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Dependence modeling with applications in financial econometrics
Dependence modeling with applications in financial econometrics
The amount of data available in banking, finance and economics steadily increases due to the ongoing technological progress and the continuing digitalization. A key element of many econometric models for analyzing this data are methods for assessing dependencies, cross-sectionally as well as intertemporally. For this reason, the thesis is centered around statistical and econometric methods for dependence modeling with applications in financial econometrics. The first part of this cumulative dissertation consists of three contributions. The first contribution provides a thorough explanation of the partial copula. It is a natural generalization of the partial correlation coefficient and several of its properties are investigated. In the second contribution, a different multivariate generalization of the partial correlation, the partial vine copula (PVC), is introduced. The PVC is a specific simplified vine copula (SVC) consisting of bivariate higher-order partial copulas, which are copula-based generalizations of sequentially computed partial correlations. Several properties of the PVC are presented and it is shown that, if SVCs are considered as approximations of multivariate distributions, the PVC has a special role as it is the limit of stepwise estimators. The third contribution introduces statistical tests for the simplifying assumption with a special focus on high-dimensional vine copulas. We propose a computationally feasible test for the simplifying assumption in high-dimensions, which is successfully applied to data sets with up to 49 dimensions. The novel test procedure is based on a decision tree which is used to identify the possibly strongest violation of the simplifying assumption. The asymptotic distribution of the test statistic is derived under consideration of estimation uncertainty in the copula parameters. The finite sample performance is analyzed in an extensive simulation study and the results show that the power of the test only slightly decreases in the dimensionality of the test problem. In the second part of the dissertation, the assessment of risk measures is studied with a special focus on the financial return data used for estimation. It is shown that the choice of the sampling scheme can greatly affect the results of risk assessment procedures if the assessment frequency and forecasting horizon are fixed. Specifically, we study sequences of variance estimates and show that they exhibit spurious seasonality, if the assessment frequency is higher than the sampling frequency of non-overlapping return data. The root cause of spurious seasonality is identified by deriving the theoretical autocorrelation function of sequences of variance estimates under general assumptions. To overcome spurious seasonality, alternative variance estimators based on overlapping return data are suggested. The third part of the dissertation is about state space methods for systems with lagged states in the measurement equation. Recently, a low-dimensional modified Kalman filter and smoother for such systems was proposed in the literature. Special attention is paid to the modified Kalman smoother, for which it is shown that the suggested smoother in general does not minimize the mean squared error (MSE). The correct MSE-minimizing modified Kalman smoother is derived and computationally more efficient smoothing algorithms are discussed. Finally, a comparison of the competing smoothers with regards to the MSE is performed.
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Kurz, Malte Simon
2018
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Kurz, Malte Simon (2018): Dependence modeling with applications in financial econometrics. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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Abstract

The amount of data available in banking, finance and economics steadily increases due to the ongoing technological progress and the continuing digitalization. A key element of many econometric models for analyzing this data are methods for assessing dependencies, cross-sectionally as well as intertemporally. For this reason, the thesis is centered around statistical and econometric methods for dependence modeling with applications in financial econometrics. The first part of this cumulative dissertation consists of three contributions. The first contribution provides a thorough explanation of the partial copula. It is a natural generalization of the partial correlation coefficient and several of its properties are investigated. In the second contribution, a different multivariate generalization of the partial correlation, the partial vine copula (PVC), is introduced. The PVC is a specific simplified vine copula (SVC) consisting of bivariate higher-order partial copulas, which are copula-based generalizations of sequentially computed partial correlations. Several properties of the PVC are presented and it is shown that, if SVCs are considered as approximations of multivariate distributions, the PVC has a special role as it is the limit of stepwise estimators. The third contribution introduces statistical tests for the simplifying assumption with a special focus on high-dimensional vine copulas. We propose a computationally feasible test for the simplifying assumption in high-dimensions, which is successfully applied to data sets with up to 49 dimensions. The novel test procedure is based on a decision tree which is used to identify the possibly strongest violation of the simplifying assumption. The asymptotic distribution of the test statistic is derived under consideration of estimation uncertainty in the copula parameters. The finite sample performance is analyzed in an extensive simulation study and the results show that the power of the test only slightly decreases in the dimensionality of the test problem. In the second part of the dissertation, the assessment of risk measures is studied with a special focus on the financial return data used for estimation. It is shown that the choice of the sampling scheme can greatly affect the results of risk assessment procedures if the assessment frequency and forecasting horizon are fixed. Specifically, we study sequences of variance estimates and show that they exhibit spurious seasonality, if the assessment frequency is higher than the sampling frequency of non-overlapping return data. The root cause of spurious seasonality is identified by deriving the theoretical autocorrelation function of sequences of variance estimates under general assumptions. To overcome spurious seasonality, alternative variance estimators based on overlapping return data are suggested. The third part of the dissertation is about state space methods for systems with lagged states in the measurement equation. Recently, a low-dimensional modified Kalman filter and smoother for such systems was proposed in the literature. Special attention is paid to the modified Kalman smoother, for which it is shown that the suggested smoother in general does not minimize the mean squared error (MSE). The correct MSE-minimizing modified Kalman smoother is derived and computationally more efficient smoothing algorithms are discussed. Finally, a comparison of the competing smoothers with regards to the MSE is performed.