Yule-Walker Equations Applied to Hessians of the Characteristic Function for Improved AR Estimation

Estimation of the autoregressive (AR) parameters of an AR process often involves applying Yule-Walker (YW) equations to the estimated correlations. When the process is Gaussian, the resulting estimate is asymptotically optimal, coinciding with the maximum-likelihood (ML) estimate. However, for non-Gaussian processes, applying the YW equations to the estimated correlations may be significantly sub-optimal, whereas computation of the exact ML estimate may be prohibitively cumbersome. In this paper we show how the YW equations may be applied to an alternative statistic, namely to off-origin Hessians of the second characteristic function. Although still not optimal, we show in simulation that the resulting estimate can significantly outperform the classical correlation-based estimate, as well as a cumulants-based estimate.