Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic
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.
This complex demodulation phase plot shows that:
The complex demodulation phase plot is formed by:
The complex demodulation phase plot answers the following
|Importance of a Good Initial Estimate for the Frequency||
The non-linear fitting for the sinusoidal model:
Complex Demodulation Phase Plot
|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.|