Bayesian Model Selection for Beta Autoregressive Processes

Casarin, Roberto; Valle, Luciana Dalla; Leisen, Fabrizio

doi:10.1214/12-ba713

Cited by 28 publications

(22 citation statements)

References 37 publications

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“…Unemployment data is one of the most studied in the time series analysis literature (see, for example, Montgomery et al 1998;Koop and Potter 1999). In this line, Casarin et al (2012) pointed out that "modeling and forecasting the unemployment rate still represent some of the most challenging issues in econometrics". In this context, our methodology will be applied to these data to illustrate the flexibility of the proposed model.…”

Section: Real Data Applicationsmentioning

confidence: 99%

“…da-Silva et al (2011) introduced a dynamic model in which the observation equation is represented by a beta distribution. A Bayesian method for the determination of the number of lags in beta autoregressive (AR hereafter) models was proposed by Casarin et al (2012). Jara et al (2013) formulated a Bayesian AR model for variables lying on the unit interval.…”

Section: Introductionmentioning

confidence: 99%

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Partially linear beta regression model with autoregressive errors

Ferreira

Figueroa-Zúñiga

Castro

2015

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This paper is focused on developing a methodology to deal with time series data on the unit interval modeled by a partially linear model with correlated disturbances from a Bayesian perspective. In this context, the linear predictor of the beta regression model incorporates an unknown smooth function with time as an auxiliary covariate and a set of regressors. In addition, an autoregressive dependence structure is proposed for the errors of the model. This formulation can capture the dynamic evolution of curves using both non-stochastic explanatory variables and non-parametric components, allowing an accurate fit with a limited number of parameters. Diagnostic measures are derived from the case-deletion approach and an influence measure based on the Kullback-Leibler divergence is studied and thus, a new method to determine the optimal order of the autoregressive processes through an adaptive procedure using the conditional predictive ordinate statistic is presented. A simulation study is conducted to assess some properties of the Bayesian estimator. Finally, the proposed methodology is illustrated in two real-life applications.

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Section: Real Data Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Partially linear beta regression model with autoregressive errors

Ferreira

Figueroa-Zúñiga

Castro

2015

TEST

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“…O modelo sem variáveis exógenasé um caso particular do modelo apresentado, o qualé obtido fixando φ k = 0 , ∀ k = 1, 2, ... em (3-10) e (3)(4)(5)(6)(7)(8)(9)(10)(11).…”

Section: Modelo Gas Gama Com Evolução Do Tipo Sarimaunclassified

“…Dessa forma, a média condicional do processo será dada por λ t = exp(f t ), e a equação do vetor score ponderadoé dada pela Eq. (3)(4)(5)(6)(7)(8)(9)(10)(11). Nesta construção, a inclusão de variáveis exógenasé feita na equação de evolução do parâmetro variante no tempo f t , sendo possível separar o efeito da tendência, da sazonalidade e de variáveis externas ao modelo.…”

Section: Modelo Gas Gama De Componentes Não Observáveisunclassified

“…A linha preta correspondeà reta de regressão da série de Vazão pelo Fator de Capacidade. Os resultados apresentados nesta seção correspondem a modelos GAS (12,12) definidos pelas equações (3-10) - (3)(4)(5)(6)(7)(8)(9)(10)(11)(12). Os coeficientes A i e B j da equação de evolução dos parâmetros variantes no tempo foram escolhidos por tentativa e erro, de tal forma que os resíduos quantílicos fossem bem comportados, do ponto de vista dos correlogramas (FAC e FACP) e dos testes de autocorrelação serial nos resíduos e em seus quadrados.…”

Section: Análise Descritivaunclassified

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Modelos Gas Aplicados a Series Temporais De Vazao E Vento

MATOS¹

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The GAS models (generalized autoregressive score) are time series models with time-varying parameters, which have their update mechanism drived by the scaled score of the likelihood function. The likelihood evaluation in these models is quite simple, as well as the incorporation of effects like asymmetry, long memory and other dynamics. Because they are based in the scaled score of the likelihood, it exploits the full structure of the predictive distribution to the update mechanism of the parameters, and not just mean or higher order moments. These characteristics, coupled with the ability to handle with multivariate and non-stationary processes, make the studied class a new alternative to the construction of models with time-varying parameters, particularly for non-Gaussian time series. In this dissertation, univariate GAS models were developed to analyze monthly series of streamflow of Paraibuna river (MG) and of capacity factor of a wind farm undisclosed in Northeast, using the gamma and beta distributions, respectively. In addition, a new bivariate GAS model with gamma and beta marginals was derived for the joint modeling of the streamflow and wind processes, in order to explore the seasonal complementarity between the series.

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Copula directional dependence for inference and statistical analysis of whole‐brain connectivity from fMRI data

Lee

Kim

2018

Brain and Behavior

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IntroductionInferring connectivity between brain regions has been raising a lot of attention in recent decades. Copula directional dependence (CDD) is a statistical measure of directed connectivity, which does not require strict assumptions on probability distributions and linearity.MethodsIn this work, CDDs between pairs of local brain areas were estimated based on the fMRI responses of human participants watching a Pixar animation movie. A directed connectivity map of fourteen predefined local areas was obtained for each participant, where the network structure was determined by the strengths of the CDDs. A resampling technique was further applied to determine the statistical significance of the connectivity directions in the networks. In order to demonstrate the effectiveness of the suggested method using CDDs, statistical group analysis was conducted based on graph theoretic measures of the inferred directed networks and CDD intensities. When the 129 fMRI participants were grouped by their age (3–5 year‐old, 7–12 year‐old, adult) and gender (F, M), nonparametric two‐way analysis of variance (ANOVA) results could identify which cortical regions and connectivity structures correlated with the two physiological factors.ResultsEspecially, we could identify that (a) graph centrality measures of the frontal eye fields (FEF), the inferior temporal gyrus (ITG), and the temporopolar area (TP) were significantly affected by aging, (b) CDD intensities between FEF and the primary motor cortex (M1) and between ITG and TP were highly significantly affected by aging, and (c) CDDs between M1 and the anterior prefrontal cortex (aPFC) were highly significantly affected by gender.SoftwareThe R source code for fMRI data preprocessing, estimation of directional dependences, network visualization, and statistical analyses are available at https://github.com/namgillee/ CDDforFMRI.

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Bayesian Model Selection for Beta Autoregressive Processes

Abstract: We deal with Bayesian model selection for beta autoregressive processes. We discuss the choice of parameter and model priors with possible parameter restrictions and suggest a Reversible Jump Markov-Chain Monte Carlo (RJMCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm

Cited by 28 publications

References 37 publications

Partially linear beta regression model with autoregressive errors

Partially linear beta regression model with autoregressive errors

Modelos Gas Aplicados a Series Temporais De Vazao E Vento

Copula directional dependence for inference and statistical analysis of whole‐brain connectivity from fMRI data

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