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, , in the sinusoidal model
This spectral plot 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
|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.|