_3[j+cusum72_3[i-1],4]
}
for(j in 1:no.freq72_3[i]){
for(l in 1:((dim(window72_3)[1])+length)){
tt72_3[l,j] <- a72_3[j]*cos((2*pi*(1/t72_3[j])*l)+ph72_3[j])
}
}
forecast72_3[,i] <- rowSums(tt72_3, na.rm=TRUE)
}
Now, this is the function I've written to plot whatever window you require:
fore_win72_3 <- function(x){
data <- window72_3[, x]
fore <- forecast72_3[, x]
trend <- time(data)
reg1 <- lm(data ~ trend, na.action=NULL)
detrend <- data - fitted(reg1)
plot(detrend, xlim=c(0, dim(forecast72_3)[1]))
lines(fore)
}
fore_win72_3(100)
I would add plots but I do not have enough reputation. Any help would be greatly appreciated! If there are any edits I can do to make anything easier than let me know! Thanks.
