Análise bayesiana do modelo fatorial dinâmico para um vetor de séries temporais utilizando a distribuição t multivariada

The multivariate t models are symmetric and with heavier tail than the normal distribution, important feature in financial data. In this theses is presented the Bayesian estimation of a dynamic factor model, where the factors follow a multivariate autoregressive model, using multivariate t distribution. Since the multivariate t distribution is complex, it was represented in this work as a mix between a multivariate normal distribution and a square root of a chi-square distribution. This method allowed to define the posteriors. The inference on the parameters was made taking a sample of the posterior distribution, through the Gibbs Sampler. The convergence was verified through graphical analysis and the convergence tests Geweke (1992) and Raftery & Lewis (1992a). The method was applied in simulated data and in the indexes of the major stock exchanges in the world.

Componentes principais na elaboração de índices de provas de desempenho em bovinos

The principal component analysis assists the producers in making decision of which evaluated features must be maintained in performance tests indexes, according to the variation present in these animals evaluated. The objective in this study was to evaluate a set of characteristics measured in a performance test in semifeedlot cattle of the Simmental and Angus breeds, by means principal component analysis (PC), aim to identify the features that represent most of the phenotypic variation for preparation of indexes. It was used data from 39 Angus and 38 Simmental bulls from the Santa Éster farm, located in Silvianópolis - MG. The performance test period was from october 2014 to february 2015. The features evaluated in the test were: final weight (FW), average daily gain weight (GW), respiratory rate (RR), haircoat temperature (HT) and rectal (RT), hair number (HN), hair length (HL), hair thickness (HT), muscularity (MUSC), racial characteristics, angulation, reproductive and balance (BAL), height of the front and back, width and length of croup, body length, depth and heart girth, subcutaneous fat thickness and rump (FTR), loin eye area and marbling (MAR). It was used PRINCOMP from SAS program for procedure the PC analysis. It was found that of the 27 features evaluated, the first four PC for Simmental breed explained 74% total variation data. The four PC selected with the corresponding weighting coefficients formed the following index: (0.27 * FW) + (0.47 * MUSC) + (0.50 * HL) + (0.39 * HT). Since the characteristics related to the adaptability of great importance for the studied breed, it was decided to keep the index of evidence for the Angus breed, the feature hair number, because there is a feature that presented a great variability and occupied one of the first principal component. Thus, the Angus index was composed by five features, with 79% total variation data, resulting in the following formula: (0.26 * FW) + (0.33 * BAL) + (0.58 * MAR) - (0.43 * FTR) – (0.38 * HN). By the principal component analysis it was possible to minimize the features number to be evaluated on performance tests from that farm, making the animal selection rapidly and accurate.