Remove Linear Trends

Removes the mean value or (piecewise) linear trend from a vector or from each column of a matrix.

detrend(x, tt = 'linear', bp = c())

Arguments

x

vector or matrix, columns considered as the time series.

tt

trend type, `constant' or `linear', default is `linear'.

bp

break points, indices between 1 and nrow(x).

Details

detrend computes the least-squares fit of a straight line (or composite line for piecewise linear trends) to the data and subtracts the resulting function from the data.

To obtain the equation of the straight-line fit, use polyfit.

Value

removes the mean or (piecewise) linear trend from x and returns it in y=detrend(x), that is x-y is the linear trend.

Note

Detrending is often used for FFT processing.

See also

polyfit

Examples

t <- 1:9
x <- c(0, 2, 0, 4, 4, 4, 0, 2, 0)
x - detrend(x, 'constant')
#>           [,1]
#>  [1,] 1.777778
#>  [2,] 1.777778
#>  [3,] 1.777778
#>  [4,] 1.777778
#>  [5,] 1.777778
#>  [6,] 1.777778
#>  [7,] 1.777778
#>  [8,] 1.777778
#>  [9,] 1.777778
x - detrend(x, 'linear')
#>           [,1]
#>  [1,] 1.777778
#>  [2,] 1.777778
#>  [3,] 1.777778
#>  [4,] 1.777778
#>  [5,] 1.777778
#>  [6,] 1.777778
#>  [7,] 1.777778
#>  [8,] 1.777778
#>  [9,] 1.777778

y <- detrend(x, 'linear', 5)
if (FALSE) { # \dontrun{
plot(t, x, col="blue")
lines(t, x - y, col="red")
grid()} # }