Estimation of the covariance matrix of asset returns is a key component of portfolio optimization. Inherent in any estimation technique is the capacity to inaccurately reflect current market conditions. Typical of Markowitz portfolio optimization theory, which we use as the basis for our analysis, is to assume that asset returns are stationary. This assumption inevitably causes an optimized portfolio to fail during a market crash since estimates of covariance matrices of asset returns no longer reflect current conditions. We use the market crash of 2008 to exemplify this fact. A current industry-standard benchmark for estimation is the Ledoit covariance matrix, which attempts to adjust a portfolio’s aggressiveness during varying market conditions. We test this technique against the CALM (Covariance Adjustment for Liability Management Method), which incorporates forward-looking signals for market volatility to reduce portfolio variance, and assess under certain criteria how well each model performs during recent market crash. We show that CALM should be preferred against the sample convariance matrix and Ledoit covariance matrix under some reasonable weight constraints.

No description available.

Estimation of the covariance matrix of asset returns is a key component of portfolio optimization. Inherent in any estimation technique is the capacity to inaccurately reflect current market conditions. Typical of Markowitz portfolio optimization theory, which we use as the basis for our analysis, is to assume that asset returns are stationary. This assumption inevitably causes an optimized portfolio to fail during a market crash since estimates of covariance matrices of asset returns no longer re ect current conditions. We use the market crash of 2008 to exemplify this fact. A current industry standard benchmark for estimation is the Ledoit covariance matrix, which attempts to adjust a portfolio's aggressiveness during varying market conditions. We test this technique against the CALM (Covariance Adjustment for Liability Management Method), which incorporates forward-looking signals for market volatility to reduce portfolio variance, and assess under certain criteria how well each model performs during recent market crash. We show that CALM should be preferred against the sample convariance matrix and Ledoit covariance matrix under some reasonable weight constraints.

High dimensional covariance matrix estimation is considered in the context of empirical asset pricing. In order to see the effects of covariance matrix estimation on asset pricing, parameter estimation, model specification test, and misspecification problems are explored. Along with existing techniques, which is not yet tested in applications, diagonal variance matrix is simulated to evaluate the performances in these problems. We found that modified Stein type estimator outperforms all the other methods in all three cases. In addition, it turned out that heuristic method of diagonal variance matrix works far better than existing methods in Hansen-Jagannathan distance test. High dimensional covariance matrix as a transformation matrix in generalized least squares is also studied. Since the feasible generalized least squares estimator requires ex ante knowledge of the covariance structure, it is not applicable in general cases. We propose fully banding strategy for the new estimation technique. First we look into the sparsity of covariance matrix and the performances of GLS. Then we move onto the discussion of diagonals of covariance matrix and column summation of inverse of covariance matrix to see the effects on GLS estimation. In addition, factor analysis is employed to model the covariance matrix and it turned out that communality truly matters in efficiency of GLS estimation.

The information on the volume of traffic flowing between all possible origin and destination pairs in an IP network during a given period of time is generally referred to as traffic matrix (TM). This information, which is very important for various traffic engineering tasks, is very costly and difficult to obtain on large operational IP network, consequently it is often inferred from readily available link load measurements. In this thesis, we evaluated 5 TM estimation techniques, namely Tomogravity (TG), Entropy Maximization (EM), Quadratic Programming (QP), Linear Programming (LP) and Neural Network (NN) with gravity and worst-case bound (WCB) initial estimates. We found that the EM technique performed best, consistently, in most of our simulations and that the gravity model yielded better initial estimates than the WCB model. A hybrid of these techniques did not result in considerable decrease in estimation errors. We, however, achieved most significant reduction in errors by combining iterative proportionally-fitted estimates with the EM technique. Therefore, we propose this technique as a viable approach for estimating the traffic matrix of large-scale IP networks.

The information on the volume of traffic flowing between all possible origin and destination pairs in an IP network during a given period of time is generally referred to as traffic matrix (TM). This information, which is very important for various traffic engineering tasks, is very costly and difficult to obtain on large operational IP network, consequently it is often inferred from readily available link load measurements. In this thesis, we evaluated 5 TM estimation techniques, namely Tomogravity (TG), Entropy Maximization (EM), Quadratic Programming (QP), Linear Programming (LP) and Neural Network (NN) with gravity and worst-case bound (WCB) initial estimates. We found that the EM technique performed best, consistently, in most of our simulations and that the gravity model yielded better initial estimates than the WCB model. A hybrid of these techniques did not result in considerable decrease in estimation errors. We, however, achieved most significant reduction in errors by combining iterative proportionally-fitted estimates with the EM technique. Therefore, we propose this technique as a viable approach for estimating the traffic matrix of large-scale IP networks.

The problem of estimating mean and covariances of a multivariate normal distributedrandom vector has been studied in many forms. This thesis focuses on the estimatorsproposed in [15] for a banded covariance structure with m-dependence. It presents theprevious results of the estimator and rewrites the estimator when m = 1, thus makingit easier to analyze. This leads to an adjustment, and a proposition for an unbiasedestimator can be presented. A new and easier proof of consistency is then presented.This theory is later generalized into a general linear model where the correspondingtheorems and propositions are made to establish unbiasedness and consistency. In thelast chapter some simulations with the previous and new estimator verifies that thetheoretical results indeed makes an impact.

No description available.

O objetivo deste trabalho é testar um modelo de distribuição de viagens do tipo gravitacional para a calibração de matrizes origem/destino (O/D) em linhas de transporte público por ônibus a partir de dados de pesquisa de contagem de embarque/desembarque (E/D). A metodologia proposta possibilita a obtenção de matrizes O/D de forma rápida e barata, pois combina um método de pesquisa simples e de baixo custo (pesquisa de contagem de usuários) com um modelo de distribuição de viagens. O modelo associa a cada ponto de origem um valor de parâmetro. A utilização de um valor de parâmetro associado a cada origem busca neste caso reproduzir o custo médio de distribuição de viagens de uma origem em relação aos seus diferentes destinos. O modelo incorpora ainda como restrição a probabilidade de um passageiro desembarcar no ponto seguinte ao seu ponto de embarque. Os dados de pesquisa foram cedidos pelo Departamento de Transportes da Universidade Federal do Paraná. O teste de desempenho do modelo foi realizado através da comparação entre matrizes O/D observadas e simuladas para as cidades de Curitiba e Paranaguá. / The aim of this work is to test a gravity model for trip distribution designed to estimate bus routes origin/destination (O/D) matrices based on boarding and alighting data. The proposed method combines a simple and low-cost survey method (on/off passenger counting) with a mathematical model for trip distribution, which enables the estimation of an O/D matrix in a fast and inexpensive manner. The model assumption that each origin point is associated to a parameter value tries to reproduce the average costs of the actual trip distribution from each origin to every single destination along the bus route. The model brings also as a built-in restriction an expected (usually low) probability of passengers getting off the vehicle in the bus stop following the boarding point. The survey data used in this work have been collected by researchers of the Transportation Department at the Federal University of Paraná. The model performance has been tested by the comparison of observed and simulated O/D matrices in the cities of Curitiba and Paranaguá. The results found in most of the simulations showed that for an estimated trip frequencies did not statistically differ from the actual values for a required level of significance.

O objetivo deste trabalho é testar um modelo de distribuição de viagens do tipo gravitacional para a calibração de matrizes origem/destino (O/D) em linhas de transporte público por ônibus a partir de dados de pesquisa de contagem de embarque/desembarque (E/D). A metodologia proposta possibilita a obtenção de matrizes O/D de forma rápida e barata, pois combina um método de pesquisa simples e de baixo custo (pesquisa de contagem de usuários) com um modelo de distribuição de viagens. O modelo associa a cada ponto de origem um valor de parâmetro. A utilização de um valor de parâmetro associado a cada origem busca neste caso reproduzir o custo médio de distribuição de viagens de uma origem em relação aos seus diferentes destinos. O modelo incorpora ainda como restrição a probabilidade de um passageiro desembarcar no ponto seguinte ao seu ponto de embarque. Os dados de pesquisa foram cedidos pelo Departamento de Transportes da Universidade Federal do Paraná. O teste de desempenho do modelo foi realizado através da comparação entre matrizes O/D observadas e simuladas para as cidades de Curitiba e Paranaguá. / The aim of this work is to test a gravity model for trip distribution designed to estimate bus routes origin/destination (O/D) matrices based on boarding and alighting data. The proposed method combines a simple and low-cost survey method (on/off passenger counting) with a mathematical model for trip distribution, which enables the estimation of an O/D matrix in a fast and inexpensive manner. The model assumption that each origin point is associated to a parameter value tries to reproduce the average costs of the actual trip distribution from each origin to every single destination along the bus route. The model brings also as a built-in restriction an expected (usually low) probability of passengers getting off the vehicle in the bus stop following the boarding point. The survey data used in this work have been collected by researchers of the Transportation Department at the Federal University of Paraná. The model performance has been tested by the comparison of observed and simulated O/D matrices in the cities of Curitiba and Paranaguá. The results found in most of the simulations showed that for an estimated trip frequencies did not statistically differ from the actual values for a required level of significance.