Complex Roots

The Plot Roots option is available in the AR Modeling and Prediction procedure for inspecting the complex roots of the parametric model.

The inspection of the roots can offer an indication of signal space, similar to that of the Graphically Select Signal and Noise Sub-Spaces signal selection in the SVD procedures. This inspection can also confirm the stability of the filter arising from the fit.

Pole and magnitude plots are offered. The AR roots are plotted with the + symbol. In an AR fit, the poles on or near the unit circle are usually comprised of signal, while those within the interior of the unit circle are generally noise. In a Unit Circle plot, all of the roots are plotted. For real data, there will be symmetry across the imaginary axis.

Magnitude plots are also available. Here the signal components should lie at or near 1.0 while the noise components will have lower magnitudes.

The AR Out information field reports the number of AR roots that lie outside the unit circle. These roots have a magnitude greater than 1.0. An AR model can be stabilized in the AR Modeling and Prediction option. Spectral factorization is available to map these roots either to the unit circle or reflectively into the interior of the unit circle.

In general, the least-squares AR algorithms yield stable filters, but are not assured to do so. Typically, precision losses due to roundoff error generate the instability. Roots with magnitudes that are only slightly above 1.0, as in the fourth decimal place, may be indicative of borderline precision issues attributable to overspecifying the model order or accumulated algorithm roundoff errors. The Data AR algorithms, which directly fit a data matrix, will generally fare better than the Nrml AR algorithms which give up precision when constructing the normal equations matrix.

List

The List Data option lists the roots in a table containing type, real, imaginary, magnitude, and frequency columns. Only positive frequencies are listed. If the Unit Circle option is selected, the roots will be sorted by increasing frequency. If the Magnitude option is selected, the roots will be sorted by decreasing magnitude. The listing uses the TableCurve 2D text viewer facility.

Copy

The Copy Data to Clipboard option copies the information in the List Data option the clipboard. Formats include full precision binary (for spreadsheets such as Excel) and ASCII (for pasting into text editors).

Save

The Save Data to Disk option writes the information in the List Data option to a supported file format. These formats include ASCII, Excel 97/2000, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.