Positive time series regression models: theoretical and computational aspects

Abstract

This paper discusses dynamic ARMA-type regression models for positive time series, which can handle bounded non-Gaussian time series without requiring data transformations. Our proposed model includes a conditional mean modeled by a dynamic structure containing autoregressive and moving average terms, time-varying covariates, unknown parameters, and link functions. Additionally, we present the PTSR package and discuss partial maximum likelihood estimation, asymptotic theory, hypothesis testing inference, diagnostic analysis, and forecasting for a variety of regression-based dynamic models for positive time series. A Monte Carlo simulation and a real data application are provided.