Beta AutoRegressive Models for Forecasting Percentage Series

Forecasts positive percentage time series (0<Yt<1) that have a stationary Beta distribution B(a,b) and Autoregressive dynamics AR(p).

Positive percentage time series Yt are present in many empirical applications; they take values in the continuous interval (0<Yt<1) and are often modeled with linear dynamic models. Risks of biased predictions (outside the admissible range) and problems of heteroskedasticity in the presence of asymmetric distributions are ignored by practitioners. Alternative modellings are proposed in the statistical literature; the most suitable is the dynamic beta regression, which belongs to generalized linear models (GLM) and uses the logit transformation as a link function. Assuming that Yt have a stationary beta distribution B(a,b) and autoregressive dynamics AR(p), maximum likelihood is necessary for estimating the parameters and the forecasts.