Stationarity

Many forecasting and statistical methods assume that the patterns in a time series are stable, so that the past is a reliable guide to the future. A stationary series fluctuates around a constant average with a constant spread.

Many economic and financial series are not stationary. Share prices, GDP and price levels tend to trend upwards over time, so their averages change. However, the changes in these series, such as daily returns or growth rates, are often closer to stationary.

For example, a stock index level is not stationary because it has drifted upwards over decades, but its daily percentage returns fluctuate around a fairly stable average, making them more suitable for many statistical models.

Using non-stationary data in models designed for stationary data can produce misleading results, such as apparent relationships between two unrelated trending series, a problem called spurious regression. Analysts test for stationarity and often transform data, for example by taking differences or growth rates, before modelling.