The following inner-outer type factorization is obtained for the sequence space ℓp: if the complex sequence F = (F0, F1,F2,...) decays geometrically, then for an p sufficiently close to 2 there exists J and G in ℓp such that F = J * G; J is orthogonal in the Birkhoff-James sense to all of its forward shifts SJ, S2J, S3J, ...; J and F generate the same S-invariant subspace of ℓp; and G is a cyclic vector for S on ℓp.

These ideas are used to show that and ARMA equation with characteristic roots inside and outside of the unit circle has Symmetric-α-Stable solution,s in which the process and the given white noise are expressed as causal moving averages of a related i.i.d. SαS white noise. An autregressive representation of the process is similarly obtained.

Document Type

Post-print Article

Publication Date


Publisher Statement

Copyright © 2016 Elsevier Inc.

DOI: 10.1016/j.jmaa.2016.01.009

The definitive version is available at:

Full Citation:

Cheng, Raymond, and William T. Ross. "An Inner–outer Factorization in ℓ P with Applications to ARMA Processes." Journal of Mathematical Analysis and Applications 437, no. 1 (2016): 396-418. doi:10.1016/j.jmaa.2016.01.009.