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.
Examplesopen allclose all
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:
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: