detectOutliersByHampel: detectOutliersByHampel
In twMisc: Utility functions of tw

Description Usage Arguments Details Value Author(s) Examples

detect unusual local values, i.e. outliers, in univariate time series by The Hampel Filter

1 2	detectOutliersByHampel(x, k = 3, t0 = 3, minWidth = as.integer(1.5 * k))

`x`	numeric vector representing a time series
`k`	window length 2*k+1 in indices, default to window length of 5
`t0`	threshold, default is 3 (Pearson's rule), see below.
`minWidth`	minimum number of records in window, to apply detection

Based on hampel function of the pracma package

The 'median absolute deviation' computation is done in the [-k...k] vicinity of each point at least k steps away from the end points of the interval. At the lower and upper end the time series values are preserved. A high threshold makes the filter more forgiving, a low one will declare more points to be outliers. t0<-3 (the default) corresponds to Ron Pearson's 3 sigma edit rule, t0<-0 to John Tukey's median filter.

In each window, NA-values are omitted. If the time resulting series is too short, no outlier detection for this index is performed.

A list with entires

`y`	the corrected time series
`ind`	the indices of detected outliers

Thomas Wutzler

set.seed(0815)
x <- diffinv(rnorm(99)/5)	# autocorrelated time series
x[20:25] <- NA
x[10] <- x[10] + median(abs(x[7:13]-x[10]))*3
x[30] <- x[30] - median(abs(x[27:33]-x[30]))*3
(iOut <- (res <- detectOutliersByHampel(x, k=4))$ind)
(iOut <- (res <- detectOutliersBySuperSmoother(x))$ind)
plot( x )
points( x[iOut] ~ iOut, col="blue")
points( res$y[iOut] ~ iOut, col="red")