STATIONARITY TESTS UNDER TIME-VARYING SECOND MOMENTS
分析了时变方差对I(0)原假设下平稳性检验的影响，推导了检验统计量的极限分布，并通过蒙特卡洛模拟量化了方差突变和趋势方差对检验性质的影响，最后提出了自助法版本解决推断问题。
In this paper we analyze the effects of a very general class of time-varying variances on well-known “stationarity” tests of the I(0) null hypothesis. Our setup allows, among other things, for both single and multiple breaks in variance, smooth transition variance breaks, and (piecewise-) linear trending variances. We derive representations for the limiting distributions of the test statistics under variance breaks in the errors of I(0), I(1), and near-I(1) data generating processes, demonstrating the dependence of these representations on the precise pattern followed by the variance processes. Monte Carlo methods are used to quantify the effects of fixed and smooth transition single breaks and trending variances on the size and power properties of the tests. Finally, bootstrap versions of the tests are proposed that provide a solution to the inference problem.We are grateful to Peter Phillips, a co-editor, and two anonymous referees whose comments on an earlier draft have led to a considerable improvement in the paper.