gives conditions for the process proc to be weakly stationary.


  • Weakly stationary processes are also known as wide-sense stationary or covariance stationary.
  • A random process proc is weakly stationary if its mean function is independent of time, and its covariance function is independent of time translation.


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Basic Examples  (3)

Check if a process is weakly stationary:

Check if an autoregressive time series is weakly stationary:

Generate conditions for a time series to be weakly stationary:

Scope  (6)

Check if an ARProcess is weakly stationary:

Check if the mean function is constant in time:

Check if the covariance function is a function of time difference:

Compare covariance functions of stationary and nonstationary OrnsteinUhlenbeckProcess:

Visualize conditions for an ARProcess to be weakly stationary:

For three parameters:

Find a weakly stationary ARProcess:


Some processes known to be non-weakly stationary:

Some known weakly stationary processes:

Properties & Relations  (4)

Every MAProcess without fixed initial conditions is weakly stationary:

Time series processes with fixed initial conditions are not weakly stationary:

The conditions for an ARMAProcess to be weakly stationary depend only on the autoregressive parameters:

ARIMAProcess may be weakly stationary:

Introduced in 2012