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A General Frequency Domain Estimation Method for Gegenbauer Processes

Abstract In this paper a new method for estimation of all the parameters of a k-factor Gegenbauer process is developed using a broadband nonlinear least-squares regression technique in the frequency-domain, with similarities to a Whittle estimator. Simulation studies where the underlying distribution is symmetric suggest that while the new method may have a slightly lower level of accuracy than existing methods (Whittle, conditional sum-of-squares), it can improve the accuracy in determining the values for the short-memory parameters of highly skewed non-Gaussian data (e.g., χ2), while having the added advantage of being evaluated considerably faster. In a supplementary addendum we provide some theoretical results under a Gaussian assumption.