英文文献：Numerical distribution functions of fractional unit root and cointegration tests-分数单位根的数值分布函数和协整检验
英文文献作者：James G. MacKinnon,Morten ?rregaard Nielsen
英文文献摘要：
We calculate numerically the asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter, b, which must be estimated, simple tabulation is not feasible. Partly due to the presence of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is usually the case. We deal with model uncertainty by model averaging rather than by model selection. We make available a computer program which, given the dimension of the problem, q, and a value of b, provides either a set of critical values or the asymptotic P value for any value of the likelihood ratio statistic. The use of this program is illustrated by means of an empirical example involving opinion poll data.

数值计算了分数单位根和协整秩的似然比检验的渐近分布函数。因为这些分布依赖于一个实值参数，b，它必须被估计，简单的制表是不可行的。部分由于这个参数的存在，用于获得数值分布函数的响应面回归的模型规格的选择比通常情况下更加复杂。我们通过模型平均而不是模型选择来处理模型的不确定性。我们提供一个计算机程序，给定问题的维数q和一个值b，提供一组临界值或概率比统计量的任意值的渐近P值。通过一个涉及民意调查数据的实证例子说明了该程序的使用。