Further results on robust multivariate time series analysis in nonlinear models with autoregressive and t-distributed errors
- authored by
- Hamza Alkhatib, Boris Kargoll, Jens-André Paffenholz
- 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.
- Organisation(s)
-
Geodetic Institute
- External Organisation(s)
-
Anhalt University of Applied Sciences
Clausthal University of Technology
- Type
- Conference contribution
- Pages
- 25-38
- No. of pages
- 13
- Publication date
- 04.10.2018
- Publication status
- Published
- Peer reviewed
- Yes
- Electronic version(s)
-
https://doi.org/10.1007/978-3-319-96944-2_3 (Access:
Closed)
-
Details in the research portal "Research@Leibniz University"
