Beta autoregressive moving average models

Rocha, Andréa V.; Cribari‐Neto, Francisco

doi:10.1007/s11749-008-0112-z

Cited by 104 publications

(119 citation statements)

References 14 publications

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“…The initial value of φ is considered in the same way as 4 in the beta regression (Ferrari and Cribari-Neto, 2004). For more theoretical details regarding large sample inferences and matrix expressions to the score vector and the Fisher information matrix (K(γ)), see Rocha and Cribari-Neto (2009).…”

Section: The Beta Autoregressive Moving Average Modelmentioning

confidence: 99%

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Bootstrap-based inferential improvements in beta autoregressive moving average model

Palm

Bayer

2017

Communications in Statistics - Simulation and Computation

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We consider the issue of performing accurate small sample inference in beta autoregressive moving average model, which is useful for modeling and forecasting continuous variables that assumes values in the interval (0, 1). The inferences based on conditional maximum likelihood estimation have good asymptotic properties, but their performances in small samples may be poor. This way, we propose bootstrap bias corrections of the point estimators and different bootstrap strategies for confidence interval improvements. Our Monte Carlo simulations show that finite sample inference based on bootstrap corrections is much more reliable than the usual inferences. We also presented an empirical application.

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Section: The Beta Autoregressive Moving Average Modelmentioning

confidence: 99%

“…In order to produce forecasts, the MLE of γ, γ, must be used to obtain estimates for µ t , µ t (Rocha and Cribari-Neto, 2009). This way, the mean response estimate at n + h, where h = 1, 2, .…”

Section: The Beta Autoregressive Moving Average Modelmentioning

confidence: 99%

Bootstrap-based inferential improvements in beta autoregressive moving average model

Palm

Bayer

2017

Communications in Statistics - Simulation and Computation

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“…To incorporate a dependence structure in the errors, we follow [13] considering an AR(p) process for { t }. In order to do that, first let ξ t = g(y t ) − x t β − f (t).…”

Section: The Modelmentioning

confidence: 99%

“…Weihua et al [17] proposed a partially linear single-index beta regression model and a penalized likelihood function have been employed in order to estimate the parameters. On the other hand, for time series data, some models based on the beta distribution were proposed by Vermaak et al [16], Rocha and Cribari-Neto [13], da Silva et al [4], and recently by Jara et al [10].…”

Section: Introductionmentioning

confidence: 99%

Conditional Predictive Inference for Beta Regression Model with Autoregressive Errors

Ferreira

Navarrete

Castro

et al. 2015

Springer Proceedings in Mathematics &Amp; Statistics

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In this chapter, we study a partially linear model with autoregressive beta distributed errors [6] from the Bayesian point of view. Our proposal also provides a useful method to determine the optimal order of the autoregressive processes through an adaptive procedure using the conditional predictive ordinate (CPO) statistic [9]. In this context, the linear predictor of the beta regression model g(μ t ) incorporates an unknown smooth function for the auxiliary time covariate t and a sequence of autoregressive errors t , i.e., g(μ t ) = x t β + f (t) + t , for t = 1, . . . , T , where x t is a k × 1 vector of nonstochastic explanatory variable values and β is a k × 1 fixed parameter vector. Furthermore, these models have a convenient hierarchical representation allowing to us an easily implementation of a Markov chain Monte Carlo (MCMC) scheme. We also propose to modify the traditional conditional predictive ordinate (CPO) to obtain what we call the autoregressive CPO, which is computed for each new observation using only the data from previous time periods.

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“…In this approach, the linear predictor is considered as a linear function both in the fixed effects and random effects. Time series analysis, on the other hand, has been previously used to evaluate the serial dependence of proportions or rates using beta regression models; see, for example, Vermaak et al (2004), Rydlewski (2007) and Rocha and Cribari-Neto (2009).…”

Section: Introductionmentioning

confidence: 99%

Partially linear beta regression model with autoregressive errors

Ferreira

Figueroa-Zúñiga

Castro

2015

TEST

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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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Beta autoregressive moving average models

Abstract: ARMA, Beta distribution, Beta ARMA, Forecasts, 62M10, 91B84,

Cited by 104 publications

References 14 publications

Bootstrap-based inferential improvements in beta autoregressive moving average model

Bootstrap-based inferential improvements in beta autoregressive moving average model

Conditional Predictive Inference for Beta Regression Model with Autoregressive Errors

Partially linear beta regression model with autoregressive errors

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