Linear predictive model convolution
Averaging AR-coefficients is a risky business - this could cause drastic shifts in the position of the zeroes of the corresponding polynomial, resulting in instabilities!

If I were to approach the problem the first thing I would try would be the following:


Compute the spectrogram (short-term fourier transform)
Run VQ on the spectral slices with a codebook size of 16, using euclidian distance on the log
Once you have 16 spectral template, convert them back to autocorrelation functions, solve yule-walker for the 16 templates and you get your 16 models.


Or another "safe" way:


For each frame, extract the AR coefficients.
Convert them into reflection coefficients or any other alternative representation like line spectral pairs which can be safely interpolated.
Run VQ on these with a codebook size of 16 to get your 16 models.
Convert back to AR coefficients.


But I really doubt this is a path worth exploring. My two intuitions would be that:


If an audio file is long and diverse enough the 16 specialized models you would get out of it won't be very different form the 16 "universal" models you would obtain out of running the procedure once and for all on a large collection of audio files.
Learning 16 models from a large collection of audio files is likely to give you the kind of naive "fixed predictors" used in FLAC (polynomial interpolators).


One related result is that running a KLT on mel-frequency spectra on a sufficiently long audio clip is going to yield something very similar to the DCT base - that's why audio codecs like mp3 or AAC are not using per-file optimized transforms - the DCT is a good, universal one, and the advantage of using universal transforms is that they don't even require any side-information. This is what motivates my intuition - you are looking at a large dataset (an entire audio file), 16 is small. You'd rather think of 16 good universal predictors and use them than instead of trying to optimize your 16 predictors per file.