• 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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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

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

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

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derivative processes non-stationary processes


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.

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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).