Patterns › Time series

Periodogram / spectral analysis

Spectral analysis estimates an FFT-based periodogram with a 10% cosine taper, with optional detrending and modified-Daniell smoothing spans.

What is Periodogram / spectral analysis?

The periodogram decomposes a series's variance into contributions from each frequency. Peaks identify cyclical components — annual cycles, weekly cycles, biological rhythms. The 10% cosine taper reduces spectral leakage; modified-Daniell smoothing trades resolution for stability.

Frequency vs period: a peak at frequency f corresponds to a cycle of length 1/f observations. For monthly data, a peak at f = 1/12 cycles/month means an annual cycle.

When should I use Periodogram / spectral analysis?

  • Finding dominant cyclical components in a stationary-ish series.
  • Confirming or rejecting suspected periodicities (circadian rhythms, business cycles).

What data does it need?

One numeric series + detrend toggle + smoothing spans string (e.g. "3,5").

What does it report?

Spectral density on log y-axis vs frequency + peak frequency + corresponding period.

How do I interpret the result?

Multiple peaks at integer-multiple frequencies (f, 2f, 3f) usually mean the underlying cycle is non-sinusoidal — the higher harmonics are the same cycle's shape, not separate periodicities.

See also

References

  • Bloomfield (2000). Fourier Analysis of Time Series, 2nd ed.