The AIC criterion has become a standard tool in time series model fitting, and its computation is available in many time series programs. To illustrate how AIC works for the AR model, we consider a noisy signal
where .In this example the noise is slightly stronger than the sine wave (Figure 6).
|Figure 6. An example of a noisy signal that contains a sine wave and random noise.|
|Figure 7. (Top) Fourier power spectra for the sine wave, random noise, and the combined signal from Figure 6. (Bottom) AR spectra. AR orders are determined by minimizing AIC.|