An irregularly spaced ARMA(1,1) model and an application to contamination data

Missing observations and unevenly spaced data are problems common to different disciplines in the context of time series analysis. This paper introduces a new approach to deal with both issues, by considering an irregularly spaced autoregressive moving average process of order (1,1) that is stationary (and therefore homoscedastic) and invertible allowing temporal variations in its coefficients. We test our model in the analysis of greenhouse time series by comparing it with a standard benchmark in the literature. As a result, our methodology leads to a huge advantage in the computational time with respect to the competitor.