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Use scipy periodogram to identify dominant seasonal frequencies in a time series before selecting Fourier feature orders or ARIMA seasonal parameters
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| name | timeseries-periodogram-seasonality-detection |
| description | Use scipy periodogram to identify dominant seasonal frequencies in a time series before selecting Fourier feature orders or ARIMA seasonal parameters |
Before adding seasonal features, determine which frequencies actually exist in the data. The periodogram decomposes a time series into its frequency components, revealing peaks at dominant cycles (weekly, monthly, annual). This avoids overfitting to phantom seasonality and guides the choice of Fourier order or SARIMA seasonal period.
import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import periodogram
fs = 365.25 # samples per year (daily data)
freqs, spectrum = periodogram(
series.dropna().values,
fs=fs,
detrend="linear",
window="boxcar",
scaling="spectrum",
)
plt.figure(figsize=(10, 4))
plt.step(freqs, spectrum)
plt.xscale("log")
plt.xlabel("Cycles per year")
plt.ylabel("Power")
plt.axvline(1, color="r", alpha=0.3, label="Annual")
plt.axvline(52, color="g", alpha=0.3, label="Weekly")
plt.legend()
plt.show()
# Find top 3 peaks
top_idx = np.argsort(spectrum)[-3:]
dominant_periods = 1.0 / freqs[top_idx] # in days
scipy.signal.periodogramfs=365.25 (cycles/year), hourly → fs=8766"linear" removes simple trends; for nonstationary data, difference first"boxcar" (no taper) for maximum frequency resolution; "hann" reduces spectral leakage