Hampel Filter
Median absolute deviation (MAD) outlier in Time Series
hampel(x, k, t0 = 3)
x |
numeric vector representing a time series |
k |
window length |
t0 |
threshold, default is 3 (Pearson's rule), see below. |
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.
Returning a list L with L$y the corrected time series and
L$ind the indices of outliers in the ‘median absolut deviation’
sense.
Don't take the expression outlier too serious. It's just a hint to values in the time series that appear to be unusual in the vicinity of their neighbors under a normal distribution assumption.
Pearson, R. K. (1999). “Data cleaning for dynamic modeling and control”. European Control Conference, ETH Zurich, Switzerland.
set.seed(8421)
x <- numeric(1024)
z <- rnorm(1024)
x[1] <- z[1]
for (i in 2:1024) {
x[i] <- 0.4*x[i-1] + 0.8*x[i-1]*z[i-1] + z[i]
}
omad <- hampel(x, k=20)
## Not run:
plot(1:1024, x, type="l")
points(omad$ind, x[omad$ind], pch=21, col="darkred")
grid()
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.