Goodness‐of‐fit tests for β ARMA hydrological time series modeling

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 ( β ARMA) 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 β ARMA model. It is worth noticing that our results imply the asymptotic validity of standard portmanteau tests in the class of β ARMA 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 β ARMA 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 β ARMA model outperforms three alternative models and an exponential smoothing algorithm.