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CPS1461 Michal P. et. al
From the statistical point of view, the panel data with changepoints are
represented as some multivariate data points across different subjects and
they are usually assessed using an ordinary least squares approach.
Hypothetical changepoints are firstly detected, they are tested for their
significance, and then the overall model structure is estimated using the
knowledge about the existing changepoints. The available literature falls into
two main categories: in the first one, the authors consider the changepoint
detection problem within homogeneous panel data (see, for instance, De
Watcher and Tzavalis, 2012; Qian and Su, 2016) and, in the second category,
they deal with the changepoint detection and estimation in heterogeneous
panel data (Baltagi et al., 2016; Kim, 2011; Pesaran, 2006). In all these
situations, however, the authors firstly need to detect existing changepoints
and, later, they can adopt some tests to decide whether these structural breaks
in the panels are statistically significant or not. Moreover, the panels are
considered to be independent in the aforementioned literature.
On the other hand, the changepoint detection problem is mostly
considered for situations where the number of panels NN and the number of
observations in each panel TN are both sufficiently large—they are both
supposed to tend to infinity (see Horvath and Huskova, 2012; Chan et al.,
2013). For practical applications, however, it may not be possible to have a
long follow up period. Therefore, the changepoint estimation is also studied
for the panel data, where the number of observations in the panel is fixed and
does not depend on N (for instance, Bai, 2010) or it is even extremely small
(Pestova and Pesta, 2015, 2017).
In this paper, we propose a statistical test where no changepoint
estimation is needed apriori and the panel data are assumed to form a very
general structure: the panels are allowed to be dependent with some common
dependence factor; the panels are heteroscedastic; the follow-up period is
extremely short; and different jump magnitudes are possible across the panels
accounting also for a situation that only some panels contain the jump and
the remaining ones do not. Finally, the observations within each panel may
preserve some form of dependence (for instance, an autoregresive process or
even GARCH sequence). We are specifically interested in testing the null
hypothesis that there is no common change in the means of such general
panels: the no changepoint situation can be expressed as = T and the
corresponding alternative hypothesis is that there is at least one panel
i{1,…,N} with the jump in its mean, located at < T, with a nonzero magnitude
i ≠ 0.

2. Methodology
The motivation for the model presented in this paper can be taken, for
instance, from a non-life insurance business, where multiple insurance

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