Robust Autoregressive–Regression Time Series Model for Censored, Missing, Outlying, and Asymmetric Data with Applications in Environmental Data

Time-dependent datasets frequently exhibit irregularities such as missing values, censoring, skewness, and extreme observations, all of which complicate conventional statistical analysis. This study proposes a new modeling framework for such data: a censored regression model with autoregressive errors whose innovations are drawn from the two-piece scale mixture of normal (TP–SMN) family. The TP–SMN class offers remarkable flexibility, capturing symmetry and asymmetry as well as light- and heavy-tailed characteristics, thereby enhancing robustness against outliers and distributional deviations. Model estimation is carried out using a stochastic approximation to the expectation–maximization algorithm (SAEM), which maintains accuracy while improving computational efficiency relative to the standard EM procedure. The method’s properties are examined through simulation experiments and applications to three empirical time series exhibiting varying forms of censoring, missingness, outlying and asymmetrical behaviors. Findings confirm that the proposed approach provides a resilient and adaptable tool for analyzing complex temporal data.