stationarization

Stationarization is a statistical technique used to transform a non-stationary time series into a stationary one. A time series is considered stationary if its statistical properties, such as mean, variance, and autocorrelation, do not change over time. Non-stationary time series, on the other hand, exhibit trends, seasonality, or other time-dependent structures that can complicate analysis and forecasting.

The primary goal of stationarization is to remove these time-dependent structures, allowing for more accurate modeling and forecasting. There are several methods to achieve stationarization, including differencing, transformation, and detrending.

Differencing involves subtracting the previous observation from the current one to eliminate trends. For example, first differencing (y_t - y_{t-1}) can remove linear trends, while second differencing can handle quadratic trends. Transformation methods, such as taking the logarithm or square root of the data, can stabilize the variance and make the series more stationary. Detrending involves fitting a trend model to the data and then subtracting this trend from the original series.

Once a time series is stationarized, it can be analyzed using various statistical techniques, such as autocorrelation and partial autocorrelation functions, to identify patterns and relationships. This process is crucial in time series analysis and forecasting, as it ensures that the underlying assumptions of the models are met, leading to more reliable and accurate results.