Stationary process

In the mathematical sciences, a stationary process (or strict(ly) stationary process) is a stochastic process in which the probability density function of some random variable X does not change over time or position. As a result, parameters such as the mean and variance also do not change over time or position.

Related Topics:
Mathematical sciences - Stochastic process - Probability density function - Random variable - Mean - Variance

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As an example, the measurement of white noise is stationary. Alternatively, the measurement of a cymbal clashing is not stationary. Although a cymbal clash is basically white noise, the measurement of that noise varies over time: Before the clash, there is silence, and after the clash, the noise gradually diminishes.

Related Topics:
White noise - Cymbal

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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 the price level. Processes are described as trend stationary if they are a linear combination of a stationary process and one or more processes exhibiting a trend. Transforming this data to leave a stationary data set for analysis is referred to as de-trending.

Related Topics:
Time series analysis - Economic - Trend

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A discrete-time stationary process where the sample space is also discrete (so that the random variable may take one of N possible values) is known as a Bernoulli scheme. When N=2, the process is called a Bernoulli process.

Related Topics:
Discrete-time - Bernoulli scheme - Bernoulli process

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