{'fraction_non_alphanumeric': 0.02709492194509241, 'fraction_numerical': 0.019020276332316528, 'mean_word_length': 4.618951612903226, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, 'https://': 1, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Cross correlations in European government bonds and EuroStoxx

We use principle component analysis (PCA) of cross correlations in European government bonds and European stocks to investigate the systemic risk contained in the European economy. We tackle the task to visualize the evolution of risk, introducing the conditional average rolling sum (CARS). Using this tool we see that the risk of government bonds and stocks had an independent movement. But in the course of the European sovereign debt crisis the coupling between bonds and stocks has strongly ncreased. This results in an in-phase oscillation of risk for both markets since mid 2010. In our data, we observe a steep amplitude increase, suggesting a high vulnerability of the two coupled systems.


Introduction
The inability to refinance their sovereign debts of some European states and the outbreak of the financial crisis in 2008 led in 2010 to the still ongoing European sovereign debt crisis. To stabilize the markets and give incentives to invest in Europe, the European Union implemented the European Financial Stability Facility (EFSF) and later the European Stability Mechanism (ESM). Heavily indebted European nations can use these tools to refinance their government debt. [1] The utilization of this bailout support has to be accompanied by fiscal consolidation, reforms and privatization of public goods. [8] Recent studies have shown, that principle component analysis (PCA) is a viable tool to monitor the systemic risk [14,2,6,11,12]. Zheng et al. have used the first eigenvalues of the crosscorrelations of returns of different stock indices and stocks to reveal the rise in systemic risk, that lead to the financial crisis in 2007. In financial correlation matrices the first eigenvalue dominates. This shows that most of the information is contained in the largest eigenvalue and its eigenvector. Smaller eigenvalues are typically in the random regime and therefore carry less information of the system, but are not pure noise. 1 [13,7] Furthermore we compare government bonds with national stocks indices and see, that government bonds react show an earlier but not so distinct rise in systemic risk than stocks indices.

Results
We analyzed the principle components λ i of the correlations between European government bonds in moving time windows with 12 and 24 months. In figure 1 it can be observed, that the rise in the first principle component strongly depends on the chosen time window, as was already reported by [14]. Graph a) and b) have its steepest rise in λ 1 in July 2010 and indicate the beginning of the European debt crisis. It can also be seen, that the first eigenvalue increases in May 2007. This corresponds to the financial crisis, that started in December 2007 in the USA and took some time to spread to Europe.

Discussion
A rise in the largest eigenvalue corresponds to a rise in the systemic risk, because the eigenvalue explains most of the variation in data [14]. There is a distinct rise in λ 1 in 2008 for both the European government bonds and the European national stocks indices. This shows the connection in Europe between the financial crisis and the dept crisis. Kaminsky et al. already observed that a banking crisis can lead to currency crisis. [5] An interesting fact is, that the bonds react earlier than the stocks indices. Only the bonds show the higher systemic risk, that originates from the fear of sovereign debt defaults surfaced in late 2009 [3], which eventually lead to a consecutive financial crisis in 2011. We see that the CARS of the government bonds has risen in 2013 and holds high values since then. We hypothesize, that sovereign bailout tools like the European Stability Mechanism, which was ratified in the last quarter of 2012 [4], coupled the fiscal budget of the European states more tightly and this is reflected in the CARS. Furthermore a alarming increase in the CARS of the indices and the bonds (in the 24 months time window) can be observed in December 2014. We assume that this surge can be associated with recent political uncertainties.

Conclusion
We showed that the method used in [14] to indicate the rise in systemic risk, leading to the financial crisis of 2008, can also be used to indicate the European debt crisis. The start of the Euro crisis can be seen by applying principle component analysis to European government bonds, while its impact on the financial markets can be tracked using national stock indices instead of bonds. We introduced the conditional average rolling sum (CARS), which gives distinct spikes indicating a strong rise in correlation. The CARS shows alarming values since 2013 and a very steep surge in the end of 2014. This leads us to the conclusion, that the European debt crisis, despite its unusual duration in terms of a financial crisis [10], it is not subsiding but an ongoing process with an uncertain outcome.

Data
We used the website https://research.stlouisfed.org/fred2/, which offers data for economic research. In

Method
The conditional averaged rolling sum CARS is defined by λ1 λ (t)>0 where λ 1 is the first principal component of the correlation matrix C(t) at time t for the time frame ω = {t ′ |t − ∆ ≤ t ′ ≤ t}. In our case, we choose a set of ω with different time lags ∆ = 1, 2, ..., 12month. In general the CARS · cond. Ω can be used to identify time-dependent events of importance and reveal their memory effects. The advantage of CARS is that past events are not forgotten and bubbles, which are usually building up over a period of time, can be detected.