Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/230097
Authors: 
Fasen‐Hartmann, Vicky
Kimmig, Sebastian
Year of Publication: 
2020
Citation: 
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] 41 [Issue:] 5 [Pages:] 620-651
Abstract: 
In this article, we present a robust estimator for the parameters of a stationary, but not necessarily Gaussian, continuous‐time ARMA(p,q) (CARMA(p,q)) process that is sampled equidistantly. Therefore, we propose an indirect estimation procedure that first estimates the parameters of the auxiliary AR(r) representation (r ≥ 2p−1) of the sampled CARMA process using a generalized M‐ (GM‐)estimator. Since the map which maps the parameters of the auxiliary AR(r) representation to the parameters of the CARMA process is not given explicitly, a separate simulation part is necessary where the parameters of the AR(r) representation are estimated from simulated CARMA processes. Then, the parameters which take the minimum distance between the estimated AR parameters and the simulated AR parameters give an estimator for the CARMA parameters. First, we show that under some standard assumptions the GM‐estimator for the AR(r) parameters is consistent and asymptotically normally distributed. Then, we prove that the indirect estimator is also consistent and asymptotically normally distributed when the asymptotically normally distributed LS‐estimator is used in the simulation part. The indirect estimator satisfies several important robustness properties such as weak resistance, πdn‐robustness and it has a bounded influence functional. The practical applicability of our method is illustrated in a small simulation study with replacement outliers.
Subjects: 
AR process
CARMA process
indirect estimator
influence functional
GM‐estimator
LS‐estimator
outlier
resistance
robustness
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
Document Version: 
Published Version

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