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We introduce a dynamic model tailored for positively valued time series. It accommodates both autoregressive and moving average dynamics and allows for explanatory variables. The underlying assumption is that each random variable follows, conditional on the set of previous information, the beta prime distribution. A novel feature of the proposed model is that both the conditional mean and conditional precision evolve over time. The model thus comprises two dynamic submodels, one for each parameter. The proposed model for the conditional precision parameter is parsimonious, incorporating first‐order time dependence. Changes over time in the shape of the density are determined by the time evolution of two parameters, and not just of the conditional mean. We present simple closed‐form expressions for the model's conditional log‐likelihood function, score vector, and Fisher's information matrix. Monte Carlo simulation results are presented. Finally, we use the proposed approach to model and forecast two seasonal water flow time series. Specifically, we model the inflow and outflow rates of the reservoirs of two hydroelectric power plants. Overall, the forecasts obtained using the proposed model are more accurate than those yielded by alternative models. [ABSTRACT FROM AUTHOR]

The simplex regression model is tailored to response variables that assume values in the standard unit interval, such as rates and proportions. The estimation of the parameters that index the model is performed by maximum likelihood, and test inferences are commonly reached using the likelihood ratio test. Such a test is based on an asymptotic approximation, and thus the resulting inferences may be misleading when the sample size is not large. In this paper, Bartlett‐corrected likelihood ratio tests are obtained for varying dispersion simplex regressions. Monte Carlo simulations are performed to compare the finite sample behavior of the corrected tests to that of standard likelihood ratio. The numerical results show that one of the corrected tests displays excellent control of the type I error frequency. An empirical application is presented and discussed. [ABSTRACT FROM AUTHOR]

The beta regression model is tailored for responses that assume values in the standard unit interval. It comprises two submodels, one for the mean response and another for the precision parameter. We develop tests of correct specification for such a model. The tests are based on the information matrix equality, which holds when the model is correctly specified. We establish the validity of the tests in the class of varying precision beta regressions, provide closed-form expressions for the quantities used in the test statistics, and present simulation evidence on the tests' null and non-null behavior. We show that it is possible to achieve very good control of the type I error probability when data resampling is employed and that the tests are able to reliably detect incorrect model specification, especially when the sample size is not small. An empirical application is presented and discussed. • Two model misspecification tests for beta regressions are presented. • Monte Carlo simulation evidence on the tests' null and non-null behavior is presented. • An empirical application is presented and discussed. [ABSTRACT FROM AUTHOR]

Beta regressions are commonly used with responses that assume values in the standard unit interval, such as rates, proportions and concentration indices. Hypothesis testing inferences on the model parameters are typically performed using the likelihood ratio test. It delivers accurate inferences when the sample size is large, but can otherwise lead to unreliable conclusions. It is thus important to develop alternative tests with superior finite sample behavior. We derive the Bartlett correction to the likelihood ratio test under the more general formulation of the beta regression model, i.e. under varying precision. The model contains two submodels, one for the mean response and a separate one for the precision parameter. Our interest lies in performing testing inferences on the parameters that index both submodels. We use three Bartlett-corrected likelihood ratio test statistics that are expected to yield superior performance when the sample size is small. We present Monte Carlo simulation evidence on the finite sample behavior of the Bartlett-corrected tests relative to the standard likelihood ratio test and to two improved tests that are based on an alternative approach. The numerical evidence shows that one of the Bartlett-corrected typically delivers accurate inferences even when the sample is quite small. An empirical application related to behavioral biometrics is presented and discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class of beta seasonal autoregressive moving average (βSARMA) models for modelling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta autoregressive moving average models [Rocha AV and Cribari-Neto F. Beta autoregressive moving average models. Test. 2009;18(3):529-545] by incorporating seasonal dynamics to the model dynamic structure. Besides introducing the new class of models, we develop parameter estimation, hypothesis testing inference, and diagnostic analysis tools. We also discuss out-of-sample forecasting. In particular, we provide closed-form expressions for the conditional score vector and for the conditional Fisher information matrix. We also evaluate the finite sample performances of conditional maximum likelihood estimators and white noise tests using Monte Carlo simulations. An empirical application is presented and discussed. [ABSTRACT FROM AUTHOR]

The log-Birnbaum-Saunders regression model introduced by Rieck and Nedelman (1991) is useful for modeling lifetimes of materials and equipments subject to different conditions. Our goal in this article is twofold. First, we numerically evaluate the finite sample performances of the likelihood ratio, score and Wald tests in the log-Birnbaum-Saunders regression model. Second, we introduce a RESET-like misspecification test for that model. The null hypothesis is that the model is correctly specified which is tested against the alternative hypothesis of model misspecification. The power of the test is evaluated using Monte Carlo simulations. Bootstrap-based inference is also considered. An empirical application is presented and discussed. [ABSTRACT FROM AUTHOR]

We address the issue of model selection in beta regressions with varying dispersion. The model consists of two submodels, namely: for themean and for the dispersion. Our focus is on the selection of the covariates for each submodel. Our Monte Carlo evidence reveals that the joint selection of covariates for the two submodels is not accurate in finite samples. We introduce twonewmodel selection criteria that explicitly account for varying dispersion and propose a fast two step model selection scheme which is considerably more accurate and is computationally less costly than usual joint model selection.Monte Carlo evidence is presented and discussed. We also present the results of an empirical application. [ABSTRACT FROM AUTHOR]

This paper considers edge interval estimation between two regions of a synthetic aperture radar (SAR) image, which differ in texture. This is a difficult task because SAR images are contaminated with speckle noise. Different point estimation strategies under multiplicative noise are discussed in the literature. It is important to assess the quality of such point estimates and to also perform inference under a given confidence level. This can be achieved through interval parameter estimation. To that end, we propose bootstrap-based edge confidence interval. The relative merits of the different inference strategies are compared using Monte Carlo simulation. The results show that interval edge estimation can be used to assess the accuracy of an edge point estimate. They also show that interval estimates can be quite accurate and that they can indicate the absence of an edge. In order to illustrate interval edge estimation, we also analyze a real data set. [ABSTRACT FROM PUBLISHER]

We address the issue of constructing prediction intervals for responses that assume values in the standard unit interval, $$(0,1)$$ . The response is modeled using the class of beta regression models and we introduce percentile and $$\hbox {BC}_a$$ (bias-corrected and accelerated) bootstrap prediction intervals. We present Monte Carlo evidence on the finite sample behavior of such intervals. An empirical application is presented and discussed. [ABSTRACT FROM AUTHOR]

Beta regression models are useful for modeling data that assume values in the standard unit interval (0, 1), such as rates and proportions. These models, however, cannot be used when the data contain observations that equal zero or one (the limits of the unit interval). Ospina and Ferrari (2012) developed the class of inflated beta regressions to handle situations in which the data contain positive mass at zero and/or one. The model is quite general and contains three submodels: for the mean, for the precision, and for the probability that the variate equals zero or one (α). In this article, we propose a misspecification test for inflated beta regressions with fixed and variable dispersion. In particular, we propose two variants of the test. In the first variant, we only add testing variables to the mean submodel. The second variant follows from adding testing variables to all submodels. We perform extensive Monte Carlo simulations in order to assess the finite-sample properties of the tests (size and power), and also to gain insight on which variables should be used as testing variable and on which asymptotic testing procedure delivers the most reliable inferences. We consider a number of different misspecifications, namely: neglected nonlinearities, omitted independent variables, incorrect link functions, neglected spatial correlation, and neglected variable dispersion. Finally, an empirical illustration is presented and discussed. [ABSTRACT FROM AUTHOR]

Abstract: We consider the issue of performing accurate small-sample testing inference in beta regression models, which are useful for modeling continuous variates that assume values in (0,1), such as rates and proportions. We derive the Bartlett correction to the likelihood ratio test statistic and also consider a bootstrap Bartlett correction. Using Monte Carlo simulations we compare the finite sample performances of the two corrected tests to that of the standard likelihood ratio test and also to its variant that employs Skovgaard''s adjustment; the latter is already available in the literature. The numerical evidence favors the corrected tests we propose. We also present an empirical application. [Copyright &y& Elsevier]

We propose two new residuals for the class of beta regression models, and numerically evaluate their behaviour relative to the residuals proposed by Ferrari and Cribari-Neto. Monte Carlo simulation results and empirical applications using real and simulated data are provided. The results favour one of the residuals we propose. [ABSTRACT FROM AUTHOR]

This paper reviews the matrix programminglanguage Ox from the viewpoint of an econometrician/statistician.We focus on scientific programming using Ox and discussexamples of possible interest to econometricians and statisticians, such as random number generation, maximum likelihood estimation, andMonte Carlo simulation. Ox is a remarkable matrix programming language which is well suited to research and teaching in econometrics and statistics. [ABSTRACT FROM AUTHOR]

The heteroscedasticity‐consistent covariance matrix estimator proposed by White (1980) is commonly used in practical applications and is implemented into a number of pieces of statistical software. However, although consistent, it can display substantial bias in small to moderately large samples, as shown by Monte Carlo simulations elsewhere. This paper defines modified White estimators which are approximately bias‐free. Numerical results show that the modified estimators display much smaller bias than White's estimator in small samples. We also show that the bias correction leads to some variance inflation. In hypothesis testing based on heteroscedasticity‐consistent covariance matrix estimators, numerical results suggest that tests based on the proposed bias‐corrected estimators typically display smaller size distortions. [ABSTRACT FROM PUBLISHER]

We introduce the class of inflated Kumaraswamy autoregressive and moving average models for modeling and forecasting hydro-environmental time series that assume values in [ 0 , 1) or (0 , 1 ]. The main goal of our proposal is to handle doubly-bounded times series in the presence of inflated data. Conditioned on past observations, the response variable is assumed to follow an inflated Kumaraswamy (IK) distribution, a composite of continuous and discrete distributions. The Kumaraswamy distribution family is particularly useful for modeling hydro-environmental and related data. In the proposed model, the random component follows the IK distribution, while the systematic component comprises two dynamic structures, one for the conditional median and one for the mixture parameter, the latter being simple and parsimonious. The dynamic structure used for the conditional median encompasses autoregressive and moving average dynamics and allows for the inclusion of regressors. Statistical inference based on conditional maximum likelihood is presented. Results from Monte Carlo simulations based on synthetic hydro-environmental series are used to evaluate the accuracy of inferences in finite sample sizes. Finally, three empirical applications using hydro-environmental data are presented and discussed. They showcase the applicability of the proposed model in the context of data-driven water and environmental management. • The class of inflated Kumaraswamy ARMA (IKARMA) models is introduced. • The IKARMA is useful for modeling time series that assume values in [ 0 , 1) or (0 , 1 ]. • The introduced model is capable of predicting inflated points. • Three empirical applications that use hydro-environmental data are discussed. [ABSTRACT FROM AUTHOR]