Measurement Error in Dynamic Models
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Many time series contain measurement (often sampling) error and the problem of assessing the impacts of such errors and accounting for them has been receiving increasing attention of late. This paper provides a survey of this problem with an emphasis on estimating the coefficients of the underlying dynamic model, primarily in the context of fitting linear and nonlinear autoregressive models. An overview is provided of the biases induced by ignoring the measurement error and of methods that have been proposed to correct for it, and remaining inferential challenges are outlined.
KeywordsAutoregressive models Bayesian bootstrapping Maximum likelihood Pseudo-maximum likelihood Ricker model Simex State space models Time series Yule-Walker
I wish to express my appreciation to Brajendra Sutradhar for organizing the International Symposium in Statistics on Longitudinal Data Analysis and for serving as editor for the written contributions to this volume. I would also like to thank the members of the audience at the conference for helpful feedback and particularly thank the two referees whose comments and corrections helped improve the initial draft of this paper. Portions of this work grew out of earlier joint work with John Staudenmayer, which was supported by NSF-DMS-0306227, and with David Resendes. I am grateful to David for allowing the use of some results here from his dissertation. This paper also grew out of a seminar presented at the Center for Ecological and Evolutionary Synthesis (CEES), at the University of Oslo, in spring of 2010. I am very grateful to Nils Stenseth and CEES for support during my stay there.
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