Softplus Affine(1, 1) Processes: Enlarged Stationarity Region, Stationary Unit Roots, and Inference 3S1VFGYWQE

URI	`m2://res/3S1VFGYWQE`
Kind	preprint
Creators	Yang Lu, Fukang Zhu
Date	2026-10-14
MSC	62-XX
Subjects	arxiv math.ST, arxiv stat.TH
Scope	in

Expressions

e1: version, preprint

Language	en
Date	2026-10-14
Ids	arXiv 2610.19421

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Integrable upper envelope for the quasi-likelihood contrast	statement	lemma 18	arxiv
Affine boundary expansions	statement	lemma 8	arxiv
Uniqueness and mixing in the strict region	statement	theorem 2	arxiv
Short- and long-memory regimes	statement	theorem 4	arxiv
Association	statement	lemma 15	arxiv
Initialization of the criterion, score, and information	statement	lemma 20	arxiv
Overlap for infinite-activity density families	statement	lemma 13	arxiv
Conditional central limit theorem	statement	lemma 1	arxiv
Fixed-point geometry above the unit root	statement	lemma 2	arxiv
Feller compactness and invariant limits	statement	lemma 14	arxiv
Nonstationarity above the unit root	statement	theorem 5	arxiv
Uniform invertibility of the candidate mean recursion	statement	lemma 4	arxiv
Boundary invariant tail	statement	lemma 16	arxiv
Rare relative innovations at the stationary unit root	statement	lemma 21	arxiv
Fixed-\(c\) Poisson QMLE at and below the unit root	statement	theorem 6	arxiv
No stationary law for a nonnegative intercept	statement	lemma 11	arxiv
Stationarity and moments in the strict region	statement	theorem 1	arxiv
Persistence from a high state	statement	lemma 17	arxiv
State--observation moment equivalence	statement	lemma 6	arxiv
Moments and polynomial concentration	statement	lemma 5	arxiv
QMLE envelopes	statement	lemma 19	arxiv
Boundary likelihood envelopes under a first moment	statement	lemma 22	arxiv
Boundary nonconfinement	statement	lemma 10	arxiv
At the unit root	statement	theorem 3	arxiv
Local power of the unit-root test	statement	theorem 7	arxiv
Uniform square-root increments	statement	lemma 9	arxiv
Conditionally Poisson observations	example	example	arxiv
Finite-activity coupling and observation mixing	statement	lemma 12	arxiv
Softplus calculus	statement	lemma 3	arxiv
Affine softplus cancellation	statement	lemma 7	arxiv

Catalogue records

arxiv: 2610.19421 (work)
arxiv_text: 2610.19421 (work)