Statistics and Its Interface

Volume 4 (2011)

Number 2

Testing for measurement errors with discrete-time data sampled from a CARMA model

Pages: 235 – 242

DOI: http://dx.doi.org/10.4310/SII.2011.v4.n2.a17

Authors

Kung-Sik Chan (Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Ia., U.S.A.)

Patrick Fayard (Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada)

Henghsiu Tsai (Institute of Statistical Science, Academia Sinica, Taipei, Taiwan)

Abstract

We consider the problem of testing for measurement errors with discrete-time data sampled from a continuoustime autoregressive moving-average process. We develop an efficient algorithm for computing the likelihood ratio test (LRT) statistic, and derive the non-standard asymptotic null distribution of the LRT. The efficacy of the proposed test is illustrated by simulations and a real application from an environmental study.

Keywords

forecasting, Gaussian distribution, Kalman filter, likelihood ratio test, non-standard asymptotics

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