Abstract: Detection of variance change points is statistically difficult when the data exhibit a varying mean structure and autocorrelation. Existing variance change point tests either require the assumption of mean constancy or sacrifice testing power due to serial dependence. This article addresses these problems by proposing a trend-robust and autocorrelation-efficient variance change point test via a differencing approach. This approach removes the mean effect without fitting the mean function. It also allows the test to retrieve the reduced power due to serial dependence. We prove that the optimal difference-based test should minimize the long-run coefficient of variation of the sample second moment of the noise instead of the long-run variance in the presence of serial dependence. The optimal solution can be efficiently computed by fractional quadratic programming. The asymptotic relative efficiency under a local alternative hypothesis is derived. A rate-optimal long-run variance estimator is also proposed. It is proven to be doubly robust against varying mean and variance change points.

Key words and phrases: Change point, cumulative sum, difference sequence, long-run variance, non-linear time series.