Bayesian Dynamic Factor Models and Portfolio Allocation

We discuss the development of dynamic factor models for multivariate financial time series, and the incorporation of stochastic volatility components for latent factor processes. Bayesian inference and computation is developed and explored in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The models are direct generalizations of univariate stochastic volatility models and represent specific varieties of models recently discussed in the growing multivariate stochastic volatility literature. We discuss model fitting based on retrospective data and sequential analysis for forward filtering and short-term forecasting. Analyses are compared with results from the much simpler method of dynamic variance-matrix discounting that, for over a decade, has been a standard approach in applied financial econometrics. We study these models in analysis, forecasting, and sequential portfolio allocation for a selected set of international exchange-rate-return time series. Our goals are to understand a range of modeling questions arising in using these factor models and to explore empirical performance in portfolio construction relative to discount approaches. We report on our experiences and conclude with comments about the practical utility of structured factor models and on future potential model extensions.     

Multivariate trimmed means based on the Tukey depth

In univariate statistics, the trimmed mean has long been regarded as a robust and efficient alternative to the sample mean. A multivariate analogue calls for a notion of trimmed region around the center of the sample. Using Tukey's depth to achieve this goal, this paper investigates two types of multivariate trimmed means obtained by averaging over the trimmed region in two different ways. For both trimmed means, conditions ensuring asymptotic normality are obtained; in this respect, one of the main features of the paper is the systematic use of Hadamard derivatives and empirical processes methods to derive the central limit theorems. Asymptotic efficiency relative to the sample mean as well as breakdown point are also studied. The results provide convincing evidence that these location estimators have nice asymptotic behavior and possess highly desirable finite-sample robustness properties; furthermore, relative to the sample mean, both of them can in some situations be highly efficient for dimensions between 2 and 10.     

The Multivariate Randomized Complete Block Design: A Novel Permutation Solution in Case of Ordered Categorical Variables

In this article, multivariate extensions of the combination-based test statistics for the comparison of several treatments in the multivariate Randomized Complete Block designs are introduced in case of categorical response variables. Several tests for the multivariate Randomized Complete Block designs, including MANOVA procedure, are compared with the method proposed via a Monte Carlo simulation study. The method has also been applied to a real case study in the field of sensorial testing studies. Results suggest that in each experimental situation where normality of the supposed underlying continuous model is hard to justify and especially when errors have heavy-tailed distributions, the proposed nonparametric procedure can be considered as a valid solution.     

C472. The expected value of a conditional variance: An upper bound

The article derives Bartlett corrections for improving the chi-square approximation to the likelihood ratio statistics in a class of symmetric nonlinear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. In this paper we present, in matrix notation, Bartlett corrections to likelihood ratio statistics in nonlinear regression models with errors that follow a symmetric distribution. We generalize the results obtained by Ferrari, S. L. P. and Arellano-Valle, R. B. (1996). Modified likelihood ratio and score tests in linear regression models using the t distribution. Braz. J. Prob. Statist., 10, 15–33, who considered a t distribution for the errors, and by Ferrari, S. L. P. and Uribe-Opazo, M. A. (2001). Corrected likelihood ratio tests in a class of symmetric linear regression models. Braz. J. Prob. Statist., 15, 49–67, who considered a symmetric linear regression model. The formulae derived are simple enough to be used analytically to obtain several Bartlett corrections in a variety of important models. We also present simulation results comparing the sizes and powers of the usual likelihood ratio tests and their Bartlett corrected versions.     

Analysis of repeated failures or durations, with application to shunt failures for patients with paediatric hydrocephalus

We consider studies involving the repeated occurrence of certain events, in which the emphasis is on the gaps or times between events. Interesting methodological issues arise in such situations, including the validity of semiparametric methods for multiplicative hazard-based models and the possibilities for marginal analysis of successive gap times. We discuss these and other points in conjunction with an examination of observational data on repeated shunt failures for a population of children with hydrocephalus.     

Conditional Gaussian mixture modelling for dietary pattern analysis

Summary.  Free-living individuals have multifaceted diets and consume foods in numerous combinations. In epidemiological studies it is desirable to characterize individual diets not only in terms of the quantity of individual dietary components but also in terms of dietary patterns. We describe the conditional Gaussian mixture model for dietary pattern analysis and show how it can be adapted to take account of important characteristics of self-reported dietary data. We illustrate this approach with an analysis of the 2000–2001 National Diet and Nutrition Survey of adults. The results strongly favoured a mixture model solution allowing clusters to vary in shape and size, over the standard approach that has been used previously to find dietary patterns.     

Evaluation of statistical protocols for quality control of ecosystem carbon dioxide fluxes

Summary.  The process of quality control of micrometeorological and carbon dioxide (CO₂) flux data can be subjective and may lack repeatability, which would undermine the results of many studies. Multivariate statistical methods and time series analysis were used together and independently to detect and replace outliers in CO₂ flux data derived from a Bowen ratio energy balance system. The results were compared with those produced by five experts who applied the current and potentially subjective protocol. All protocols were tested on the same set of three 5-day periods, when measurements were conducted in an abandoned agricultural field. The concordance of the protocols was evaluated by using the experts' opinion (mean ± 1.96 standard deviations) as a reference interval (the Bland–Altman method). Analysing the 15 days together, the statistical protocol that combined multivariate distance, multiple linear regression and time series analysis showed a concordance of 93% on a 20-min flux basis and 87% on a daily basis (only 2 days fell outside the reference interval), and the overall flux differed only by 1.7% (3.2 g CO₂ m⁻²). An automated version of this or a similar statistical protocol could be used as a standard way of filling gaps and processing data from Bowen ratio energy balance and other techniques (e.g. eddy covariance). This would enforce objectivity in comparisons of CO₂ flux data that are generated by different research groups and streamline the protocols for quality control.     

Development and comparative study of two near-exact approximations to the distribution of the product of an odd number of independent Beta random variables

Using the concept of near-exact approximation to a distribution we developed two different near-exact approximations to the distribution of the product of an odd number of particular independent Beta random variables (r.v.'s). One of them is a particular generalized near-integer Gamma (GNIG) distribution and the other is a mixture of two GNIG distributions. These near-exact distributions are mostly adequate to be used as a basis for approximations of distributions of several statistics used in multivariate analysis. By factoring the characteristic function (c.f.) of the logarithm of the product of the Beta r.v.'s, and then replacing a suitably chosen factor of that c.f. by an adequate asymptotic result it is possible to obtain what we call a near-exact c.f., which gives rise to the near-exact approximation to the exact distribution. Depending on the asymptotic result used to replace the chosen parts of the c.f., one may obtain different near-exact approximations. Moments from the two near-exact approximations developed are compared with the exact ones. The two approximations are also compared with each other, namely in terms of moments and quantiles.     

The impact of Serbian public relations on economic indices

This study presents the research results whose aim was to examine and define dependences and the impact of public relations on business effects (economic indices are taken as representatives of business effects). Serbian companies were the object of this research. The data were collected by polling 100 managers from 100 companies. Multivariate regression and correlation were applied in order to determine the observed dependences. The research results confirm the existence of a significant direct relation between public relations and economic indices.     

Adjusted Likelihood Inference in an Elliptical Multivariate Errors-in-Variables Model

In this paper, we obtain an adjusted version of the likelihood ratio (LR) test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as a special case. We derive a modified LR statistic that follows a chi-squared distribution with a high degree of accuracy. Our results generalize those in Melo and Ferrari (Advances in Statistical Analysis, 2010, 94, pp. 75–87) by allowing the parameter of interest to be vector-valued in the multivariate errors-in-variables model. We report a simulation study which shows that the proposed test displays superior finite sample behavior relative to the standard LR test.