A Mean-Parameterized Maxwell Time Series Model for Positive Data

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.