Portmanteau testing inference in beta autoregressive moving average models

Abstract

The class of beta autoregressive moving average (bARMA) models is useful for modeling time series data that assume values in the standard unit interval, such as rates and proportions. This thesis is composed of two main and independent chapters. In the first part, we consider portmanteau testing inference in the class of bARMA models. To that end, we use tests that have been developed for Gaussian models, such as the Ljung and Box, Monti, Dufour and Roy, Kwan and Sim, and Lin and McLeod tests. We also consider bootstrap variants of the Ljung and Box, Monti, Dufour and Roy, and Kwan and Sim tests. Moreover, we propose two new test statistics which, like the Monti statistic, are based on residual partial autocorrelations. Additionally, we present and discuss results from Monte Carlo simulations and an empirical application. The second part of the thesis focuses on the recursive nature of bARMA loglikelihood derivatives under moving average dynamics. We provide closed form expressions for the relevant derivatives by considering errors in the predictor scale.