Abstract This paper considers a residual-based approach to diagnose the adequacy of both the univariate and vector multiplicative error model (MEM). Two residual-based statistics are constructed based on the parameter estimates of the linear autoregressions with the standardized residuals as dependent variables. Since the autoregressions involve estimated standardized residuals, the correct asymptotic distributions of test statistics are obtained by taking into account the impact of parameter estimation uncertainty. Monte Carlo simulations indicate that the proposed test statistics perform well against their competitors in terms of empirical size and power. An empirical application further shows the usefulness of the proposed test in evaluating MEMs.

中文翻译：

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评估乘法误差模型：一种基于残差的方法

摘要 本文考虑了一种基于残差的方法来诊断单变量和向量乘法误差模型 (MEM) 的充分性。基于线性自回归的参数估计构建了两个基于残差的统计量，并将标准化残差作为因变量。由于自回归涉及估计的标准化残差，因此通过考虑参数估计不确定性的影响来获得检验统计量的正确渐近分布。Monte Carlo 模拟表明，所提出的测试统计数据在经验规模和功效方面与竞争对手相比表现良好。实证应用进一步表明了所提议的测试在评估 MEM 方面的有用性。