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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.

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