hampel_anomalies: Identify anomalies using the Hampel filter

In weird: Functions and Data Sets for "That's Weird: Anomaly Detection Using R" by Rob J Hyndman

Identify anomalies using the Hampel filter

Description

The Hampel filter is designed to find anomalies in time series data using mean absolute deviations in the vicinity of each observation.

Usage

hampel_anomalies(y, bandwidth, k = 3)

Arguments

y	numeric vector containing time series
bandwidth	integer width of the window around each observation
k	numeric number of standard deviations to declare an outlier

Details

First, a moving median is calculated using windows of size 2 * bandwidth + 1. Then the median absolute deviations from this moving median are calculated in the same moving windows. A point is declared an anomaly if its MAD is value is more than k standard deviations. The MAD is converted to a standard deviation using MAD * 1.482602, which holds for normally distributed data. The first bandwidth and last bandwidth observations cannot be declared anomalies.

Value

logical vector identifying which observations are anomalies.

Author(s)

Rob J Hyndman

References

Rob J Hyndman (2026) "That's weird: Anomaly detection using R", Section 9.2, https://OTexts.com/weird/.

Examples

set.seed(1)
df <- tibble(
  time = seq(41),
  y = c(rnorm(20), 5, rnorm(20))
) |>
  mutate(hampel = hampel_anomalies(y, bandwidth = 3, k = 4))
df |> ggplot(aes(x = time, y = y)) +
  geom_line() +
  geom_point(data = df |> filter(hampel), col = "red")

weird documentation built on Jan. 27, 2026, 9:06 a.m.