Directly to content
  1. Publishing |
  2. Search |
  3. Browse |
  4. Recent items rss |
  5. Open Access |
  6. Jur. Issues |
  7. DeutschClear Cookie - decide language by browser settings

Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes

Dahlhaus, Rainer ; Neumann, Michael H. ; von Sachs, Rainer

In: Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability, 5 (1999), Nr. 5. pp. 873-906. ISSN 1350-7265

PDF, English
Download (2MB) | Terms of use

Citation of documents: Please do not cite the URL that is displayed in your browser location input, instead use the DOI, URN or the persistent URL below, as we can guarantee their long-time accessibility.


We consider nonparametric estimation of the coefficients, of atime-varying autoregressive process. Choosing an orthonormal wavelet basisrepresentation of the coefficient functions, the empirical wavelet coefficientsare derived from the time series data as the solution of a least squares minimizationproblem. In order to allow the coefficient functions to be of inhomogeneous regularity,we apply nonlinear thresholding to the empirical coefficients and obtain locally smoothedestimates of the coefficient functions. We show that the resulting estimators attain theusual minimax L_2-rates up to a logarithm factor, simultaneously in a large scale of Besovclasses.

Item Type: Article
Journal or Publication Title: Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability
Volume: 5
Number: 5
Place of Publication: Aarhus
Date Deposited: 01 Jul 2016 07:47
Date: 1999
ISSN: 1350-7265
Page Range: pp. 873-906
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Nonlinear thresholding; non-stationary processes; time series; time-varying autoregression; wavelet estimators
Schriftenreihe ID: Beiträge zur Statistik > Reports
About | FAQ | Contact | Imprint |
OA-LogoDINI certificate 2013Logo der Open-Archives-Initiative