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Gradual variance change point detection with a smoothly changing mean trend

In contrast to the analysis of abrupt changes, methods for detecting gradual change points are less developed. In this paper, we are interested in the scenario that the variance of data may vary gradually while the mean of data changes in a smooth fashion. We propose a penalized weighted least squares approach with an iterative estimation procedure to detect the gradual variance change point with a smoothly changing mean function. The null distribution of the test statistic is derived in association with the consistency of estimates. The performance of our method is illustrated by means of a simulation study and a real data example.