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Is Cauchy distribution stationary?
For example, an iid process with standard Cauchy distribution is strictly stationary but not weak stationary because the second moment of the process is not finite.
What is strong stationary time series?
A strong form of stationarity is when the distribution of a time-series is exactly the same trough time. In other words, the distribution of original time-series is exactly same as lagged time-series (by any number of lags) or even sub-segments of the time-series.
How to determine stationarity in time series analysis?
Indeed, for many cases involving time series, you will find that you have to be able to determine if the data was generated by a stationary process, and possibly to transform it so it has the properties of a sample generated by such a process.
Can a stochastic process generate time series data?
Without a formal definition for processes generating time series data (yet; they are called stochastic processes and we will get to them in a moment), it is already clear that stationary processes are a sub-class of a wider family of possible models of reality. This sub-class is much easier to model and investigate.
What does stationarity mean in a stochastic process?
Having a basic definition of stochastic processes to build on, we can now introduce the concept of stationarity. Intuitively, stationarity means that the statistical properties of the process do not change over time. However, several different notions of stationarity have been suggested in econometric literature over the years.
What does it mean when a time series does not change?
In the most intuitive sense, stationarity means that the statistical properties of a process generating a time series do not change over time. It does not mean that the series does not change over time, just that the way it changes does not itself change over time.