FFTPeriodicityDetector

class pyriodicity.FFTPeriodicityDetector

Fast Fourier Transform (FFT) based periodicity detector.

Find the periods in a given signal or series using FFT [1].

See also

pyriodicity.OnlineFFTPeriodicityDetector

Online Fast Fourier Transform (FFT) based periodicity detector.

References

[1]

Hyndman, R.J., & Athanasopoulos, G. (2021) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia. https://OTexts.com/fpp3/useful-predictors.html#fourier-series. Accessed on 09-15-2024.

Examples

Start by loading Mauna Loa Weekly Atmospheric CO2 Data from statsmodels and downsampling its data to a monthly frequency.

>>> from statsmodels.datasets import co2
>>> data = co2.load().data
>>> data = data.resample("ME").mean().ffill()

Use FFTPeriodicityDetector to find the list of periods using FFT, ordered by corresponding frequency amplitudes in a descending order.

>>> from pyriodicity import FFTPeriodicityDetector
>>> FFTPeriodicityDetector.detect(data)
array([ 12,   6, 175,  44, 132,  88,  11,  13, 105,  58,  66,  75,  14,
    25,  18,  48,  10,  31,   4,   9,   7,  19,  23,   8,  38,  35,
    40,  28,  20,   3,   5,  15,  29,  22,   2,  24,  53,  33,  26,
    16,  17,  21])

FFTPeriodicityDetector tends to be quite sensitive to noise and can find many false period lengths. Depending on your data, you can choose to apply a window function to get different results. You can also limit the number returned period length values to the 3 most signficant ones.

>>> FFTPeriodicityDetector.detect(window_func="blackman", max_period_count=3)
array([12, 13, 11])

As you can see, results are concentrated around the period length value 12, indicating a yearly periodicity.

Methods

detect(data[, window_func, detrend_func, ...])

Find periods in the given series.