Howtosignalprocessing
- What is Ergodicity in time series?
- What makes a process ergodic?
- Can a non stationary process be ergodic?
- What does non ergodic mean?
What is Ergodicity in time series?
In general, the ergodicity of time series refers to the ergodicity of stationary processes, which means that the process averaged over time behaves identical to the process averaged over space.
What makes a process ergodic?
A random process for which ensemble averages are identical to time or spatial averages is said to be ergodic. (See Stochastic Process for definitions of averages.) Both types of averaging are acceptable ways of describing a random process.
Can a non stationary process be ergodic?
For an example of the opposite case (i.e., a random process that is ergodic but not stationary), consider a white noise process that is amplitude modulated by a deterministic square wave. The time average of of every sample function is equal to zero, as is the ensemble average over all time. So the process is ergodic.
What does non ergodic mean?
In a non-ergodic system, the individual, over time, does not get the average outcome of the group. This is what we saw in our gambling thought experiment. A way to identify an ergodic situation is to ask do I get the same result if I: look at one individual's trajectory across time.
