This is a short summary of a recent survey [FR03] focusing on the observed evidence, that Internet connectivity is positively correlated with spread of democracy at high levels of significance. The results of multivariate correlation analysis and probabilities regression estimate models are based on the combined analysis of mid - 1991's, to 2001 data series of the Eurostat's and US Census Bureau, the World Bank, and OECD's statistical data service which track the growth of information technology and rating of freedom and democracy worldwide.(author's abstract)

Many human neurological and psychiatric disorders are substantially heritable and there is growing inter-est in searching for genetic variants explaining variability in disease-induced alterations of brain anatomy and function, as measured using neuroimaging techniques. The standard analysis approach in genetic neuroimaging is the mass-univariate linear modeling approach, which is disadvantageous, since it cannot account for dependencies among collinear variables and has to be corrected for multiple testing. In con-trast, multivariate methods include combined information from multiple variants simultaneously into the analysis, and can therefore account for the correlation structure in both the neuroimaging and the genetic data. Partial Least Squares Analysis and Canonical Correlation Analysis are common multivariate ap-proaches and different variants have been established for genetic neuroimaging. However, a compre-hensive comparison with respect to data characteristics and strengths and weaknesses of these methods was missing to date. This thesis elaborately compared three multivariate techniques, Sparse Canonical Correlation Analysis (Sparse CCA), Bayesian Inter-Battery Factor Analysis (Bayesian IBFA) and Partial Least Squares Corre-lation (PLSC) in order to express a clear statement on which method in to choose for analysis in genetic neuroimaging. It was shown that for highly collinear neuroimaging data, Bayesian IBFA could not be recommended, since additional post-processing steps were required to differentiate between causal and non-informative components. In contrast, Sparse CCA and PLSC were suitable for genetic neuroimaging data. Among the two, the use of Sparse CCA was recommended in situations with relatively low-dimensional neuroimaging and genetic data, since its predictive power was higher when data dimension-ality was below 400 times sample size. For higher dimensionalities, the predictive power of PLSC ex-ceeded that of Sparse CCA. Thus, for multivariate modeling of high-dimensional neuroimaging-genetics-associations, a preference for the usage of PLSC was indicated. The remainder of this thesis dealt with the improvement of the computational efficiency of multivariate statistics in genetic neuroimaging, since it can be expected that there will be a growth in cost- and time-efficient DNA sequencing as well as neuroimaging techniques in the coming years, which will result in excessively long computation times due to increasing data dimensionality. To accommodate this large number of variables, a new and computational efficient statistical approach named PLSC-RP was pro-posed, which incorporates a method for dimensionality reduction named Random projection (RP) into traditional PLSC in order to represent the originally high-dimensional data in lower dimensional spaces. Subsequently, PLSC is used for multivariate analysis of compressed data sets. Finally, the results are transformed back to the original spaces to enable the interpretation of original variables. It was demon-strated that the usage of PLSC-RP reduced computation times from hours to seconds compared to its state-of-the-art counterpart PLSC. Nonetheless, the accuracy of the results was not impaired, since the results of PLSC-RP and PLSC were statistically equivalent. Furthermore, PLSC-RP could be used for inte-grative analysis of data sets containing high-dimensional neuroimaging data, high-dimensional genetic data or both, and was therefore shown to be independent of the statistical data type. Thus, PLSC-RP opens up a wide range of possible applications.

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This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit. / This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit.