There has been much attention in recent years to the problem of detecting mean changes in a piecewise constant time series. Often, methods assume that the noise can be taken to be independent, identically distributed (IID), which in practice may not be a reasonable assumption. There is comparatively little work studying the problem of mean changepoint detection in time series with nontrivial autocovariance structure. In this article, we propose a likelihood‐based method using wavelets to detect changes in mean in time series that exhibit time‐varying autocovariance. Our proposed technique is shown to work well for time series with a variety of error structures via a simulation study, and we demonstrate its effectiveness on two data examples arising in economics.

中文翻译：

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在存在时变自协方差的情况下检测均值变化

近年来，人们越来越关注检测分段恒定时间序列中的均值变化的问题。通常，方法假定噪声可以被认为是独立的，均匀分布的（IID），实际上这可能不是一个合理的假设。研究具有非平凡自协方差结构的时间序列中的均值变化点检测问题的工作相对较少。在本文中，我们提出了一种基于小波的方法，该方法使用小波来检测时间序列中均值随时间变化的自协方差的变化。通过仿真研究表明，我们提出的技术对于具有各种误差结构的时间序列非常有效，并且我们在经济学中产生的两个数据示例中证明了其有效性。