Time series comes from measurements, and measurements are never absolutely accurate. Traditionally, when we deal with an individual measurement or with a sample of measurement results, we subdivide a measurement error into random and systematic components: systematic error does not change from measurement to measurement which random errors corresponding to different measurements are independent. In time series, when we measure the same quantity at different times, we can also have correlation between measurement errors corresponding to nearby moments of time. To capture this correlation, environmental science researchers proposed to consider the third type of measurement errors: periodic. This extended classification of measurement error may seem ad hoc at first glance, but it leads to a good description of the actual errors. In this paper, we provide a theoretical explanation for this semi-empirical classification, and we show how to efficiently propagate all types of uncertainty via computations.