Fourier methods for analyzing piecewise constant volatilities

On variance estimation under shifts in the mean

In many situations, it is crucial to estimate the variance properly. Ordinary variance estimators perform poorly in the presence of shifts in the mean. We investigate an approach based on non-overlapping blocks, which yields good results in change-point scenarios. We show the strong consistency and the asymptotic normality of such blocks-estimators of the variance under independence. Weak consistency is shown for short-range dependent strictly stationary data. We provide recommendations on the appropriate choice of the block size and compare this blocks-approach with difference-based estimators. If level shifts occur frequently and are rather large, the best results can be obtained by adaptive trimming of the blocks.