Autocorrelation distortion function for improved AR modeling

For noisy signals it is not enough to achieve a match between the first p+1 correlations of the measured data and that of the AR model. The higher order correlations begin to diverge as the level of data noise increases. In an effort to perform extended correlation matching we have found the need to use an Autocorrelation Distortion Function (ADF), defined as the difference between the sample acf of the noisy-data and the statistical acf of the true signal. Using the model bα^|n|for the ADF we develop a procedure for improved AR modeling of a stationary time series. In this procedure we estimate the parameters of the ADF in such a way that while the autocorrelation of the signal model plus noise matches the data acf exactly for the first p+1 lags, simultaneously, the mismatch at certain higher-order lags is minimized. These higher-order lags are taken to be p+1, .... ,p+q or, alternatively, they are chosen according to a peak-picking scheme described in the paper.