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


Purpose: Improve the estimate of frequency in sinusoidal time series models 
As stated previously, in the frequency analysis of time series
models, a common model is the sinusoidal model:
The complex demodulation phase plot (Granger, 1964) is used to improve the estimate of the frequency (i.e., ω) in this model. If the complex demodulation phase plot shows lines sloping from left to right, then the estimate of the frequency should be increased. If it shows lines sloping right to left, then the frequency should be decreased. If there is essentially zero slope, then the frequency estimate does not need to be modified. 

Sample Plot: 
This complex demodulation phase plot of the LEW.DAT data set shows that:


Definition 
The complex demodulation phase plot is formed by:


Questions 
The complex demodulation phase plot answers the following
question:


Importance of a Good Initial Estimate for the Frequency 
The nonlinear fitting for the sinusoidal model:


Related Techniques 
Spectral Plot Complex Demodulation Phase Plot NonLinear Fitting 

Case Study  The complex demodulation amplitude plot is demonstrated in the beam deflection data case study.  
Software  Complex demodulation phase plots are available in some, but not most, general purpose statistical software programs. 