Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models

In this paper, we propose several finite-sample specification tests for multivariate linear regressions (MLR) with applications to asset pricing models. We focus on departures from the assumption of i.i.d. errors assumption, at univariate and multivariate levels, with Gaussian and non-Gaussian (including Student t) errors. The univariate tests studied extend existing exact procedures by allowing for unspecified parameters in the error distributions (e.g., the degrees of freedom in the case of the Student t distribution). The multivariate tests are based on properly standardized multivariate residuals to ensure invariance to MLR coefficients and error covariances. We consider tests for serial correlation, tests for multivariate GARCH and sign-type tests against general dependencies and asymmetries. The procedures proposed provide exact versions of those applied in Shanken (1990) which consist in combining univariate specification tests. Specifically, we combine tests across equations using the MC test procedure to avoid Bonferroni-type bounds. Since non-Gaussian based tests are not pivotal, we apply the “maximized MC” (MMC) test method [Dufour (2002)], where the MC p-value for the tested hypothesis (which depends on nuisance parameters) is maximized (with respect to these nuisance parameters) to control the test’s significance level. The tests proposed are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995. Our empirical results reveal the following. Whereas univariate exact tests indicate significant serial correlation, asymmetries and GARCH in some equations, such effects are much less prevalent once error cross-equation covariances are accounted for. In addition, significant departures from the i.i.d. hypothesis are less evident once we allow for non-Gaussian errors.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

An investigation into the interference rejection capability of a linear array in a wireless communications system

The suitable use of an array antenna at the base station of a wireless communications system can result in improvement in the signal-to-interference ratio (SIR). In general, the SIR is a function of the direction of arrival of the desired signal and depends on the configuration of the array, the number of elements, and their spacing. In this paper, we consider a uniform linear array antenna and study the effect of varying the number of its elements and inter-element spacing on the SIR performance. (C) 2002 Wiley Periodicals, Inc.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

METHODOLOGY FOR AUTOMATICALLY DELIMITING PERMANENT PRESERVATION AREAS ALONG WATER COURSES - THE USE OF GIS IN THE HYDROLOGICAL BASIN OF THE SERGIPE RIVER, BRAZIL

ABSTRACT Permanent Preservation Areas (PPAs) along watercourses have been the focus of numerous studies, not only because of the fragility and ecological relevance of riverine vegetation, but also because of the inefficiency demonstrated in conforming to the legislation protecting it. One of the major difficulties encountered in terms of guaranteeing the effective conservation of these riverside areas is the absence of methodologies that can be used to define them rapidly and accurately without manually determining the widths of the rivers or assigning only uniform linear values for the entire watercourse. The present work sought to develop a spatial analysis methodology capable of automatically defining permanent preservation areas along watercourses using geographic information system (GIS) software. The present study was undertaken in the Sergipe River basin, "considering the river itself and its principal affluents. We used the database of the Digital Atlas of Hydrological Resources (SEMARH/SE), and the delimitations of the PPAs were performed using ArcGIS 10.1 and the XToolPro 9.0 extension. A total of 5,003.82 hectares of Permanent Preservation Areas were delimited along the margins of the rivers analyzed, with a margin of error of <1% in delimiting the widths of the rivers within the entire area considered. The methodology described here can be used to define PPAs efficiently, relatively rapidly, and with very small margins of error, thus representing a technological advance in terms of using GIS for land management.

Variations in the mainstreaming of sustainability: a case study approach

The construction sector has a major role to play in delivering the transition to a low carbon economy and in contributing to sustainable development; however, integrating sustainability into everyday business remains a major challenge for the sector. This research explores the experience of three large construction and engineering consultancy firms in mainstreaming sustainability. The aim of the paper is to identify and explain variations in firm level strategies for mainstreaming sustainability. The three cases vary in the way in which sustainability is ramed – as a problem of risk, business opportunity or culture – and in its location within the firm. The research postulates that the mainstreaming of sustainability is not the uniform linear process often articulated in theories of strategic change and management, but varies with the dominant organisational culture and history of each firm. he paper concludes with a reflection on the implications of this analysis for management theories and for firm level strategies.

From eventual to atomic and locally atomic CC programs: A concurrent semantics

We present a concurrent semantics (i.e. a semantics where concurrency is explicitely represented) for CC programs with atomic tells. This allows to derive concurrency, dependency, and nondeterminism information for such languages. The ability to treat failure information puts CLP programs also in the range of applicability of our semantics: although such programs are not concurrent, the concurrency information derived in the semantics may be interpreted as possible parallelism, thus allowing to safely parallelize those computation steps which appear to be concurrent in the net. Dually, the dependency information may also be interpreted as necessary sequentialization, thus possibly exploiting it to schedule CC programs. The fact that the semantical structure contains dependency information suggests a new tell operation, which checks for consistency only the constraints it depends on, achieving a reasonable trade-off between efficiency and atomicity.

Modelo de computación conexionista inspirado en las redes de procesadores evolutivos y su aprendizaje

La informática teórica es una disciplina básica ya que la mayoría de los avances en informática se sustentan en un sólido resultado de esa materia. En los últimos a~nos debido tanto al incremento de la potencia de los ordenadores, como a la cercanía del límite físico en la miniaturización de los componentes electrónicos, resurge el interés por modelos formales de computación alternativos a la arquitectura clásica de von Neumann. Muchos de estos modelos se inspiran en la forma en la que la naturaleza resuelve eficientemente problemas muy complejos. La mayoría son computacionalmente completos e intrínsecamente paralelos. Por este motivo se les está llegando a considerar como nuevos paradigmas de computación (computación natural). Se dispone, por tanto, de un abanico de arquitecturas abstractas tan potentes como los computadores convencionales y, a veces, más eficientes: alguna de ellas mejora el rendimiento, al menos temporal, de problemas NPcompletos proporcionando costes no exponenciales. La representación formal de las redes de procesadores evolutivos requiere de construcciones, tanto independientes, como dependientes del contexto, dicho de otro modo, en general una representación formal completa de un NEP implica restricciones, tanto sintácticas, como semánticas, es decir, que muchas representaciones aparentemente (sintácticamente) correctas de casos particulares de estos dispositivos no tendrían sentido porque podrían no cumplir otras restricciones semánticas. La aplicación de evolución gramatical semántica a los NEPs pasa por la elección de un subconjunto de ellos entre los que buscar los que solucionen un problema concreto. En este trabajo se ha realizado un estudio sobre un modelo inspirado en la biología celular denominado redes de procesadores evolutivos [55, 53], esto es, redes cuyos nodos son procesadores muy simples capaces de realizar únicamente un tipo de mutación puntual (inserción, borrado o sustitución de un símbolo). Estos nodos están asociados con un filtro que está definido por alguna condición de contexto aleatorio o de pertenencia. Las redes están formadas a lo sumo de seis nodos y, teniendo los filtros definidos por una pertenencia a lenguajes regulares, son capaces de generar todos los lenguajes enumerables recursivos independientemente del grafo subyacente. Este resultado no es sorprendente ya que semejantes resultados han sido documentados en la literatura. Si se consideran redes con nodos y filtros definidos por contextos aleatorios {que parecen estar más cerca a las implementaciones biológicas{ entonces se pueden generar lenguajes más complejos como los lenguajes no independientes del contexto. Sin embargo, estos mecanismos tan simples son capaces de resolver problemas complejos en tiempo polinomial. Se ha presentado una solución lineal para un problema NP-completo, el problema de los 3-colores. Como primer aporte significativo se ha propuesto una nueva dinámica de las redes de procesadores evolutivos con un comportamiento no determinista y masivamente paralelo [55], y por tanto todo el trabajo de investigación en el área de la redes de procesadores se puede trasladar a las redes masivamente paralelas. Por ejemplo, las redes masivamente paralelas se pueden modificar de acuerdo a determinadas reglas para mover los filtros hacia las conexiones. Cada conexión se ve como un canal bidireccional de manera que los filtros de entrada y salida coinciden. A pesar de esto, estas redes son computacionalmente completas. Se pueden también implementar otro tipo de reglas para extender este modelo computacional. Se reemplazan las mutaciones puntuales asociadas a cada nodo por la operación de splicing. Este nuevo tipo de procesador se denomina procesador splicing. Este modelo computacional de Red de procesadores con splicing ANSP es semejante en cierto modo a los sistemas distribuidos en tubos de ensayo basados en splicing. Además, se ha definido un nuevo modelo [56] {Redes de procesadores evolutivos con filtros en las conexiones{ , en el cual los procesadores tan solo tienen reglas y los filtros se han trasladado a las conexiones. Dicho modelo es equivalente, bajo determinadas circunstancias, a las redes de procesadores evolutivos clásicas. Sin dichas restricciones el modelo propuesto es un superconjunto de los NEPs clásicos. La principal ventaja de mover los filtros a las conexiones radica en la simplicidad de la modelización. Otras aportaciones de este trabajo ha sido el dise~no de un simulador en Java [54, 52] para las redes de procesadores evolutivos propuestas en esta Tesis. Sobre el término "procesador evolutivo" empleado en esta Tesis, el proceso computacional descrito aquí no es exactamente un proceso evolutivo en el sentido Darwiniano. Pero las operaciones de reescritura que se han considerado pueden interpretarse como mutaciones y los procesos de filtrado se podrían ver como procesos de selección. Además, este trabajo no abarca la posible implementación biológica de estas redes, a pesar de ser de gran importancia. A lo largo de esta tesis se ha tomado como definición de la medida de complejidad para los ANSP, una que denotaremos como tama~no (considerando tama~no como el número de nodos del grafo subyacente). Se ha mostrado que cualquier lenguaje enumerable recursivo L puede ser aceptado por un ANSP en el cual el número de procesadores está linealmente acotado por la cardinalidad del alfabeto de la cinta de una máquina de Turing que reconoce dicho lenguaje L. Siguiendo el concepto de ANSP universales introducido por Manea [65], se ha demostrado que un ANSP con una estructura de grafo fija puede aceptar cualquier lenguaje enumerable recursivo. Un ANSP se puede considerar como un ente capaz de resolver problemas, además de tener otra propiedad relevante desde el punto de vista práctico: Se puede definir un ANSP universal como una subred, donde solo una cantidad limitada de parámetros es dependiente del lenguaje. La anterior característica se puede interpretar como un método para resolver cualquier problema NP en tiempo polinomial empleando un ANSP de tama~no constante, concretamente treinta y uno. Esto significa que la solución de cualquier problema NP es uniforme en el sentido de que la red, exceptuando la subred universal, se puede ver como un programa; adaptándolo a la instancia del problema a resolver, se escogerín los filtros y las reglas que no pertenecen a la subred universal. Un problema interesante desde nuestro punto de vista es el que hace referencia a como elegir el tama~no optimo de esta red.---ABSTRACT---This thesis deals with the recent research works in the area of Natural Computing {bio-inspired models{, more precisely Networks of Evolutionary Processors first developed by Victor Mitrana and they are based on P Systems whose father is Georghe Paun. In these models, they are a set of processors connected in an underlying undirected graph, such processors have an object multiset (strings) and a set of rules, named evolution rules, that transform objects inside processors[55, 53],. These objects can be sent/received using graph connections provided they accomplish constraints defined at input and output filters processors have. This symbolic model, non deterministic one (processors are not synchronized) and massive parallel one[55] (all rules can be applied in one computational step) has some important properties regarding solution of NP-problems in lineal time and of course, lineal resources. There are a great number of variants such as hybrid networks, splicing processors, etc. that provide the model a computational power equivalent to Turing machines. The origin of networks of evolutionary processors (NEP for short) is a basic architecture for parallel and distributed symbolic processing, related to the Connection Machine as well as the Logic Flow paradigm, which consists of several processors, each of them being placed in a node of a virtual complete graph, which are able to handle data associated with the respective node. All the nodes send simultaneously their data and the receiving nodes handle also simultaneously all the arriving messages, according to some strategies. In a series of papers one considers that each node may be viewed as a cell having genetic information encoded in DNA sequences which may evolve by local evolutionary events, that is point mutations. Each node is specialized just for one of these evolutionary operations. Furthermore, the data in each node is organized in the form of multisets of words (each word appears in an arbitrarily large number of copies), and all the copies are processed in parallel such that all the possible events that can take place do actually take place. Obviously, the computational process just described is not exactly an evolutionary process in the Darwinian sense. But the rewriting operations we have considered might be interpreted as mutations and the filtering process might be viewed as a selection process. Recombination is missing but it was asserted that evolutionary and functional relationships between genes can be captured by taking only local mutations into consideration. It is clear that filters associated with each node allow a strong control of the computation. Indeed, every node has an input and output filter; two nodes can exchange data if it passes the output filter of the sender and the input filter of the receiver. Moreover, if some data is sent out by some node and not able to enter any node, then it is lost. In this paper we simplify the ANSP model considered in by moving the filters from the nodes to the edges. Each edge is viewed as a two-way channel such that the input and output filters coincide. Clearly, the possibility of controlling the computation in such networks seems to be diminished. For instance, there is no possibility to loose data during the communication steps. In spite of this and of the fact that splicing is not a powerful operation (remember that splicing systems generates only regular languages) we prove here that these devices are computationally complete. As a consequence, we propose characterizations of two complexity classes, namely NP and PSPACE, in terms of accepting networks of restricted splicing processors with filtered connections. We proposed a uniform linear time solution to SAT based on ANSPFCs with linearly bounded resources. This solution should be understood correctly: we do not solve SAT in linear time and space. Since any word and auxiliary word appears in an arbitrarily large number of copies, one can generate in linear time, by parallelism and communication, an exponential number of words each of them having an exponential number of copies. However, this does not seem to be a major drawback since by PCR (Polymerase Chain Reaction) one can generate an exponential number of identical DNA molecules in a linear number of reactions. It is worth mentioning that the ANSPFC constructed above remains unchanged for any instance with the same number of variables. Therefore, the solution is uniform in the sense that the network, excepting the input and output nodes, may be viewed as a program according to the number of variables, we choose the filters, the splicing words and the rules, then we assign all possible values to the variables, and compute the formula.We proved that ANSP are computationally complete. Do the ANSPFC remain still computationally complete? If this is not the case, what other problems can be eficiently solved by these ANSPFCs? Moreover, the complexity class NP is exactly the class of all languages decided by ANSP in polynomial time. Can NP be characterized in a similar way with ANSPFCs?

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Estimation and hypothesis testing in mixed linear models

Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia

The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength.