Articles | Volume 15, issue 4
Nonlin. Processes Geophys., 15, 591–599, 2008
https://doi.org/10.5194/npg-15-591-2008
Nonlin. Processes Geophys., 15, 591–599, 2008
https://doi.org/10.5194/npg-15-591-2008

  23 Jul 2008

23 Jul 2008

A propagation-separation approach to estimate the autocorrelation in a time-series

D. V. Divine1,*, J. Polzehl2, and F. Godtliebsen3 D. V. Divine et al.
  • 1Department of Mathematics and Statistics, Faculty of Science, University of Tromsø, 9037, Norway
  • 2Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
  • 3Department of Mathematics and Statistics, Faculty of Science, University of Tromsø, 9037, Norway
  • *also at: Norwegian Polar Institute, Polar Environmental Centre, 9296 Tromsø, Norway

Abstract. The paper presents an approach to estimate parameters of a local stationary AR(1) time series model by maximization of a local likelihood function. The method is based on a propagation-separation procedure that leads to data dependent weights defining the local model. Using free propagation of weights under homogeneity, the method is capable of separating the time series into intervals of approximate local stationarity. Parameters in different regions will be significantly different. Therefore the method also serves as a test for a stationary AR(1) model. The performance of the method is illustrated by applications to both synthetic data and real time-series of reconstructed NAO and ENSO indices and GRIP stable isotopes.