A property of data in a dataset, in which the data distribution stays constant across one or more dimensions. Most commonly, that dimension is time.
Card 1 of 259. Answer: A property of data in a dataset, in which the data distribution stays constant across one or more dimensions. Most commonly, that dimension is time.
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Stationarity means the statistical properties of the data do not change along a dimension, almost always time. Strict stationarity requires the whole joint distribution to stay the same. Most methods need only weak stationarity: a constant mean, a constant variance, and a covariance between two points that depends only on the gap between them.
A random walk is the standard counterexample. If yₜ = yₜ₋₁ + εₜ with independent shocks of variance σ², the variance after t steps is tσ², which keeps growing. Its first difference, εₜ, is white noise, which is stationary. Stock prices behave roughly like the first and daily returns like the second; trends and seasonality also break stationarity.
It matters because ARMA models assume it, which is why ARIMA differences the series first, and regressing one random walk on another often gives a high R² for unrelated series, the spurious regression problem. The augmented Dickey-Fuller test has a unit root as its null and KPSS has stationarity as its null, so they are often paired.
