Extreme Value Theory versus traditional GARCH approaches applied to financial data: a comparative evaluation

Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normal distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalized assumption of normal distributed financial returns. Thus it is crucial to properly model the distribution tails so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by McNeil and Frey (2000) and combine the GARCH-type models with the Extreme Value Theory (EVT) to estimate the tails of three financial index returns DJI,FTSE 100 and NIKKEI 225 representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are much more accurate than those from conventional AR-GARCH models assuming normal or Student’s t-distribution innovations when doing out-of-sample estimation (within the insample estimation, this is so for the right tail of the distribution of returns).

A multivariate analysis of socio-demographic factors, water contact patterns and Schistosoma mansoni infection in an endemic area in Brazil

Associations between socio-demographic factors, water contact patterns and Schistosoma mansoni infection were investigated in 506 individuals (87% of inhabitants over 1 year of age) in an endemic area in Brazil (Divino), aiming at determining priorities for public health measures to prevent the infection. Those who eliminated S. mansoni eggs (n = 198) were compared to those without eggs in the stools (n = 308). The following explanatory variables were considered: age, sex, color, previous treatment with schistosomicide, place of birth, quality of the houses, water supply for the household, distance from houses to stream, and frequency and reasons for water contact. Factors found to be independently associated with the infection were age (10-19 and > 20 yrs old), and water contact for agricultural activities, fishing, and swimming or bathing (Adjusted relative odds = 5.0, 2.4, 3.2, 2.1 and 2.0, respectively). This suggests the need for public health measures to prevent the infection, emphasizing water contact for leisure and agricultural activities in this endemic area.

Optimization of River Water Quality Surveys by Multivariate Analysis of Physicochemical, Bacteriological and Ecotoxicological Data

This study aims to optimize the water quality monitoring of a polluted watercourse (Leça River, Portugal) through the principal component analysis (PCA) and cluster analysis (CA). These statistical methodologies were applied to physicochemical, bacteriological and ecotoxicological data (with the marine bacterium Vibrio fischeri and the green alga Chlorella vulgaris) obtained with the analysis of water samples monthly collected at seven monitoring sites and during five campaigns (February, May, June, August, and September 2006). The results of some variables were assigned to water quality classes according to national guidelines. Chemical and bacteriological quality data led to classify Leça River water quality as “bad” or “very bad”. PCA and CA identified monitoring sites with similar pollution pattern, giving to site 1 (located in the upstream stretch of the river) a distinct feature from all other sampling sites downstream. Ecotoxicity results corroborated this classification thus revealing differences in space and time. The present study includes not only physical, chemical and bacteriological but also ecotoxicological parameters, which broadens new perspectives in river water characterization. Moreover, the application of PCA and CA is very useful to optimize water quality monitoring networks, defining the minimum number of sites and their location. Thus, these tools can support appropriate management decisions.

A multivariate analysis of the relationship between work ability and S. japonicum infection in Dongting Lake Region, in China

A cross-sectional case-control study on the association between the reduced work ability and S. japonicum infection was carried out in a moderate endemic area for schistosomiasis japonica in the southern part of Dongting lake in China. A total of 120 cases with reduced work ability and 240 controls paired to the case by age, sex, occupation and without reduced work ability, participated in the study. The mean age for individuals was 37.6 years old (21-60), the ratio of male: female was 60:40, the prevalence of S. japonicum in the individuals was 28.3%. The results obtained in this study showed that the infection of S. japonicum in case and control groups was 49.2% (59/120) and 17.9% (43/240), respectively. Odds ratio for reduced work ability among those who had schistosomiasis was 4.34 (95%), confidence interval was 2.58-7.34, and among those who had S. japonicum infection (egg per gram > 100) was up to 12.67 (95%), confidence interval was 3.64-46.39. After odds ratio was adjusted by multiple logistic regression, it was confirmed that heavier intensity of S. japonicum infection and splenomegaly due to S. japonicum infection were the main risk factors for reduced work ability in the population studied.

Analyzing Multiple Outcomes: Is it Really Worth the use of Multivariate Linear Regression?

In health related research it is common to have multiple outcomes of interest in a single study. These outcomes are often analysed separately, ignoring the correlation between them. One would expect that a multivariate approach would be a more efficient alternative to individual analyses of each outcome. Surprisingly, this is not always the case. In this article we discuss different settings of linear models and compare the multivariate and univariate approaches. We show that for linear regression models, the estimates of the regression parameters associated with covariates that are shared across the outcomes are the same for the multivariate and univariate models while for outcome-specific covariates the multivariate model performs better in terms of efficiency.

Exploraty Multivariate Statistical Methods Applied to Pharmaceutical Industry CRM Data

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Multivariate analysis applied to clinical analysis data

Dissertação para obtenção do Grau de Mestre em Engenharia e Gestão Industrial

Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions and the conditional distribution of gap times. In this work we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a data set from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.

Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.

Application of multivariate statistical process control to fuel cell manufacturing

Univariate statistical control charts, such as the Shewhart chart, do not satisfy the requirements for process monitoring on a high volume automated fuel cell manufacturing line. This is because of the number of variables that require monitoring. The risk of elevated false alarms, due to the nature of the process being high volume, can present problems if univariate methods are used. Multivariate statistical methods are discussed as an alternative for process monitoring and control. The research presented is conducted on a manufacturing line which evaluates the performance of a fuel cell. It has three stages of production assembly that contribute to the final end product performance. The product performance is assessed by power and energy measurements, taken at various time points throughout the discharge testing of the fuel cell. The literature review performed on these multivariate techniques are evaluated using individual and batch observations. Modern techniques using multivariate control charts on Hotellings T2 are compared to other multivariate methods, such as Principal Components Analysis (PCA). The latter, PCA, was identified as the most suitable method. Control charts such as, scores, T2 and DModX charts, are constructed from the PCA model. Diagnostic procedures, using Contribution plots, for out of control points that are detected using these control charts, are also discussed. These plots enable the investigator to perform root cause analysis. Multivariate batch techniques are compared to individual observations typically seen on continuous processes. Recommendations, for the introduction of multivariate techniques that would be appropriate for most high volume processes, are also covered.

Statistical analysis in multivariate sampling

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Multivariate Analysis for Animal Selection in Experimental Research

Background: Several researchers seek methods for the selection of homogeneous groups of animals in experimental studies, a fact justified because homogeneity is an indispensable prerequisite for casualization of treatments. The lack of robust methods that comply with statistical and biological principles is the reason why researchers use empirical or subjective methods, influencing their results. Objective: To develop a multivariate statistical model for the selection of a homogeneous group of animals for experimental research and to elaborate a computational package to use it. Methods: The set of echocardiographic data of 115 male Wistar rats with supravalvular aortic stenosis (AoS) was used as an example of model development. Initially, the data were standardized, and became dimensionless. Then, the variance matrix of the set was submitted to principal components analysis (PCA), aiming at reducing the parametric space and at retaining the relevant variability. That technique established a new Cartesian system into which the animals were allocated, and finally the confidence region (ellipsoid) was built for the profile of the animals’ homogeneous responses. The animals located inside the ellipsoid were considered as belonging to the homogeneous batch; those outside the ellipsoid were considered spurious. Results: The PCA established eight descriptive axes that represented the accumulated variance of the data set in 88.71%. The allocation of the animals in the new system and the construction of the confidence region revealed six spurious animals as compared to the homogeneous batch of 109 animals. Conclusion: The biometric criterion presented proved to be effective, because it considers the animal as a whole, analyzing jointly all parameters measured, in addition to having a small discard rate.

Advancing the understanding of brain function with multivariate pattern analysis

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2009

Optimal designs for multivariate linear models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013