Convolutions of Bivariate Appell
Polynomials with Long-Range Dependence
The convergence in distribution of a quadratic form of a non-instantaneous,
filter is established. The input to the filter is assumed to have long memory,
but is not necessarily Gaussian. The limit is representable as a
integral. While instantaneous functions of long-memory processes
typically have limit theorems with normalization exponents greater than
or equal to 1/2, for the non-instantaneous filter studied here,
exponents less than 1/2 are possible.
Keywords and Phrases: long memory, multiple Wiener-Itô integrals,
non-instantaneous, non-linear, power counting.