AR Model Order Selection

This option is available when AR fit information is available at multiple orders. In the following descriptions, n is the data length, SSE is normalized error in the AR model fit, order is the AR model order, and SSM is the sum of squares about the mean for the original data.

Selection Criteria

The AIC (Akaike Information Criterion) is defined as n*log(SSE)+order*2.

The MDL (Minimum Description Length) is defined as n*log(SSE)+order*log(n).

The criteria are graphed using normalizations where the values are mapped from 1E-4 to 1.0. This is a convenience for comparing the different criteria. The minimum in the curve is supposedly the optimum AR model order. On the whole, the MDL is generally regarded as the best overall AR order selection criterion.

In practice, the use of any order selection criterion is fraught with considerable peril, especially when applied blindly. If you are using the non-SVD Data options, the MDL is probably better than nothing at all. The MDL can also be used in conjunction with inspection of the complex roots.

The SVD Alternative

You will generally find the Data SVD or Nrml SVD options a better way to approach order selection. When a sufficiently large order is used to effect a good signal noise separation within the eigenmodes, it is often straightforward to graphically select the signal space. Further, the SVD procedures automatically discard the noise eigenmodes, removing the influence of noise in the prediction.

List

The List Data option lists a table of the selected criteria. The listing uses the TableCurve 2D text viewer facility.

Copy

The Copy Data to Clipboard option copies the criteria information to 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 criteria information to a supported file format. These formats include ASCII, Excel 97/2000, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.