Removes a linear trend line or mean value from a series.
DETREND(series, "opt", bp)
series 
 
An input series. 

"opt" 
 
Optional. A string, the trend type. 





bp 
 
Optional. A series, a list of breakpoint indices that determine the locations of a piecewise continuous linear trend. Defaults to a single regression line computed over the entire series. 
A series, the detrended output.
W1: gnorm(10, 1)
W2: W1 + 100
W3: detrend(w2, "constant")
W4: demean(w2)
W2 contains a 10 point random series with a mean of 10. Both W3 and W4 remove the mean value to recover the original series in W1.
W1: gcos(1000, 1/1000, 10)
W2: 10 * gtri(length(w1), deltax(w1), 1)
W3: W1 + W2
W4: detrend(w3, maxidx(w2))
W3 contains a 1000 point cosine with a triangular linear trend. W4 removes the trend and recovers W1 by setting a breakpoint at the index of the apex of the triangle wave.
If breakpoints are specified, each point represents the index shared by adjacent line segments. A piecewise continuous regression line is computed for each segment.
If no breakpoints are specified, a trend line computed over the entire input series is removed. This is equivalent to:
series  linreg(series)
See TREND to fit a linear trend to a series.