# Spectral Plot: Definition

## What is a Spectral Plot?

A spectral plot is a graph which allows us to examine the cyclic structure, in the frequency domain, of a time series. A time series represents a progression of some parameter in time. We can think of it as a function of time, but it is typically random; We can’t predict exactly what it will do in the future; only what it might do.

In technical terms, a spectral plot is a smoothed Fourier transform of the auto-covariance function of the time series. But you don’t need to understand that sentence to understand how to read and use spectral plots.

In a spectral plot:

• The horizontal axis is the frequency—recorded in cycles per observation, which is the same as cycles per unit time when time is defined as the distance between points.
• The vertical axis is smoothed variance. This is computed from the data by a series of rather complicated computations which are typically left to a computer.

## Importance of Spectral Plots

Spectral plots are important because they are the prime technique used in statistic and data analysis for determining the cyclic nature of univariate (one-variable) time series in the frequency domain. In typical frequency domain analysis, a run chart is first generated, followed by a spectral plot.

The spectral plot answers such questions as whether or not there is a dominant cyclic frequency, what that might be, and how many cyclic components there are.

Most general statistical software packages have the ability to compute and graph spectral plots, and so since the computation is involved they are now rarely figured out by hand.

## References

NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.3.27. Spectral Plot. retrieved from https://www.itl.nist.gov/div898/handbook/eda/section3/spectrum.htm on April 5, 2018

Donman, Kenneth. Spectral Analysis: A Summary of the Theory and Techniques