Abstract: The present disclosure relates to computer-implemented methods, software, and systems for identifying cycle patterns in data observations collected as time series based on a planning calendar with a time hierarchy. Time series can include data observations associated with a respective date. Model variables derived based on each date associated with each data observation can be determined. The model variables can map a date of a data observation to an occurrence of the date according to a time hierarchy of a planning calendar. The time hierarchy can include periods of sub-periods as a hierarchy level, where each period is defined to comprise a number of sub-periods based on a week-based pattern of the planning calendar. A predictive model is generated for a predicted variable identified at the data observations based on the model variables. The predictive model is executed to predict values for the predicted variable over a time horizon.

Abstract: A system and method including determining, for a calculation of a predicted value specified by a recursive equation, an equivalent representation based on a cumulative sum; determining a trend component for the determined equivalent representation of the predicted value; decomposing the determined equivalent representation of the predicted value into the trend component and a cyclic component; and generating a visualization for a set of time series data expressed by the decomposition.