To satisfy the stationarity assumption of linear time series models, we need to transform the original time series, often in several steps. Common transformations include the application of the (natural) logarithm to convert an exponential growth pattern into a linear trend and stabilize the variance. Deflation implies dividing a time series by another series that causes trending behavior, for example dividing a nominal series by a price index to convert it into a real measure.

A series is trend-stationary if it reverts to a stable long-run linear trend. It can often be made stationary by fitting a trend line using linear regression and using the residuals, or by including the time index as an independent variable in a regression or AR(I)MA model (see the following section on univariate time series models), possibly combined with logging or deflating.

In many cases, de-trending is not sufficient to make the series stationary. Instead, we need to transform the original data into a series of period-to-period and/or season-to-season differences. In other words, we use the result of subtracting neighboring data points or values at seasonal lags from each other. Note that when such differencing is applied to a log-transformed series, the results represent instantaneous growth rates or returns in a financial context. 

If a univariate series becomes stationary after differencing d times, it is said to be integrated of the order of d, or simply integrated if d=1. This behavior is due to so-called unit roots.