Detrend a Set of Observations

Detrends y by subtracting a linear trend in x, to create a vector that is zero for its first and last finite value. If the second parameter (y) is missing, then x is taken to be y, and a new x is constructed with seq_along(). Any NA values are left as-is.

Usage

detrend(x, y)

Arguments

x: a vector of numerical values. If y is not given, then x is taken for y.
y: an optional vector

Value

A list containing Y, the detrended version of y, and the intercept a and slope b of the linear function of x that is subtracted from y to yield Y.

Details

A common application is to bring the end points of a time series down to zero, prior to applying a digital filter. (See examples.)

Author

Dan Kelley

Examples

x <- seq(0, 0.9 * pi, length.out = 50)
y <- sin(x)
y[1] <- NA
y[10] <- NA
plot(x, y, ylim = c(0, 1))
d <- detrend(x, y)
points(x, d$Y, pch = 20)
abline(d$a, d$b, col = "blue")
abline(h = 0)
points(x, d$Y + d$a + d$b * x, col = "blue", pch = "+")