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Further Results on a Robust Multivariate Time Series Analysis in Nonlinear Models with Autoregressive and t-Distributed Errors

  • Hamza AlkhatibEmail author
  • Boris Kargoll
  • Jens-André Paffenholz
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

We investigate a time series model which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance stationary autoregressive (AR) processes whose white noise components obey independent scaled t-distributions. These distributions enable the stochastic modeling of heavy tails or outlier-afflicted observations and present the framework for a partially adaptive, robust maximum likelihood (ML) estimation of the deterministic model parameters, of the AR coefficients, of the scale parameters, and of the degrees of freedom of the underlying t-distributions. To carry out the ML estimation, we derive a generalized expectation maximization (GEM) algorithm, which takes the form of linearized, iteratively reweighted least squares. In order to derive a quality assessment of the resulting estimates, we extend this GEM algorithm by a Monte Carlo based bootstrap algorithm that enables the computation of the covariance matrix with respect to all estimated parameters. We apply the extended GEM algorithm to a multivariate global navigation satellite system (GNSS) time series, which is approximated by a three-dimensional circle while taking into account the colored measurement noise and partially heavy-tailed white noise components. The precision of the circle model fitted by the GEM algorithm is superior to that of the previous standard estimation approach.

Keywords

Multivariate time series Nonlinear regression model AR process Scaled t-distribution Partially adaptive estimation Robust parameter estimation GEM algorithm Bootstrapping GNSS time series 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Geodätisches Institut, Leibniz Universität HannoverHannoverGermany

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