Modeling and Forecasting of Realized Covariance Matrices of Asset Returns using State-Space Models

This thesis comprises three self-contained essays on the modeling and prediction of realized covariance matrices of asset returns using state-space models

Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models

We propose a dynamic factor state-space model for the prediction of high-dimensional realized covariance matrices of asset returns. Using a block LDL decomposition of the joint covariance matrix of assets and factors, we express the realized covariance matrix of the individual assets similar to an approximate factor model. We model the individual parts, i.e., the factor and residual covariances as well as the factor loadings, independently via a tractable state-space approach. This results in closed-form Matrix-F predictive densities for the distinct covariance elements and Student's t predictive densities for the factor loadings. In an out-of-sample forecasting and portfolio selection exercise we compare the performance of the proposed factor model under different specifications of the residual dynamics. These includes block diagonal residuals based on the GICS sector classifications and strict diagonality assumptions as well as combinations of both using linear shrinkage. We find that the proposed model performs very well in an empirical application to realized covariance matrices for 225 NYSE-traded stocks using the well-known Fama-French factors and sector-specific factors represented by exchange traded funds

Factor state-space models for high-dimensional realized covariance matrices of asset returns

We propose a dynamic factor state-space model for high-dimensional covariance matrices of asset returns. It makes use of observed risk factors and assumes that the latent integrated joint covariance matrix of the assets and the factors is observed through their realized covariance matrix with a Wishart measurement density. For the latent integrated covariance matrix of the assets we impose a strict factor structure allowing for dynamic variation in the covariance matrices of the factors and the residual components as well as in the factor loadings. This factor structure translates into a factorization of the Wishart measurement density which facilitates statistical inference based on simple Bayesian MCMC procedures making the approach scalable w.r.t. the number of assets. An empirical application to realized covariance matrices for 60 NYSE traded stocks using the Fama-French factors and sector-specific factors represented by Exchange Traded Funds (ETFs) shows that the model performs very well in- and out of sample

Comparison of quantification methods to measure fire-derived (black/elemental) carbon in soils and sediments using reference materials from soil, water, sediment and the atmosphere

Black carbon (BC), the product of incomplete combustion of fossil fuels and biomass (called elemental carbon (EC) in atmospheric sciences), was quantified in 12 different materials by 17 laboratories from different disciplines, using seven different methods. The materials were divided into three classes: (1) potentially interfering materials, (2) laboratory-produced BC-rich materials, and (3) BC-containing environmental matrices (from soil, water, sediment, and atmosphere). This is the first comprehensive intercomparison of this type (multimethod, multilab, and multisample), focusing mainly on methods used for soil and sediment BC studies. Results for the potentially interfering materials (which by definition contained no fire-derived organic carbon) highlighted situations where individual methods may overestimate BC concentrations. Results for the BC-rich materials (one soot and two chars) showed that some of the methods identified most of the carbon in all three materials as BC, whereas other methods identified only soot carbon as BC. The different methods also gave widely different BC contents for the environmental matrices. However, these variations could be understood in the light of the findings for the other two groups of materials, i.e., that some methods incorrectly identify non-BC carbon as BC, and that the detection efficiency of each technique varies across the BC continuum. We found that atmospheric BC quantification methods are not ideal for soil and sediment studies as in their methodology these incorporate the definition of BC as light-absorbing material irrespective of its origin, leading to biases when applied to terrestrial and sedimentary materials. This study shows that any attempt to merge data generated via different methods must consider the different, operationally defined analytical windows of the BC continuum detected by each technique, as well as the limitations and potential biases of each technique. A major goal of this ring trial was to provide a basis on which to choose between the different BC quantification methods in soil and sediment studies. In this paper we summarize the advantages and disadvantages of each method. In future studies, we strongly recommend the evaluation of all methods analyzing for BC in soils and sediments against the set of BC reference materials analyzed here

Comparison of quantification methods to measure fire-derived (black/elemental) carbon in soils and sediments using reference materials from soil, water, sediment and the atmosphere

Black carbon (BC), the product of incomplete combustion of fossil fuels and biomass (called elemental carbon (EC) in atmospheric sciences), was quantified in 12 different materials by 17 laboratories from different disciplines, using seven different methods. The materials were divided into three classes: (1) potentially interfering materials, (2) laboratory-produced BC-rich materials, and (3) BC-containing environmental matrices (from soil, water, sediment, and atmosphere). This is the first comprehensive intercomparison of this type (multimethod, multilab, and multisample), focusing mainly on methods used for soil and sediment BC studies. Results for the potentially interfering materials (which by definition contained no fire-derived organic carbon) highlighted situations where individual methods may overestimate BC concentrations. Results for the BC-rich materials (one soot and two chars) showed that some of the methods identified most of the carbon in all three materials as BC, whereas other methods identified only soot carbon as BC. The different methods also gave widely different BC contents for the environmental matrices. However, these variations could be understood in the light of the findings for the other two groups of materials, i.e., that some methods incorrectly identify non-BC carbon as BC, and that the detection efficiency of each technique varies across the BC continuum. We found that atmospheric BC quantification methods are not ideal for soil and sediment studies as in their methodology these incorporate the definition of BC as light-absorbing material irrespective of its origin, leading to biases when applied to terrestrial and sedimentary materials. This study shows that any attempt to merge data generated via different methods must consider the different, operationally defined analytical windows of the BC continuum detected by each technique, as well as the limitations and potential biases of each technique. A major goal of this ring trial was to provide a basis on which to choose between the different BC quantification methods in soil and sediment studies. In this paper we summarize the advantages and disadvantages of each method. In future studies, we strongly recommend the evaluation of all methods analyzing for BC in soils and sediments against the set of BC reference materials analyzed here