Anomaly Detector using FFT with AMOC and CUSUM Cutoff
Source:R/hanr_fft_amoc_cusum.R
hanr_fft_amoc_cusum.RdThis function implements an anomaly detection method based on the Fast Fourier Transform (FFT) and a changepoint-based cutoff strategy using the AMOC (At Most One Change) algorithm applied to the cumulative sum (CUSUM) of the power spectrum.
The method first computes the FFT of the input time series and extracts the power spectrum. It then applies a CUSUM transformation to the spectral data to emphasize gradual changes or shifts in spectral energy. Using the AMOC algorithm, it detects a single changepoint in the CUSUM-transformed spectrum, which serves as a cutoff index to remove the lower-frequency components.
The remaining high-frequency components are then reconstructed into a time-domain signal via inverse FFT, effectively isolating rapid or local deviations. Anomalies are detected by evaluating the distance between this filtered signal and the original series, highlighting points that deviate significantly from the expected pattern.
This method is suitable for series where spectral shifts are subtle and a single significant change in behavior is expected.
This function extends the HARBINGER framework and returns an object of class hanr_fft_amoc_cusum.
Examples
library(daltoolbox)
#loading the example database
data(examples_anomalies)
#Using simple example
dataset <- examples_anomalies$simple
head(dataset)
#> serie event
#> 1 1.0000000 FALSE
#> 2 0.9689124 FALSE
#> 3 0.8775826 FALSE
#> 4 0.7316889 FALSE
#> 5 0.5403023 FALSE
#> 6 0.3153224 FALSE
# setting up time series fft detector
model <- hanr_fft_amoc_cusum()
# fitting the model
model <- fit(model, dataset$serie)
detection <- detect(model, dataset$serie)
# filtering detected events
print(detection[(detection$event),])
#> idx event type
#> 50 50 TRUE anomaly