A Comprehensive Portfolio Construction Under Stochastic Environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

Exploring the joint compositional variability of major components and trace elements in the Tellus soil geochemistry survey (Northern Ireland)

The complexity of modern geochemical data sets is increasing in several aspects (number of available samples, number of elements measured, number of matrices analysed, geological-environmental variability covered, etc), hence it is becoming increasingly necessary to apply statistical methods to elucidate their structure. This paper presents an exploratory analysis of one such complex data set, the Tellus geochemical soil survey of Northern Ireland (NI). This exploratory analysis is based on one of the most fundamental exploratory tools, principal component analysis (PCA) and its graphical representation as a biplot, albeit in several variations: the set of elements included (only major oxides vs. all observed elements), the prior transformation applied to the data (none, a standardization or a logratio transformation) and the way the covariance matrix between components is estimated (classical estimation vs. robust estimation). Results show that a log-ratio PCA (robust or classical) of all available elements is the most powerful exploratory setting, providing the following insights: the first two processes controlling the whole geochemical variation in NI soils are peat coverage and a contrast between “mafic” and “felsic” background lithologies; peat covered areas are detected as outliers by a robust analysis, and can be then filtered out if required for further modelling; and peat coverage intensity can be quantified with the %Br in the subcomposition (Br, Rb, Ni).

Estimation de la direction d'arrivée d'échos sonores à large bande noyés dans le signal direct

Ce mémoire présente deux algorithmes qui ont pour but d’améliorer la précision de l’estimation de la direction d’arrivée de sources sonores et de leurs échos. Le premier algorithme, qui s’appelle la méthode par élimination des sources, permet d’améliorer l’estimation de la direction d’arrivée d’échos qui sont noyés dans le bruit. Le second, qui s’appelle Multiple Signal Classification à focalisation de phase, utilise l’information dans la phase à chaque fréquence pour déterminer la direction d’arrivée de sources à large bande. La combinaison de ces deux algorithmes permet de localiser des échos dont la puissance est de -17 dB par rapport à la source principale, jusqu’à un rapport échoà- bruit de -15 dB. Ce mémoire présente aussi des mesures expérimentales qui viennent confirmer les résultats obtenus lors de simulations.

Measuring, Modeling, and Forecasting Volatility and Correlations from High-Frequency Data

This dissertation contains four essays that all share a common purpose: developing new methodologies to exploit the potential of high-frequency data for the measurement, modeling and forecasting of financial assets volatility and correlations. The first two chapters provide useful tools for univariate applications while the last two chapters develop multivariate methodologies. In chapter 1, we introduce a new class of univariate volatility models named FloGARCH models. FloGARCH models provide a parsimonious joint model for low frequency returns and realized measures, and are sufficiently flexible to capture long memory as well as asymmetries related to leverage effects. We analyze the performances of the models in a realistic numerical study and on the basis of a data set composed of 65 equities. Using more than 10 years of high-frequency transactions, we document significant statistical gains related to the FloGARCH models in terms of in-sample fit, out-of-sample fit and forecasting accuracy compared to classical and Realized GARCH models. In chapter 2, using 12 years of high-frequency transactions for 55 U.S. stocks, we argue that combining low-frequency exogenous economic indicators with high-frequency financial data improves the ability of conditionally heteroskedastic models to forecast the volatility of returns, their full multi-step ahead conditional distribution and the multi-period Value-at-Risk. Using a refined version of the Realized LGARCH model allowing for time-varying intercept and implemented with realized kernels, we document that nominal corporate profits and term spreads have strong long-run predictive ability and generate accurate risk measures forecasts over long-horizon. The results are based on several loss functions and tests, including the Model Confidence Set. Chapter 3 is a joint work with David Veredas. We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correlations and volatilities. We analyze different combinations of quantile- and median-based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under four data generating processes, in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that the pre-averaged version of disentangled estimators based on Gaussian ranks (for the correlations) and median deviations (for the volatilities) provide a precise, computationally efficient, and easy alternative to measure integrated covariances on the basis of noisy and asynchronous prices. Along these lines, a minimum variance portfolio application shows the superiority of this disentangled realized estimator in terms of numerous performance metrics. Chapter 4 is co-authored with Niels S. Hansen, Asger Lunde and Kasper V. Olesen, all affiliated with CREATES at Aarhus University. We propose to use the Realized Beta GARCH model to exploit the potential of high-frequency data in commodity markets. The model produces high quality forecasts of pairwise correlations between commodities which can be used to construct a composite covariance matrix. We evaluate the quality of this matrix in a portfolio context and compare it to models used in the industry. We demonstrate significant economic gains in a realistic setting including short selling constraints and transaction costs.

Knowledge about dietary fibres (KADF): development and validation of an evaluation instrument through structural equation modelling (SEM)

Objectives: Because there is scientific evidence that an appropriate intake of dietary fibre should be part of a healthy diet, given its importance in promoting health, the present study aimed to develop and validate an instrument to evaluate the knowledge of the general population about dietary fibres. Study design: The present study was a cross sectional study. Methods: The methodological study of psychometric validation was conducted with 6010 participants, residing in ten countries from 3 continents. The instrument is a questionnaire of self-response, aimed at collecting information on knowledge about food fibres. For exploratory factor analysis (EFA) was chosen the analysis of the main components using varimax orthogonal rotation and eigenvalues greater than 1. In confirmatory factor analysis by structural equation modelling (SEM) was considered the covariance matrix and adopted the Maximum Likelihood Estimation algorithm for parameter estimation. Results: Exploratory factor analysis retained two factors. The first was called Dietary Fibre and Promotion of Health (DFPH) and included 7 questions that explained 33.94 % of total variance ( = 0.852). The second was named Sources of Dietary Fibre (SDF) and included 4 questions that explained 22.46% of total variance ( = 0.786). The model was tested by SEM giving a final solution with four questions in each factor. This model showed a very good fit in practically all the indexes considered, except for the ratio 2/df. The values of average variance extracted (0.458 and 0.483) demonstrate the existence of convergent validity; the results also prove the existence of discriminant validity of the factors (r2 = 0.028) and finally good internal consistency was confirmed by the values of composite reliability (0.854 and 0.787). Conclusions: This study allowed validating the KADF scale, increasing the degree of confidence in the information obtained through this instrument in this and in future studies.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Data assimilation for advanced cross-scale unstructured-grid ocean modeling.

The coastal ocean is a complex environment with extremely dynamic processes that require a high-resolution and cross-scale modeling approach in which all hydrodynamic fields and scales are considered integral parts of the overall system. In the last decade, unstructured-grid models have been used to advance in seamless modeling between scales. On the other hand, the data assimilation methodologies to improve the unstructured-grid models in the coastal seas have been developed only recently and need significant advancements. Here, we link the unstructured-grid ocean modeling to the variational data assimilation methods. In particular, we show results from the modeling system SANIFS based on SHYFEM fully-baroclinic unstructured-grid model interfaced with OceanVar, a state-of-art variational data assimilation scheme adopted for several systems based on a structured grid. OceanVar implements a 3DVar DA scheme. The combination of three linear operators models the background error covariance matrix. The vertical part is represented using multivariate EOFs for temperature, salinity, and sea level anomaly. The horizontal part is assumed to be Gaussian isotropic and is modeled using a first-order recursive filter algorithm designed for structured and regular grids. Here we introduced a novel recursive filter algorithm for unstructured grids. A local hydrostatic adjustment scheme models the rapidly evolving part of the background error covariance. We designed two data assimilation experiments using SANIFS implementation interfaced with OceanVar over the period 2017-2018, one with only temperature and salinity assimilation by Argo profiles and the second also including sea level anomaly. The results showed a successful implementation of the approach and the added value of the assimilation for the active tracer fields. While looking at the broad basin, no significant improvements are highlighted for the sea level, requiring future investigations. Furthermore, a Machine Learning methodology based on an LSTM network has been used to predict the model SST increments.

On the identification of bridge decks aeroelastic coefficients: the covariance block hankel matrix method

Il seguente elaborato si concentra sull'identifi�cazione strutturale di sistemi soggetti a sollecitazioni aeroelastiche e nello speci�fico l'attenzione viene rivolta ad impalcati da ponte. Si analizzano i concetti principali caratterizzanti il campo dell'aeroelasticità indagando i fattori dominanti che entrano in gioco sul piano teorico. In seguito, si considera il metodo di identifi�cazione strutturale chiamato Covariance Block Hankel Matrix (CBHM) utilizzato come strumento di derivazione dei coeffi�cienti aeroelastici propri della struttura. Infi�ne, si indaga il comportamento di questo metodo di identi�ficazione al variare di una serie di parametri chiave e all'interno di diversi scenari, visionando risultati ottenuti tramite una serie di test eff�ettuati per provare l'a�dattabilità del metodo stesso al variare delle condizioni che caratterizzano il sistema.

Multivariate QST-FST comparisons: a neutrality test for the evolution of the g matrix in structured populations.

Neutrality tests in quantitative genetics provide a statistical framework for the detection of selection on polygenic traits in wild populations. However, the existing method based on comparisons of divergence at neutral markers and quantitative traits (Q(st)-F(st)) suffers from several limitations that hinder a clear interpretation of the results with typical empirical designs. In this article, we propose a multivariate extension of this neutrality test based on empirical estimates of the among-populations (D) and within-populations (G) covariance matrices by MANOVA. A simple pattern is expected under neutrality: D = 2F(st)/(1 - F(st))G, so that neutrality implies both proportionality of the two matrices and a specific value of the proportionality coefficient. This pattern is tested using Flury's framework for matrix comparison [common principal-component (CPC) analysis], a well-known tool in G matrix evolution studies. We show the importance of using a Bartlett adjustment of the test for the small sample sizes typically found in empirical studies. We propose a dual test: (i) that the proportionality coefficient is not different from its neutral expectation [2F(st)/(1 - F(st))] and (ii) that the MANOVA estimates of mean square matrices between and among populations are proportional. These two tests combined provide a more stringent test for neutrality than the classic Q(st)-F(st) comparison and avoid several statistical problems. Extensive simulations of realistic empirical designs suggest that these tests correctly detect the expected pattern under neutrality and have enough power to efficiently detect mild to strong selection (homogeneous, heterogeneous, or mixed) when it is occurring on a set of traits. This method also provides a rigorous and quantitative framework for disentangling the effects of different selection regimes and of drift on the evolution of the G matrix. We discuss practical requirements for the proper application of our test in empirical studies and potential extensions.

Asymptotic robust inferences in the analysis of mean and covariance structures

Structural equation models are widely used in economic, socialand behavioral studies to analyze linear interrelationships amongvariables, some of which may be unobservable or subject to measurementerror. Alternative estimation methods that exploit different distributionalassumptions are now available. The present paper deals with issues ofasymptotic statistical inferences, such as the evaluation of standarderrors of estimates and chi--square goodness--of--fit statistics,in the general context of mean and covariance structures. The emphasisis on drawing correct statistical inferences regardless of thedistribution of the data and the method of estimation employed. A(distribution--free) consistent estimate of $\Gamma$, the matrix ofasymptotic variances of the vector of sample second--order moments,will be used to compute robust standard errors and a robust chi--squaregoodness--of--fit squares. Simple modifications of the usual estimateof $\Gamma$ will also permit correct inferences in the case of multi--stage complex samples. We will also discuss the conditions under which,regardless of the distribution of the data, one can rely on the usual(non--robust) inferential statistics. Finally, a multivariate regressionmodel with errors--in--variables will be used to illustrate, by meansof simulated data, various theoretical aspects of the paper.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Influence-matrix diagnostic of a data assimilation system

The influence matrix is used in ordinary least-squares applications for monitoring statistical multiple-regression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis - the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the self-sensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems. Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system. Copyright © 2004 Royal Meteorological Society

Estimation of variances of the effects of incomplete diallels using a matrix approach

A matrix approach is described for assessing the variance of effects in incomplete diallels designs. The method is illustrated by reference to simulated complete and incomplete diallels using different combinations of constraints, average degree of dominance and, for the incomplete diallel, number of hybrids. Our results showed that caution should be taken in working with incomplete diallels under conditions of overdominance because there were changes in the rank of the genotypes when the excluded hybrid had parents with a low frequency of the favorable allele (i.e. the allele which increases expression of a character). The expression described in this paper is a rapid and safe approach to estimate variances and covariances of the effects of contrasts of incomplete diallels. Copyright by the Brazilian Society of Genetics.

The full Fisher matrix for galaxy surveys

Starting from the Fisher matrix for counts in cells, we derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key step is the classical approximation, which allows us to write the inverse of the covariance of the galaxy counts in terms of the naive matrix inverse of the covariance in a mixed position-space and Fourier-space basis. We then compute the Fisher matrix for the power spectrum in bins of the 3D wavenumber , the Fisher matrix for functions of position (or redshift z) such as the linear bias of the tracers and/or the growth function and the cross-terms of the Fisher matrix that expresses the correlations between estimations of the power spectrum and estimations of the bias. When the bias and growth function are fully specified, and the Fourier-space bins are large enough that the covariance between them can be neglected, the Fisher matrix for the power spectrum reduces to the widely used result that was first derived by Feldman, Kaiser & Peacock. Assuming isotropy, a fully analytical calculation of the Fisher matrix in the classical approximation can be performed in the case of a constant-density, volume-limited survey.

Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.