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.

中文翻译：

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βARMA水文时间序列建模的拟合优度检验

我们解决了使用时间序列数据执行Portmanteau测试推断的问题，这些时间序列数据采用标准单位间隔中的值。动机包括对巴西南部储备的水电能源比例的时间序列动力学进行建模。我们的重点就在于测试类的自回归移动平均（β ARMA）模型。特别是，我们希望测试此类模型的拟合优度。我们考虑针对高斯时间序列模型提出的几种测试标准，并介绍两个新的测试。我们在两种不同的情况下得出两个拟议的检验统计量的渐近零分布，即将检验应用于观察到的时间序列时以及何时将检验应用于拟合的β残差时ARMA模型。但值得注意的是，我们的研究结果意味着在类的标准混成测试的渐近有效性β ARMA模型是，在零假设下，渐近相当于我们的测试统计。我们利用蒙特卡罗模拟与配合使用时评估不同混成测试的相对优点β ARMA模型。我们目前的仿真结果表明，新测试通常比知名测试的功能更强大，后者的测试统计信息也基于残余的部分自相关。总体而言，我们建议的测试效果很好。最后，我们对巴西储备的水电能源比例的动态模型进行了建模。结果表明，βARMA模型优于三种替代模型和一种指数平滑算法。