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

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.