Stationary Stochastic Process

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A Stationary Stochastic Process is a stochastic process whose joint probability distribution does not change when shifted in time.



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/stationary_process Retrieved:2015-11-30.
    • In mathematics and statistics, 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. Consequently, parameters such as the mean and variance, if they are present, also do not change over time and do not follow any trends.

      Stationarity is used as a tool in time series analysis, where the raw data is 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". Besides, all stationary Markov random processes are time-homogeneous.