In building statistical ARMA-style forecasting models, a necessary precondition is that the time series being modeled be stationary: stationary with respect to mean; stationary with respect to covariance; and, stationary with respect to variance. Quite often, the time series that the data scientist wishes to model contains a trend - meaning that the time series is non-stationary with respect to the mean; or, alternatively may contain some periodicities (cyclic variance in data). This trend and/or periodicities must be removed before modeling may begin. . Once the data scientist has devised a formula to represent the trend or periodic behaviors, their next task is to generate a series using that formula; such that they can then input both the original series and formula driven series through a pointwise subtractor function, which forms a new series with the trend and/or periodicities subtracted out.
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