In time series analysis, stationarity means the mean and variance are changing over time

Question

BlackTom AI · Accepted Answer

In time series analysis, the term stationarity refers to properties of the process that do not depend on the time at which you observe the series. 
Option 1: True — If we say stationarity means the mean and variance are changing over time, this misstates the concept. A stationary process has a constant mean over time and a constant variance over time. If the mean or variance changes with time, the process is non-stationary in the strict sense. 
Option 2: False — This statement aligns with the standard definition of stationarity. A weakly stationary process has constant mean and variance (and constant autocovariance structure that depends only on lags, not on time). If either the mean or the variance changes with time, or if the autocovariance depends on time, that indicates non-stationarity. 
Additional nuance: In some contexts, people refer to “trend-stationary” or “difference-stationary” processes, where after removing a trend or applying differencing, the series can become stationary. However, the essential criterion remains that strict or weak stationarity requires time-invariant mean and variance (and a time-invariant covariances). If the statement claims that stationarity means changing mean and variance, it contradicts the fundamental definition, and is therefore incorrect.

In time series analysis, stationarity means the mean and variance are changing over time

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