Bootstrap-based inferential improvements in beta autoregressive moving average model

Palm, Bruna Gregory; Bayer, Fábio M.

doi:10.1080/03610918.2017.1300268

Cited by 11 publications

(4 citation statements)

References 37 publications

(77 reference statements)

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“…For instance, the bootstrap technique has been employed in time series (Kim, 2003;Franco and Reisen, 2007;Engsted and Pedersen, 2014;Palm and Bayer, 2017), in dynamic panel models (De Vos et al, 2015;Everaert and Pozzi, 2007), and regression models (Kim, 2005) to rectify bias in various estimators. It has also been used in machine learning models to minimize bias in the predicted response variable (Hooker and Mentch, 2016) and in the maximum likelihood estimation (MLE) (Ferrari and Cribari-Neto, 1998).…”

Section: Methodsmentioning

confidence: 99%

Bootstrap methods for bias correcting probability distribution parameters characterizing extreme snow accumulations

Pomeyie,

Bean

2023

Preprint

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Accurately quantifying the threat of collapse due to the weight of settled snow on the roof of a structure is crucial for ensuring structural safety. This quantification relies upon direct measurements of the snow water equivalent (SWE) of settled snow, though most weather stations in the United States only measure snow depth. The absence of direct load measurements necessitates the use of modeled estimates of SWE, which often results in the underestimation of the scale/variance ($\sigma$) parameter of the distribution of annual maximum SWE. This paper introduces a novel bias correction method that employs a bootstrap technique with regression-based models to calibrate the variance parameter of the distribution. The efficacy of this approach is demonstrated on real and simulated datasets. The findings reveal varied levels of success, with the efficacy of the proposed approach being inherently dependent on the quality of the selected regression-based model. These findings demonstrate that integrating our approach with a suitable regression-based model is able to produce unbiased or nearly unbiased annual maximum SWE distribution parameters in the absence of direct SWE measurements.

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Section: Methodsmentioning

confidence: 99%

Bootstrap methods for bias correcting probability distribution parameters characterizing extreme snow accumulations

Pomeyie,

Bean

2023

Preprint

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“…Bayesian model selection for the β ARMA model was developed by Casarin, Valle, and Leisen (), and bias‐corrected maximum likelihood of the parameters that index the model was considered by Palm and Bayer (). An extension of the model that incorporates seasonal dynamics, the β SARMA model, was recently proposed by Bayer, Cintra, and Cribari‐Neto (), and an extension of the model for compositional data, the DARMA model (“D” stands for Dirichlet), was developed by Zheng and Chen ().…”

Section: The Modelmentioning

confidence: 99%

Goodness‐of‐fit tests forβARMA hydrological time series modeling

et al. 2019

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We address the issue of performing portmanteau testing inference using time series data that assume values in the standard unit interval. The motivation involves modeling the time series dynamics of the proportion of stocked hydroelectric energy in the South of Brazil. Our focus lies in the class of beta autoregressive moving average (βARMA) models. In particular, we wish to test the goodness‐of‐fit of such models. We consider several testing criteria that have been proposed for Gaussian time series models and introduce two new tests. We derive the asymptotic null distribution of the two proposed test statistics in two different scenarios, namely, when the tests are applied to an observed time series and when they are applied to the residuals from a fitted βARMA model. It is worth noticing that our results imply the asymptotic validity of standard portmanteau tests in the class of βARMA models that are, under the null hypothesis, asymptotically equivalent to our test statistics. We use Monte Carlo simulation to assess the relative merits of the different portmanteau tests when used with fitted βARMA models. The simulation results we present show that the new tests are typically more powerful than a well‐known test whose test statistic is also based on residual partial autocorrelations. Overall, the tests we propose perform quite well. Finally, we model the dynamics of the proportion of stocked hydroelectric energy in Brazil. The results show that the βARMA model outperforms three alternative models and an exponential smoothing algorithm.

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“…This method has been widely-employed in time series modeling and it is capable of providing accurate prediction intervals and inferential improvements, as exemplified in bias correction of estimators (Palm and Bayer, 2018;Kilian, 1998), construction of confidence intervals for model parameters (Spierdijk, 2016), calculation of Fourier coefficients for the autocovariance function (Dehay et al, 2018), model selection criteria (Bayer and Cribari-Neto, 2015;Cavanaugh and Shumway, 1997), prediction intervals (Staszewska-Bystrova and Winker, 2016), and hypothesis testing (Morley and Sinclair, 2009).…”

Section: Introductionmentioning

confidence: 99%

“…The βARMA models for long-range dependence and sazonal series are derived in Pumi et al (2019) and Bayer et al (2018), respectively. Finally, bootstrap-based inferential improvements and goodness-of-fit test for hydrological time series modeling based on the βARMA model are discussed in Palm and Bayer (2018) and Scher et al (2020), respectively.…”

Section: Introductionmentioning

confidence: 99%

Prediction Intervals in the Beta Autoregressive Moving Average Model

Palm,

Bayer,

Cintra

2022

Preprint

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In this paper, we propose five prediction intervals for the beta autoregressive moving average model. This model is suitable for modeling and forecasting variables that assume values in the interval (0,1). Two of the proposed prediction intervals are based on approximations considering the normal distribution and the quantile function of the beta distribution. We also consider bootstrap-based prediction intervals, namely: (i) bootstrap prediction errors (BPE) interval; (ii) bias-corrected and acceleration (BCa) prediction interval; and (iii) percentile prediction interval based on the quantiles of the bootstrappredicted values for two different bootstrapping schemes. The proposed prediction intervals were evaluated according to Monte Carlo simulations. The BCa prediction interval offered the best performance among the evaluated intervals, showing lower coverage rate distortion and small average length. We applied our methodology for predicting the water level of the Cantareira water supply system in São Paulo, Brazil.

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Bootstrap-based inferential improvements in beta autoregressive moving average model

Cited by 11 publications

References 37 publications

Bootstrap methods for bias correcting probability distribution parameters characterizing extreme snow accumulations

Bootstrap methods for bias correcting probability distribution parameters characterizing extreme snow accumulations

Goodness‐of‐fit tests forβARMA hydrological time series modeling

Prediction Intervals in the Beta Autoregressive Moving Average Model

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