Tests of Linear and Logarithmic Transformations for Integrated Processes
针对整合过程，提出非嵌套检验来区分线性变换与对数变换，适用于无漂移和有漂移情形，并通过蒙特卡洛实验和实证例子展示其有限样本中的实用性。
Abstract This article proposes nonnested tests of linear and logarithmic transformations of integrated processes against each other, where the innovations of both series follow autoregressive processes. It is shown that the null distributions of the test statistics for both the linear and logarithmic transformations are nonstandard when the processes have no drift, whereas they are asymptotically normal when the processes have positive drift. Monte Carlo experiments and illustrative empirical examples are provided to show the practical usefulness of the tests in differentiating between linear and logarithmic transformations of a process in finite samples.