Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic
Examine Cyclic Structure
A spectral plot (
Jenkins and Watts 1968 or
is a graphical technique for examining cyclic structure in the
frequency domain. It is a smoothed Fourier transform of the
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. Equi-spaced 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
This spectral plot of the LEW.DAT data set shows one dominant frequency of approximately 0.3 cycles per observation.
Variance Versus Frequency
The spectral plot is formed by:
The spectral plot can be used to answer the following questions:
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.
Complex Demodulation Amplitude Plot
Complex Demodulation Phase Plot
|The spectral plot is demonstrated in the beam deflection data case study.
|Spectral plots are a fundamental technique in the frequency analysis of time series. They are available in many general purpose statistical software programs.