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.
Read more about Stationary Process: Definition, Examples
Famous quotes containing the words stationary and/or process:
“It is the dissenter, the theorist, the aspirant, who is quitting this ancient domain to embark on seas of adventure, who engages our interest. Omitting then for the present all notice of the stationary class, we shall find that the movement party divides itself into two classes, the actors, and the students.”
—Ralph Waldo Emerson (18031882)
“The process of education in the oldest profession in the world is like any other educational process, in that it requires time and effort and patience; it can only be acquired by taking one step at a time, though the steps become accelerated after the first few.”
—Madeleine [Blair], U.S. prostitute and madam. Madeleine, ch. 4 (1919)