Stationarity in time series analysis refers to a property of a dataset where statistical properties remain constant over time. Specifically, a stationary time series has a constant mean, variance, and autocorrelation, regardless of when you observe it. This means that the data's trends and patterns do not change over time. Stationarity is an essential concept in time series forecasting because many statistical models, such as ARIMA (AutoRegressive Integrated Moving Average), assume that the underlying data is stationary. If the data is not stationary, these models may produce unreliable predictions.
There are two main types of stationarity: strict stationarity and weak stationarity. Strict stationarity means that the joint distribution of any set of observations remains unchanged over time. In contrast, weak stationarity only requires that the mean and variance are constant, and that the covariance between any two time points depends only on the time difference, not on the actual time at which the data was observed. A practical example of weak stationarity is a time series where daily temperatures are recorded. If we look at the daily temperature over several months and find that the average temperature and its variability stay similar across those months, we can consider this series to be weakly stationary.
Detecting and achieving stationarity often involves techniques such as differencing (subtracting the previous observation from the current one), transformations (like taking the logarithm), or detrending the series to remove trends. For instance, if you have a time series of stock prices that are trending upward over time, applying a differencing method can help stabilize the mean and make the series stationary. By ensuring that the data is stationary, developers can create more accurate models for forecasting future values, ultimately leading to better decision-making in applications such as finance, inventory management, and resource allocation.