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GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS
OF CARDIOVASCULAR DATA
AKAIKE INFORMATION CRITERION

Method for the order selection of autoregressive models

The Akaike Information Criterion determines the model order p by minimizing an information theoretic function of p, AIC(p). For an AR process with Gaussian statistics, AIC(p) is defined as:

AIC(p)=N ln(s2(p))+2p
where N is the number of samples, and s2(p) is the estimated variance of the white driving noise (i.e., the prediction error), a decreasing function of p. The term 2p is a "penalty" for the use of extra AR coefficients that do not substantially reduce the prediction error.

The "AIC minimum" is only one of many criteria proposed for the selection of the AR order. Another popular criterion is the Final Prediction Error, which selects the model order p minimizing the function FPE(p) defined as:

FPE(p)=s2(p) x (N+p+1)/(N-p-1)
The term (N+p+1)/(N-p-1) increases with p and represents the inaccuracies in estimating the AR parameters.

References:
Marple SL Jr. (1987) Digital spectral analysis with applications. Prentice Hall, Englewood Cliffs, New Jersey

(PC, June 2001)
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