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Let Xᵢ be a stationary moving average with long-range dependence. Suppose EXᵢ = 0 and EX^2nᵢ < for some n 2. When the Xᵢ are Gaussian, then the Hermite polynomials play a fundamental role in the study of noncentral limit theorems for functions of Xᵢ. When the Xᵢ are not Gaussian, the relevant polynomials are Appell polynomials. They satisfy a multinomial-type expansion that can be used to establish noncentral limit theorems.
Avram et al. (Wed,) studied this question.