AR Order Selection Criteria

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.

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 Log(InvFStat) is the log of the inverse F-statistic. The F-statistic is defined as ((SSM/(ndata-order)-SSE)/order)/SSE.

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. The F-statistic is commonly used in regressions to see where additional coefficients no longer statistically contribute in a meaningful way to a parametric model. It is presented primarily as a reference for statisticians and is not recommended for order selection.

In practice, the use of any order selection criterion is fraught with considerable peril, especially when applied blindly. If you are using the AutoCorr, Burg, and non-SVD Data options, the MDL is probably better than nothing at all. In the above graph, the green plot is the Log(InvFStat), the cyan plot is the MDL, and the white plot is the AIC. These kinds of disparities in optimum model order are not unusual.

For non-SVD options, the MDL can be used in conjunction with inspection of the complex roots.

For all AR spectral options, multiple orders can also be evaluated in a 3D contour or surface graph in the AR Spectrum with Order Exploration. In the contour plot that follows, data containing 12 sinusoids plus noise (generated from sample7.sig in the Generate Signal option) is evaluated for AR orders 30 through 60 using the Data FB procedure. It is clear that order 47 is the minimum order. In this example, both the AIC and the MDL criterion estimated the optimum order at about 80.

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, resulting in a smoother AR spectrum.

List

The List Data option lists a table of the selected criteria. The listing uses the AutoSignal 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, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.