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Charrelation-based estimation of the parameters of non-Gaussian autoregressive processes

Charrelation matrices are similar in structure (and in additional properties) to correlation matrices, and are closely related to Hessians of the log-characteristic function at selected “processing-points” away from the origin. Charrelation-based estimation methods were shown to offer significant improvement over second-order (correlation-based) methods when the latter are suboptimal. However, judicious selection of the processing-points is required in order to achieve such improvement. In the context of estimating the parameters of an autoregressive process, we present here a method for proper data-driven selection of the processing-points, finding the one which minimizes the predicted mean square estimation error. The resulting performance improvement over classical competing methods is demonstrated in simulation.