Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.

The European Union and its Northern Frontier : EUropean Geopolitics and its Arctic Context

The present study explores EUropean geopolitical agency in a distinct spatio-temporal context: the Arctic region of the early 21st century. Thus, it provides an in-depth analysis of the European Union’s process to construct EUropean legitimacy and credibility in its ‘Northern Neighbourhood’ between 2008 and 2014. Embedded in a conceptual and methodological framework using critical geopolitics, this study assesses the strategic policy reasoning of the EU and the implicit geopolitical discourses that guide and determine a particular line of argumentation so as to claim a ‘legitimate’ role in the Arctic and accordingly construct a distinct ‘EUropean Arctic space’. In doing so, it establishes a clearer picture on the (narrated) regional interests of the EU and the related developed policy and concrete steps taken in order to get hold of these interests. Eventually, the analysis gets to the conceptual bottom of what exactly fashioned the EU with geopolitical agency in the circumpolar North. As a complementary explanation, this study provides a thick description of the area under scrutiny – the Arctic region – in order to explicate the systemic context that conditioned the EU’s regional demeanour and action. Elucidated along the lines of Arctic history and identity, rights, interests and responsibility, it delineates the emergence of the Arctic as a region of and for geopolitics. The findings indicate that the sui generis character of the Arctic as EUropean neighbourhood essentially determined the EU’s regional performance. It explicates that the Union’s ‘traditional’ geopolitical models of civilian or normative power got entangled in a fluid state of Arctic affairs: a distinct regional system, characterised by few strong state actors with pronounced national Arctic interests and identities, and an indefinite local context of environmental changes, economic uncertainties and social challenges. This study applies critical geopolitics in a Political Science context and essentially contributes to a broader understanding of EU foreign policy construction and behaviour. Ultimately, it offers an interdisciplinary approach on how to analyse EU external action by explicitly taking into account the internal and external social processes that ultimately condition a certain EUropean foreign policy performance.