Rolling outlier detection using the Hampel identifier — hampel

Detect outliers in a rolling window using the Hampel identifier.

hampel_outlier(x, k, threshold = 3.5)

Arguments

x: A vector of numbers.
k: Width of the rolling window (an odd integer).
threshold: Threshold for labeling outliers. For normally distributed data this is equivalent to standard deviations.

Value

A vector of boolean values, TRUE if the value is an outlier.

Details

The Hampel identifier uses the median absolute deviation (MAD) and a threshold to identify outliers based on their distance from the median (Davies and Gather 1993) . This is a robust alternative to the commonly used thresholds $mean \pm 3 \sigma$ to identify outliers (Leys et al. 2013) .

Values are classified as outliers when

$$\frac{\left| X_i - \textrm{med}(X) \right|}{\textrm{MAD}(X)} > threshold$$

When the MAD is zero this equation is undefined. In this case the function returns FALSE.

References

Davies L, Gather U (1993). “The Identification of Multiple Outliers.” Journal of the American Statistical Association, 88(423), 782--792. ISSN 0162-1459, doi:10.1080/01621459.1993.10476339 , Publisher: Taylor & Francis _ eprint: https://www.tandfonline.com/doi/pdf/10.1080/01621459.1993.10476339, https://www.tandfonline.com/doi/abs/10.1080/01621459.1993.10476339.

Leys C, Ley C, Klein O, Bernard P, Licata L (2013). “Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median.” Journal of Experimental Social Psychology, 49(4), 764--766. ISSN 0022-1031, doi:10.1016/j.jesp.2013.03.013 , http://www.sciencedirect.com/science/article/pii/S0022103113000668.

Examples

# test a dataset with an outlier
x <- rnorm(20)
x[3] <- 10
hampel_outlier(x, 5)
#>  [1] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#> [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE