Spectral Analysis (Periodogram)

Spectral analysis with the periodogram decomposes a series' variance by frequency, so peaks reveal dominant cycles and their periods in time steps.

주기도표(periodogram)를 이용한 스펙트럼 분석은 시계열의 분산을 주파수별로 나누어, 두드러진 봉우리로 지배적 주기와 그 길이를 찾는 방법이다.

Is there a hidden cycle in my daily sensor readings, and how long is it?

일별 센서 값에 숨은 주기가 있는지, 있다면 몇 일 주기인지 알고 싶어요.

The periodogram is the squared magnitude of the discrete Fourier transform at each Fourier frequency, so a large ordinate means a strong sinusoidal component at that frequency. Fisher's g test asks whether the largest ordinate is larger than expected under Gaussian white noise.

When to use Spectral Analysis (Periodogram)

• You suspect periodic behaviour but do not know the period.
• You want to confirm the seasonal period before a decomposition.
• The series is long enough to resolve the frequencies of interest.

When to use something else

• You need a smooth, consistent estimate of the spectrum; use a smoothed or Welch spectral estimate.
• The observations are irregularly spaced; use the Lomb-Scargle periodogram.

Assumptions and requirements

• Equally spaced observations.
• Approximate stationarity after detrending.
• Fisher's g assumes Gaussian white noise under the null.

What the analysis reports

• Dominant frequencies and periods ranked by power
• Share of total variance at each peak
• Fisher's g statistic and exact p-value

How to report it

The periodogram peaked at a period of [value] time steps; Fisher's g = [value], p = [value].

Related methods

• STL Decomposition
• Autocorrelation Analysis (ACF, PACF, Ljung-Box)

Run Spectral Analysis (Periodogram) on Quorant