The beta prime regression model proposed by Bourguignon, Santos-Neto, and de Castro is an alternative to the generalized linear models and useful to model positive asymmetric data. In this paper, we propose two general misspecification tests based on the RESET test for beta prime regression models with varying precision. In the first test, we add the testing variable in the mean submodel, whereas the second test focuses on adding the testing variables in all submodels. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed tests in finite sample size in terms of their sizes and powers, thus obtaining information about the best combination of test statistics and testing variables to perform the proposed tests. We also present and discuss two empirical applications to show the applicability and importance of the proposed tests.

There are practical situations in which continuous data on the positive real line contain an excess of zeros. In this context, building on the flexibility of the beta prime (BP) distribution, we introduce the zero-adjusted BP distribution that accommodate the presence of zeros and propose zero-adjusted BP regression to deal with the issue of regression estimation when there are data with zeros in the dependent variable. The maximum likelihood method is used to estimate the model parameters. Also, we consider residual analysis. Simulation studies are conducted to evaluate its finite sample performance. Finally, a real dataset from a population-based study of fumonisin production by Fusarium verticillioides in corn grains, conducted by the Institute of Biomedical Sciences at the University of São Paulo, is discussed in detail.

This paper proposes a generalized seasonal beta prime autoregressive moving average model with dynamic precision, denoted by BPSARMA, for modeling and forecasting positive-valued seasonal time series. The proposed framework extends the generalized BPARMA model by incorporating stochastic seasonal dynamics in the conditional mean through seasonal autoregressive and moving average components while allowing a flexible autoregressive structure for the conditional precision parameter, thereby accommodating time-varying uncertainty. The model also allows the inclusion of covariates and deterministic seasonal regressors. Parameter estimation is carried out by conditional maximum likelihood, and the main inferential and diagnostic tools are discussed. Monte Carlo simulations are conducted to examine the finite-sample behavior of the estimators and associated inference procedures. The practical usefulness of the proposed approach is illustrated through hydro-environmental time series applications, where its forecasting performance is evaluated using both in-sample and out-of-sample predictive measures. The empirical results indicate that the BPSARMA specification often provides competitive or superior forecasting accuracy relative to competing models, highlighting its usefulness for modeling and prediction in positive seasonal time series.