Uniqueness considerations in autoregressive modeling with third moments

The authors note that Yule-Walker equations for autoregressive (AR) modeling with second-moment (auto-correlation) sequences provide necessary and sufficient conditions for exact matching of the autocorrelation samples of a discrete stationary random process with that of the model. However, when AR modeling is done with linear equations that satisfy the necessary conditions for a match between samples of the third-moment sequence of a process and those of the model, these conditions are not sufficient for exact matching. The authors discuss approaches to fit AR models to the samples of the third-moment sequence of a process such that the corresponding third-moment samples of the model indeed match the given samples.<
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