This paper introduces a new time series model based on the reflected unit Burr XII (RUBXII) distribution that is an alternative to the Kumaraswamy autoregressive moving average and Beta autoregressive moving average models for time series analysis taking values in the standard unit interval. The proposed model describes the conditional median of RUBXII-distributed discrete-time series by a dynamic structure that includes autoregressive and moving average (ARMA) terms, a set of regressors, and a link function. We perform the model's parameter estimation using the conditional maximum likelihood method. Closed-form expressions for the score vector and observed information matrix are presented. We propose and discuss techniques of diagnostic and forecasting for the new model. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the conditional maximum likelihood estimator. Finally, the proportion of stored hydroelectric energy in Northern Brazil is analyzed through the proposed model. The results evidence that the introduced RUBXII-ARMA model is suitable for describing the dynamics of the data and provides more accurate forecasts for the proportion of stored energy in Northern Brazil than those from competitors' models.

This paper introduces a new time series model for non-negative continuous data based on the Maxwell distribution. The proposed model employs a reparameterization of the Maxwell distribution in which its parameter directly represents the mean. In this formulation, the conditional mean is modeled through a dynamic structure that combines autoregressive and moving average components, linked by an appropriate link function. Parameter estimation is carried out using the conditional maximum likelihood method, for which closed-form matrix expressions of the conditional score vector and the conditional Fisher information matrix are derived. Based on the asymptotic properties of the estimators, procedures for interval estimation and hypothesis testing are presented. Monte Carlo simulations assess the finite-sample performance, and provide evidence of the estimators' convergence toward the true parameter values as the sample size increases. An empirical application involving wind speed data from Brasília, the capital of Brazil, shows the practical relevance and effectiveness of the proposed model for real-world time series modeling and forecasting.

This paper proposes the MKSARMAX model for modeling and forecasting time series that can only take on values within a specified range, such as in the interval (0,1). The model is especially good for modeling double-bounded hydro-environmental time series since it accommodates bounded support and asymmetric distribution, making it advantageous compared to the traditional Gaussian-based time series model. The MKSARMAX models the conditional median of a modified Kumaraswamy distributed variable observed over time, by a dynamic structure considering stochastic seasonality and including autoregressive and moving average terms, exogenous regressors, and a link function. The conditional maximum likelihood method is employed to estimate the model parameters. Hypothesis tests and confidence intervals for the parameters of the proposed model are derived using the asymptotic theory of the conditional maximum likelihood estimators. Quantile residuals are defined for diagnostic analysis, and goodness-of-fit tests are subsequently implemented. Synthetic hydro-environmental time series are generated in a Monte Carlo simulation study to assess the finite sample performance of the inferences. Moreover, MKSARMAX outperforms beta SARMA, SARMAX, Holt-Winters, and KARMA models in most accuracy measures analyzed when applied to useful water volume datasets, presenting for the first-step forecast at least 98% lower MAE, RMSE, and MAPE values than competitors in the Caconde UV dataset, and 54% lower MAE, RMSE, and MAPE values than competitors in the Guarapiranga UV dataset. These findings suggest that the MKSARMAX model holds strong potential for water resource management. Its flexibility and accuracy in the early forecasting steps make it particularly valuable for predicting flood and drought periods.

Matrix approximation methods have successfully produced efficient, low-complexity approximate transforms for the discrete cosine transforms and the discrete Fourier transforms. For the DFT case, literature archives approximations operating at small power-of-two blocklenghts, such as {8, 16, 32}, or at large blocklengths, such as 1024, which are obtained by means of the Cooley-Tukey-based approximation relying on the small-blocklength approximate transforms. Cooley-Tukey-based approximations inherit the intermediate multiplications by twiddled factors which are usually not approximated; otherwise the effected error propagation would prevent the overall good performance of the approximation. In this context, the prime factor algorithm can furnish the necessary framework for deriving fully multiplierless DFT approximations. We introduced an approximation method based on small prime-sized DFT approximations which entirely eliminates intermediate multiplication steps and prevents internal error propagation. To demonstrate the proposed method, we design a fully multiplierless 1023-point DFT approximation based on 3-, 11- and 31-point DFT approximations. The performance evaluation according to popular metrics showed that the proposed approximations not only presented a significantly lower arithmetic complexity but also resulted in smaller approximation error measurements when compared to competing methods.