论文标题
无需分发测试，以改变本地固定过程的趋势功能的变化
A distribution free test for changes in the trend function of locally stationary processes
论文作者
论文摘要
在普通时间序列模型中，$ x_ {i，n} =μ（i/n） + \ varepsilon_ {i，n} $带有非平稳错误的问题，我们考虑检测平均函数$μ$与基准$ g（μ）的显着偏差的问题DT $）。该问题是由更现实的变化点分析建模来激发的，其中人们有兴趣在平稳变化的均值顺序$（μ（i/n））_ {i = 1，\ ldots，n} $中识别相关偏差，并且不能假设序列是序列常数。使用适当的估计量为平均函数和阈值的集成平方偏差开发了对这种假设的测试。通过适应非平稳过程的新概念，构建了相关偏差假设的渐近关键测试。结果通过仿真研究和数据示例说明了结果。
In the common time series model $X_{i,n} = μ(i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $μ$ from a benchmark $g (μ)$ (such as the initial value $μ(0)$ or the average trend $\int_{0}^{1} μ(t) dt$). The problem is motivated by a more realistic modelling of change point analysis, where one is interested in identifying relevant deviations in a smoothly varying sequence of means $ (μ(i/n))_{i =1,\ldots ,n }$ and cannot assume that the sequence is piecewise constant. A test for this type of hypotheses is developed using an appropriate estimator for the integrated squared deviation of the mean function and the threshold. By a new concept of self-normalization adapted to non-stationary processes an asymptotically pivotal test for the hypothesis of a relevant deviation is constructed. The results are illustrated by means of a simulation study and a data example.
