Browsing by Author "Arellano Valle, R. B."

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    A note on Bayesian identification of change points in data sequences
    (PERGAMON-ELSEVIER SCIENCE LTD, 2008) Loschi, R. H.; Cruz, F. R. B.; Takahashi, R. H. C.; Iglesias, P. L.; Arellano Valle, R. B.; Smith, J. MacGregor
    Recent research in mathematical methods for finance suggests that time series for financial data should be studied with nonstationary models and with structural changes that include both jumps and heteroskedasticity (with jumps in variance). It has been recognized that discriminating between variations caused by the continuous motion of Brownian shocks and the genuine discontinuities in the path of the process constitutes a challenge for existing computational procedures. This issue is addressed here, using the product partition model (PPM), for performing such discrimination and the estimation of process jump parameters. Computational implementation aspects of PPM applied to the identification of change points in data sequences are discussed. In particular, we analyze the use of a Gibbs sampling scheme to compute the estimates and show that there is no significant impact of such use on the quality of the results. The influence of the size of the data sequence on the estimates is also of interest, as well as the efficiency of the PPM to correctly identify atypical observations occurring in close instants of time. Extensive Monte Carlo simulations attest to the effectiveness of the Gibbs sampling implementation. An illustrative financial time series example is also presented. (C) 2006 Elsevier Ltd. All rights reserved.
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    Bayesian inference for skew-normal linear mixed models
    (TAYLOR & FRANCIS LTD, 2007) Arellano Valle, R. B.; Bolfarine, H.; Lachos, V. H.
    Linear mixed models (LMM) are frequently used to analyze repeated measures data, because they are more flexible to modelling the correlation within-subject, often present in this type of data. The most popular LMM for continuous responses assumes that both the random effects and the within-subjects errors are normally distributed, which can be an unrealistic assumption, obscuring important features of the variations present within and among the units ( or groups). This work presents skew-normal liner mixed models (SNLMM) that relax the normality assumption by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in mixed models. The MCMC scheme is derived and the results of a simulation study are provided demonstrating that standard information criteria may be used to detect departures from normality. The procedures are illustrated using a real data set from a cholesterol study.
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    Bayesian sensitivity analysis and model comparison for skew elliptical models
    (ELSEVIER SCIENCE BV, 2006) Vidal, I.; Iglesias, P.; Branco, M. D.; Arellano Valle, R. B.
    In this work we approach the problem of model comparison between skew families. For the univariate skew model, we measure the sensitivity of the skewness parameter using the L-1 distance between symmetric and asymmetric models and we obtain explicit expressions for some of these models. The main result is that the L-1 distance between a representable elliptical distribution and a representable skew elliptical distribution remains invariant and it equals to the L-1 distance between the normal and skew-normal densities. We also use the Bayes factor to test asymmetry and present some simulation results for the skew-normal and skew-t distributions obtaining expected results for adequate prior distribution. An application in stock markets is also considered. (c) 2005 Elsevier B.V. All rights reserved.
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    Full predictivistic modeling of stock market data: Application to change point problems
    (ELSEVIER SCIENCE BV, 2007) Loschi, R. H.; Iglesias, P. L.; Arellano Valle, R. B.; Cruz, F. R. B.
    In change point problems in general we should answer three questions: how many changes are there? Where are they? And, what is the distribution of the data within the blocks? In this paper, we develop a new full predictivistic approach for modeling observations within the same block of observation and consider the product partition model (PPM) for treating the change point problem. The PPM brings more flexibility into the change point problem because it considers the number of changes and the instants when the changes occurred as random variables. A full predictivistic characterization of the model can provide a more tractable way to elicit the prior distribution of the parameters of interest, once prior opinions will be required only about observable quantities. We also present an application to the problem of identifying multiple change points in the mean and variance of a stock market return time series. (c) 2006 Elsevier B.V. All rights reserved.