Nonparametric Bootstrap Tests for Independence of Generalized Errors
Nonparametric Bootstrap Tests for Independence of Generalized Errors
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DOI：
10.1111/ectj.12059
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发表时间：
2015-01
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通讯作者：
Zaichao Du
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作者：
Zaichao Du
在本文中，我们开发了一种测试不可观测广义误差独立性的一般方法。该方法可用于检验广义误差的序列独立性，以及检验广义误差与可观测协变量之间的独立性。前者可以作为检验时间序列模型充分性的统一方法，因为模型充分性通常意味着经过适当变换后得到的广义误差是独立且同分布的。后者是许多非线性经济模型中一个关键的识别假设。我们的测试基于经典的样本依赖度量，即应用于广义残差的Hoeffding-Blum-Kiefer-Rosenblatt型经验过程。我们建立了过程的均匀展开，从而推导出参数估计效果的显式表达式，这使得我们的测试不是无干扰参数的。为了避免这个问题，我们提出了一个乘法器型的自举来近似极限分布。我们的自举过程在计算上非常简单，因为它不需要在每次自举复制中重新估计参数。对每日汇率数据的模拟和经验应用突出了我们方法的优点。
In this paper, we develop a general method of testing for independence when unobservable generalized errors are involved. Our method can be applied to testing for serial independence of generalized errors, and testing for independence between the generalized errors and observable covariates. The former can serve as a unified approach to testing the adequacy of time series models, as model adequacy often implies that the generalized errors obtained after a suitable transformation are independent and identically distributed. The latter is a key identification assumption in many nonlinear economic models. Our tests are based on a classical sample dependence measure, the Hoeffding–Blum–Kiefer–Rosenblatt‐type empirical process applied to generalized residuals. We establish a uniform expansion of the process, thereby deriving an explicit expression for the parameter estimation effect, which causes our tests not to be nuisance‐parameter‐free. To circumvent this problem, we propose a multiplier‐type bootstrap to approximate the limit distribution. Our bootstrap procedure is computationally very simple as it does not require a re‐estimation of the parameters in each bootstrap replication. Simulations and empirical applications to daily exchange rate data highlight the merits of our approach.