In mathematics, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time or space. Consequently, parameters such as the mean and variance, if they exist, also do not change over time or position.
Stationarity is used as a tool in time series analysis, where the raw data are often transformed to become stationary; for example, economic data are often seasonal and/or dependent on a non-stationary price level. An important type of non-stationary process that does not include a trend-like behavior is the cyclostationary process.
Note that a "stationary process" is not the same thing as a "process with a stationary distribution". Indeed there are further possibilities for confusion with the use of "stationary" in the context of stochastic processes; for example a "time-homogeneous" Markov chain is sometimes said to have "stationary transition probabilities". On the other hand, all stationary Markov random processes are time-homogeneous.
Other articles related to "stationary process, stationary":
... Priestley uses stationary up to order m if conditions similar to those given here for wide sense stationarity apply relating to moments up to order m ... sense stationarity would be equivalent to "stationary to order 2", which is different from the definition of second-order stationarity given here ... geostatistics, where higher n-point statistics are assumed to be stationary in the spatial domain ...
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