The Annals of Statistics

Cross validation for locally stationary processes

Stefan Richter and Rainer Dahlhaus

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We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.

Article information

Ann. Statist., Volume 47, Number 4 (2019), 2145-2173.

Received: May 2017
Revised: February 2018
First available in Project Euclid: 22 May 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G20: Asymptotic properties

Locally stationary processes cross validation adaptive bandwidth selection asymptotic optimality


Richter, Stefan; Dahlhaus, Rainer. Cross validation for locally stationary processes. Ann. Statist. 47 (2019), no. 4, 2145--2173. doi:10.1214/18-AOS1743.

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Supplemental materials

  • Supplement: Technical proofs. This material contains some details of the proofs in the paper as well as the proofs of the examples.