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  "body": "\n## Summary\n\nA stationary process is a [[stochastic process|0QH5ENKZM1]] whose statistical behaviour does not change under shifts of time.\nAll its [[finite-dimensional distributions|Y0CN7V3B7E]] are invariant under a common time shift.\nA weaker notion, weak or wide-sense stationarity, asks only that the mean be constant and the covariance depend only on the time lag.\nStationary processes are the basic models of time series analysis and of ergodic theory, and their covariance has a spectral representation by the [[Wiener–Khinchin theorem|3ZXN26PW4G]].\n\n## Explanations\n\n### L1 human\n\nA process is stationary if it looks the same whenever you start watching it.\nDaily noise in a measuring device is often modelled this way, while a growing population is not.\nFor example, a sequence of independent rolls of a fair die is stationary: any stretch of five rolls has the same joint law as any other stretch of five rolls.\nA random walk is not stationary, since its spread grows with time.\n",
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