What does it mean for a time series to be non-stationary?

A time series is described as non-stationary when it exhibits characteristics that change over time, specifically in terms of its mean and variance. This means that the statistical properties of the series are not constant, and the data may reflect underlying trends or patterns that evolve as time progresses. For instance, economic time series data can show increasing averages due to inflation or decreasing averages during economic downturns.

In contrast, a stationary time series would exhibit stable and consistent statistical properties, such as a constant mean and variance, across different time periods. Such stability is essential for reliable modeling and forecasting. The presence of trends or seasonal patterns indicates non-stationarity, as these factors contribute to the changing characteristics of the series.

Recognizing non-stationarity is crucial for analysts, as it may necessitate data transformation or differencing to make the series suitable for certain analytical techniques, particularly in forecasting models.