Monitoring time series based on estimating functions

  • A large class of estimators including maximum likelihood, least squares and M-estimators are based on estimating functions. In sequential change point detection related monitoring functions can be used to monitor new incoming observations based on an initial estimator, which is computationally efficient because possible numeric optimization is restricted to the initial estimation. In this work, we give general regularity conditions under which we derive the asymptotic null behavior of the corresponding tests in addition to their behavior under alternatives, where conditions become particularly simple for sufficiently smooth estimating and monitoring functions. These regularity conditions unify and even extend a large amount of existing procedures in the literature, while they also allow us to derive monitoring schemes in time series that have not yet been considered in the literature including non-linear autoregressive time series and certain count time series such as binary or Poisson autoregressive models. We do not assume that the estimating and monitoring function are equal or even of the same dimension, allowing for example to combine a non-robust but more precise initial estimator with a robust monitoring scheme. Some simulations and data examples illustrate the usefulness of the described procedures.

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Author:Claudia Kirch, Joseph Tadjuidje Kamgaing
URN (permanent link):urn:nbn:de:hbz:386-kluedo-36939
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (148)
Document Type:Preprint
Language of publication:English
Publication Date:2014/01/27
Year of Publication:2014
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2014/01/29
Tag:Autoregressive time series; Change analysis; Integer-valued time series; Nonlinear regression; Nonparametric regression; Sequential test
Number of page:36
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012