Summary.
Let (X t ,t∈Z) be a linear sequence with non-Gaussian innovations and a spectral density which varies regularly at low frequencies. This includes situations, known as strong (or long-range) dependence, where the spectral density diverges at the origin. We study quadratic forms of bivariate Appell polynomials of the sequence (X t ) and provide general conditions for these quadratic forms, adequately normalized, to converge to a non-Gaussian distribution. We consider, in particular, circumstances where strong and weak dependence interact. The limit is expressed in terms of multiple Wiener-Itô integrals involving correlated Gaussian measures.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 22 August 1996 / In revised form: 30 August 1997
Rights and permissions
About this article
Cite this article
Giraitis, L., Taqqu, M. & Terrin, N. Limit theorems for bivariate Appell polynomials. Part II: Non-central limit theorems. Probab Theory Relat Fields 110, 333–367 (1998). https://doi.org/10.1007/s004400050151
Issue Date:
DOI: https://doi.org/10.1007/s004400050151