1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.3. Graphical Techniques: Alphabetic


Purpose: Examine Cyclic Structure 
A spectral plot (
Jenkins and Watts 1968 or
Bloomfield 1976)
is a graphical technique for examining cyclic structure in the
frequency domain. It is a smoothed Fourier transform of the
autocovariance function.
The frequency is measured in cycles per unit time where unit time is defined to be the distance between 2 points. A frequency of 0 corresponds to an infinite cycle while a frequency of 0.5 corresponds to a cycle of 2 data points. Equispaced time series are inherently limited to detecting frequencies between 0 and 0.5. Trends should typically be removed from the time series before applying the spectral plot. Trends can be detected from a run sequence plot. Trends are typically removed by differencing the series or by fitting a straight line (or some other polynomial curve) and applying the spectral analysis to the residuals. Spectral plots are often used to find a starting value for the frequency, ω, in the sinusoidal model


Sample Plot 
This spectral plot shows one dominant frequency of approximately 0.3 cycles per observation. 

Definition: Variance Versus Frequency 
The spectral plot is formed by:


Questions 
The spectral plot can be used to answer the following questions:


Importance Check Cyclic Behavior of Time Series 
The spectral plot is the primary technique for assessing the cyclic nature of univariate time series in the frequency domain. It is almost always the second plot (after a run sequence plot) generated in a frequency domain analysis of a time series.  
Examples  
Related Techniques 
Autocorrelation Plot Complex Demodulation Amplitude Plot Complex Demodulation Phase Plot 

Case Study  The spectral plot is demonstrated in the beam deflection data case study.  
Software  Spectral plots are a fundamental technique in the frequency analysis of time series. They are available in many general purpose statistical software programs. 