Panel data segmentation under finite time horizon

• We study the estimation of common changes in the context of panel data.
• We emphasize a connection between the total variation denoising approach and the weighted CUSUM estimates.
• We propose a covariance-based extension of existing weighting schemes that ensures consistency if the number of panels tends to infinity.
• We derive sharp bounds on the change to noise ratio that ensure consistency in the i.i.d. setting for classical weightings.

We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on weighted denoising estimates, involving the group fused LASSO, and on the weighted CUSUM estimates. Due to the fixed sample size, the common weighting schemes do not guarantee consistency under (serial) dependence and most typical weightings do not even provide consistency in the i.i.d. setting when the noise is too dominant.Hence, on the one hand, we propose a consistent covariance-based extension of existing weighting schemes and discuss straightforward estimates of those weighting schemes. The performance will be demonstrated empirically in a simulation study. On the other hand, we derive sharp bounds on the change to noise ratio that ensure consistency in the i.i.d. setting for classical weightings.