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Spectral Density Plot

The Spectral Density Plot is used to identify the dominant integer seasonal frequency in time series data using spectral analysis with fast Fourier transforms. The algorithm used here is the same as used in the forecast model option to automatically detect seasonal frequency. If there is multiple seasonality, up to three integer frequencies will be identified. If the peak frequency is not an integer, it is rounded.

The Y axis is Spectral Density, the X axis is Seasonal Frequency. The Spectral Density Plot is also known as a Periodogram. Note that SigmaXL’s use of the term “seasonal frequency” is the inverse of what is typically used in Fourier transforms “seasonal period”, as discussed in the Introduction.

  1. Open Chemical Process Concentration – Series A.xlsx (Sheet 1 tab). This is the Series A data from Box and Jenkins, a set of 197 concentration values from a chemical process taken at two-hour intervals.
  2. Click SigmaXL > Time Series Forecasting > Spectral Density Plot. Ensure that the entire data table is selected. If not, Use Entire Data Table. Click Next.
  3. Click Concentration, click Numeric Time Series Data (Y) >>.


  4. Click OK. A Spectral Density Plot for Concentration is produced.

    The detected seasonal frequency is 1, which means that it is a nonseasonal process. The peak at 28 does not have enough seasonal “strength” to be considered for use as seasonal frequency in a time series model.

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