论文标题
基于样品自动腔的单位根测试
Testing for unit roots based on sample autocovariances
论文作者
论文摘要
我们针对单位根替代$ H_1 $提出了针对固定零假设$ h_0 $的新单元根测试。我们的方法是非参数，因为$ H_0 $仅假定相关过程为$ i（0）$，而无需指定任何参数表格。新的测试基于以下事实：样本自动助力函数（ACVF）以$ i（0）$过程收敛到有限的ACVF，而它则与单位根的过程相差无限。因此，新的测试拒绝$ H_0 $对于样本ACVF的较大值。为了应对技术挑战“大大有多大”，我们将样本分开，并建立适当的正常近似测试统计统计量。新测试统计量的实质性歧视功率源于以下事实：它在$ h_0 $以下的有限价值在$ h_1 $下方的无限范围内分开。这使我们能够将测试的临界值截断，以使其与渐近功率一致。它还减轻了由于样本分解而导致的电力损失。该测试以用户友好的R功能实现。
We propose a new unit-root test for a stationary null hypothesis $H_0$ against a unit-root alternative $H_1$. Our approach is nonparametric as $H_0$ only assumes that the process concerned is $I(0)$ without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function (ACVF) converges to the finite population ACVF for an $I(0)$ process while it diverges to infinity for a process with unit-roots. Therefore the new test rejects $H_0$ for the large values of the sample ACVF. To address the technical challenge `how large is large', we split the sample and establish an appropriate normal approximation for the null-distribution of the test statistic. The substantial discriminative power of the new test statistic is rooted from the fact that it takes finite value under $H_0$ and diverges to infinity under $H_1$. This allows us to truncate the critical values of the test to make it with the asymptotic power one. It also alleviates the loss of power due to the sample-splitting. The test is implemented in a user-friendly R-function.
