Further results on robust multivariate time series analysis in nonlinear models with autoregressive and t-distributed errors
- verfasst von
- 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.
- Organisationseinheit(en)
-
Geodätisches Institut
- Externe Organisation(en)
-
Hochschule Anhalt
Technische Universität Clausthal
- Typ
- Aufsatz in Konferenzband
- Seiten
- 25-38
- Anzahl der Seiten
- 13
- Publikationsdatum
- 04.10.2018
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- Elektronische Version(en)
-
https://doi.org/10.1007/978-3-319-96944-2_3 (Zugang:
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