Panel data of our interest consist of a moderate or relatively large number of panels, while the panels contain a small number of observations. This paper establishes testing procedures to detect a possible common change in means of the panels. To this end, we consider a ratio type test statistic and derive its asymptotic distribution under the no change null hypothesis. Moreover, we prove the consistency of the test under the alternative. The main advantage of such an approach is that the variance of the observations neither has to be known nor estimated. On the other hand, the correlation structure is required to be calculated. To overcome this issue, a bootstrap technique is proposed in the way of a completely data driven approach without any tuning parameters. The validity of the bootstrap algorithm is shown. As a byproduct of the developed tests, we introduce a common break point estimate and prove its consistency. The results are illustrated through a simulation study. An application of the procedure to actuarial data is presented. Keywords Change point¨Panel data¨Change in mean¨Fixed panel sizeS hort panels¨Ratio type statistics¨Bootstrap Mathematics Subject Classification (2000) 62H15¨62H10¨62E206 2P05¨62F40

Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented, as well.

Detection procedures for a change in means of panel data are proposed. Unlike classical inference tools used for the changepoint analysis in the panel data framework, we allow for mutually dependent and generally non-stationary panels with an extremely short follow-up period. Two competitive self-normalized test statistics are employed and their asymptotic properties are derived for a large number of available panels. The bootstrap extensions are introduced in order to handle such a universal setup. The novel changepoint methods are able to detect a common break point even when the change occurs immediately after the first time point or just before the last observation period. The developed tests are proved to be consistent. Their empirical properties are investigated through a simulation study. The invented techniques are applied to option pricing and non-life insurance.