Stationarized

Stationarized refers to a data series that has been transformed so that its statistical properties, such as mean, variance, and autocorrelation, do not change over time. Many time series forecasting models, particularly those based on autoregressive integrated moving average (ARIMA) models, require the input data to be stationary. Non-stationary data often exhibits trends or seasonality, which can lead to unreliable forecasts if not addressed.

A common method to achieve stationarity is differencing. Differencing involves subtracting the previous observation from the current observation. If a single round of differencing is sufficient, the process is often referred to as integrated of order one, denoted as I(1). Higher-order differencing, subtracting the difference from the previous difference, may be necessary for some data series. Other methods to stationarize data include transformations like taking the logarithm or power to stabilize variance, and removing seasonal components through seasonal differencing or decomposition.

Identifying non-stationarity can be done through visual inspection of time series plots, autocorrelation function (ACF) plots, and statistical tests such as the Augmented Dickey-Fuller (ADF) test or the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. Once a series is stationarized, it can be more effectively modeled and forecasted using standard time series techniques. The process of stationarization is a crucial preprocessing step in many time series analyses.