A stationary process is a time series where the statistical properties, such as mean, variance, and autocorrelation, remain constant over time.
Here's an example:
- The daily temperature of a city: Imagine the average daily temperature in a city like London. While there will be fluctuations throughout the year, the overall average temperature, variance, and correlation between different days remain relatively consistent over long periods.
In contrast, a non-stationary process would exhibit changes in these statistical properties over time. For example, the price of a stock over a few years would be a non-stationary process, as the mean and variance can change significantly due to market fluctuations.
Stationary processes are important in various fields, including:
- Time series analysis: They allow for easier forecasting and modeling of future values.
- Signal processing: They are used in filtering and analyzing signals.
- Control systems: They are essential for designing feedback loops.
Understanding stationary processes is crucial for analyzing and interpreting time series data.
