Open Access
May 2019 Towards a general theory for nonlinear locally stationary processes
Rainer Dahlhaus, Stefan Richter, Wei Biao Wu
Bernoulli 25(2): 1013-1044 (May 2019). DOI: 10.3150/17-BEJ1011


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.


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Rainer Dahlhaus. Stefan Richter. Wei Biao Wu. "Towards a general theory for nonlinear locally stationary processes." Bernoulli 25 (2) 1013 - 1044, May 2019.


Received: 1 April 2017; Revised: 1 November 2017; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049398
MathSciNet: MR3920364
Digital Object Identifier: 10.3150/17-BEJ1011

Keywords: derivative processes , non-stationary processes

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 2 • May 2019
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