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The impact of the diagonals of polynomial forms on limit theorems with long memory

2017
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Bernoulli
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We start with an i.i.d. sequence and consider the product of two polynomial-forms moving averages based on that sequence. The coefficients of the polynomial forms are asymptotically slowly decaying homogeneous functions so that these processes have long memory. The product of these two polynomial forms is a stationary nonlinear process. Our goal is to obtain limit theorems for the normalized sums of this product process in three cases: exclusion of the diagonal terms of the polynomial form,

doi:10.3150/15-bej697
fatcat:ny4btqlii5f4rbrtk7p7rjlpvm