Effects of measurement errors on the analysis of error correction models (ECMs) of vector processes observed with measurement errors were studied in Hong et al. (2016. Analysis of cointegrated models with measurement errors. Journal of Statistical Computation and Simulation. 2016;86:623–639). It was found that statistically undesirable effects on the analysis attributable to endogeneity in the ECM induced by measurement errors, even in their simplest form. Therefore, we first propose a method using instrumental variables (IV) and derive the asymptotic distributions of the reduced rank estimator that eliminate the undesirable effect of endogeneity. Then, we propose a reduced rank maximum likelihood (ML) estimation using a moving-average term to deal with endogeneity. These methods yield estimators that are consistent and asymptotically unbiased. The first method with IV is simple to use computationally and yields good initial estimate for the second ML method. We investigate the effects of the measurement errors on the proposed methods through a Monte Carlo simulation study.

中文翻译：

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带有测量误差的误差修正模型的估计

Hong 等人研究了测量误差对通过测量误差观察到的矢量过程的误差校正模型 (ECM) 分析的影响。（2016 年。具有测量误差的协整模型分析。统计计算与模拟杂志。2016 年；86：623–639）。结果发现，即使是最简单的形式，测量误差也会导致 ECM 中的内生性对分析产生统计上的不良影响。因此，我们首先提出了一种使用工具变量 (IV) 的方法，并推导出了减少内生性的不良影响的降阶估计量的渐近分布。然后，我们提出了使用移动平均项来处理内生性的降阶最大似然 (ML) 估计。这些方法产生一致且渐近无偏的估计量。带有 IV 的第一种方法在计算上易于使用，并且为第二种 ML 方法产生良好的初始估计。我们通过蒙特卡罗模拟研究调查了测量误差对所提出方法的影响。