seasonalEsd(data, period, [hybrid], [maxAnomalies], [alpha])


data is a numeric vector.

period is an integer larger than 1 indicating the length of a time-series cycle.

hybrid (optional) is a Boolean value indicating whether to use median and median absolute deviation to replace mean and standard deviation. The results are more robust if hybrid=true. The default value is false.

maxAnomalies (optional) is a positive integer or a floating number between 0 and 0.5. The default value is 0.1.

  • If maxAnomalies is a positive integer, it must be smaller than the size of data. It indicates the upper bound of the number of anomalies.

  • If maxAnomalies is a floating number between 0 and 0.5, the upper bound of the number of anomalies is int(size(data) * maxAnomalies).

alpha (optional) alpha is a positive number indicating the significance level of the statistical test. A larger alpha means a higher likelihood of detecting anomalies.


Conduct anomaly detection with the Seasoned Extreme Studentized Deviate test (S-ESD).

The result is a table of anomalies. It has 2 columns: column index records the subscript of anomalies in data, and column anoms are the anomaly values.


n = 100
trend = 6 * sin(1..n \ 200)
seasonal = sin(pi / 6 * 1..n)
residual = rand(1.0, n) - 0.5
data = trend + seasonal + residual
data[20 50 70] += 20;

seasonalEsd(data, 12);
index anoms
50 22.6365
70 21.141346
20 19.174165