Bernoulli

  • Bernoulli
  • Volume 25, Number 2 (2019), 1013-1044.

Towards a general theory for nonlinear locally stationary processes

Rainer Dahlhaus, Stefan Richter, and Wei Biao Wu

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Abstract

In this paper, some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias expansions are proved for processes obeying an expansion in terms of the stationary approximation and derivative. In addition it is shown that this applies to some general nonlinear non-stationary Markov-models. In addition the results are applied to derive the asymptotic properties of maximum likelihood estimates of parameter curves in such models.

Article information

Source
Bernoulli, Volume 25, Number 2 (2019), 1013-1044.

Dates
Received: April 2017
Revised: November 2017
First available in Project Euclid: 6 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.bj/1551862842

Digital Object Identifier
doi:10.3150/17-BEJ1011

Mathematical Reviews number (MathSciNet)
MR3920364

Zentralblatt MATH identifier
07049398

Keywords
derivative processes non-stationary processes

Citation

Dahlhaus, Rainer; Richter, Stefan; Wu, Wei Biao. Towards a general theory for nonlinear locally stationary processes. Bernoulli 25 (2019), no. 2, 1013--1044. doi:10.3150/17-BEJ1011. https://projecteuclid.org/euclid.bj/1551862842


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Supplemental materials

  • Supplement to “Towards a general theory for nonlinear locally stationary processes”. Supplement A: Proofs of Section 2, 4 and 5. This supplement contains the remaining proofs for Sections 2, 4 and 5. Supplement B: Discussion of the Assumptions 2.3(M1), (M2). This supplement contains another counterexample where Assumption 2.3(M1) is satisfied but not (M2).