Research Reports

In the study of genetic divergence among organisms, generally the analysis is done directly from the DNA molecule. Therefore, a possible outcome is binary (dominant or recessive phenotype). Comparison of groups of molecular data is a great interest in molecular genetics and evolutionary biology. Some work have been done on analysis of variance for genetic data (Weir, 1990; Pinheiro et al., 2000; Pinheiro et al., 2001; Pinheiro et al., 2002 and others). Weir (1990) proposed a genetic diversity measure, the heterozygosity, and developed an analysis of variance for binary data in a balanced design.Here, we extend the work of Weir developing an analysis of variance for binary data with the purpose of comparing groups in unbalanced designs. In order to test the null hypothesis of homogeneity among groups, the asymptotic distribution of the test statistic was found. An application of the test to real data is illustrated using resampling methods such as the bootstrap to generate the empirical distribution of the test statistics.

rp-2003-17.pdf

The idea of volatility is fundamental to precise definition of risk and, hence, its estimation (or prediction) is a very important task in finance applications. We present some ideas on nonparamateric estimation of volatility function in diffusion models. A nonlinear wavelet estimate of the volatiltiy function is proposed and its performance is compared to three kernel estimators in both simulated and real data. Simulation is developed for eight volatility shapes and some interesting, but not unexpected, results are presented. Some issues such as online estimation and prediction, robustness to oversmoothing and performance under sudden changes in pattern of volatility are also discussed.

rp-2003-15.pdf

It is considered in this paper the modeling and forecasting, through feedforward neural networks, of a time series previouslystudied in the literature (Brubacher, 1974; Martin, 1980; Stahlbut, 1985; Allende, 1989) called RESEX series, which presentsseasonality and outliers. Some elements of the network architecture such as the input variables definition are suggestedby a previous time series analysis and other elements such as the number of intermediate layers and corresponding knots are defined through numerical methods. Not only traditional backpropagation based algorithms are used but also a robust learning algorithm is considered in order to deal more properly with the outliers. All models and methods (traditional and NN based) are then compared considering different predictive performance measures and theresults are discussed.

rp-2003-13.pdf

This paper considers monotonic (or causal) homotopy between trajectories of control systems. The main result is the construction of an analogue of the simply connected covering space. The constructed covering $\Gamma(\Sigma, x)$ has the structure of a manifold and satisfies the property that two trajectories are monotonic homotopic if and only if the end points of their liftings coincide.

rp-2003-11.pdf