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Identify anomalies using the Hampel filter

Source: R/hampel.R
hampel_anomalies.Rd

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

Value

logical vector identifying which observations are anomalies.

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.

Author

Rob J Hyndman

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")