In time series analysis, what does stationarity mean?

In time series analysis, what does stationarity mean?

• A. The autocorrelation is zero for all lags.
• B. Properties like mean and variance do not change over time.
• C. The series has constant variance but changing mean.
• D. The data are drawn from a stationary distribution with zero mean.

Answer: (B)

Stationarity means the statistical properties of a time series don’t change as time passes. In the common, practical sense, this means the mean stays the same, the variance stays the same, and the way observations relate to each other (the autocovariance) depends only on how far apart they are, not on when you look. That’s why the statement about mean and variance not changing over time is the best description. If the mean drifts or the variability grows or shrinks, the process is no longer stationary, because its basic behavior is changing over time. It helps to think of an example: a process where shocks have a consistent effect and the fluctuations around a constant level remain bounded is stationary. Conversely, a process with a changing average level or with volatility that grows over time would violate stationarity. As for the other descriptions: having zero autocorrelation at all lags isn’t required for stationarity (you can have nonzero but stable autocorrelations, like in AR processes). A constant variance with a changing mean fails because the distribution changes over time. Requiring the mean to be zero is unnecessary—the mean can be any constant value and the process remains stationary as long as it doesn’t drift.

Stationarity means the statistical properties of a time series don’t change as time passes. In the common, practical sense, this means the mean stays the same, the variance stays the same, and the way observations relate to each other (the autocovariance) depends only on how far apart they are, not on when you look.

That’s why the statement about mean and variance not changing over time is the best description. If the mean drifts or the variability grows or shrinks, the process is no longer stationary, because its basic behavior is changing over time.

It helps to think of an example: a process where shocks have a consistent effect and the fluctuations around a constant level remain bounded is stationary. Conversely, a process with a changing average level or with volatility that grows over time would violate stationarity.

As for the other descriptions: having zero autocorrelation at all lags isn’t required for stationarity (you can have nonzero but stable autocorrelations, like in AR processes). A constant variance with a changing mean fails because the distribution changes over time. Requiring the mean to be zero is unnecessary—the mean can be any constant value and the process remains stationary as long as it doesn’t drift.