Censored autoregressive regression models with Student-t innovations

Abstract

Data collected over time are common in applications and may contain censored or missing observations, making it difficult to use standard statistical procedures. This article proposes an algorithm to estimate the parameters of a censored linear regression model with errors serially correlated and innovations following a Student-$t$ distribution. This distribution is widely used in the statistical modelling of data containing outliers because its longer-than-normal tails provide a robust approach to handling such data. The maximum likelihood estimates of the proposed model are obtained through a stochastic approximation of the EM algorithm. The methods are applied to an environmental dataset regarding ammonia-nitrogen concentration, which is subject to a limit of detection (left censoring) and contains missing observations. Additionally, two simulation studies are conducted to examine the asymptotic properties of the estimates and the robustness of the model. The proposed algorithm and methods are implemented in the R package ARCensReg.