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This is a Julia implimentation of a peak finding algorithm found at http://stackoverflow.com/a/22640362/6029703
using Statistics
using Plots
function SmoothedZscoreAlgo(y, lag, threshold, influence)
# Julia implimentation of http://stackoverflow.com/a/22640362/6029703
n = length(y)
signals = zeros(n) # init signal results
filteredY = copy(y) # init filtered series
avgFilter = zeros(n) # init average filter
stdFilter = zeros(n) # init std filter
avgFilter[lag - 1] = mean(y[1:lag]) # init first value
stdFilter[lag - 1] = std(y[1:lag]) # init first value
for i in range(lag, stop=n-1)
if abs(y[i] - avgFilter[i-1]) > threshold*stdFilter[i-1]
if y[i] > avgFilter[i-1]
signals[i] += 1 # postive signal
else
signals[i] += -1 # negative signal
end
# Make influence lower
filteredY[i] = influence*y[i] + (1-influence)*filteredY[i-1]
else
signals[i] = 0
filteredY[i] = y[i]
end
avgFilter[i] = mean(filteredY[i-lag+1:i])
stdFilter[i] = std(filteredY[i-lag+1:i])
end
return (signals = signals, avgFilter = avgFilter, stdFilter = stdFilter)
end
# Data
y = [1,1,1.1,1,0.9,1,1,1.1,1,0.9,1,1.1,1,1,0.9,1,1,1.1,1,1,1,1,1.1,0.9,1,1.1,1,1,0.9,
1,1.1,1,1,1.1,1,0.8,0.9,1,1.2,0.9,1,1,1.1,1.2,1,1.5,1,3,2,5,3,2,1,1,1,0.9,1,1,3,
2.6,4,3,3.2,2,1,1,0.8,4,4,2,2.5,1,1,1]
# Settings: lag = 30, threshold = 5, influence = 0
lag = 30
threshold = 5
influence = 0
results = SmoothedZscoreAlgo(y, lag, threshold, influence)
upper_bound = results[:avgFilter] + threshold * results[:stdFilter]
lower_bound = results[:avgFilter] - threshold * results[:stdFilter]
x = 1:length(y)
yplot = plot(x,y,color="blue", label="Y",legend=:topleft)
yplot = plot!(x,upper_bound, color="green", label="Upper Bound",legend=:topleft)
yplot = plot!(x,results[:avgFilter], color="cyan", label="Average Filter",legend=:topleft)
yplot = plot!(x,lower_bound, color="green", label="Lower Bound",legend=:topleft)
signalplot = plot(x,results[:signals],color="red",label="Signals",legend=:topleft)
plot(yplot,signalplot,layout=(2,1),legend=:topleft)
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