Covariance stationary came up in my last post. That made me think maybe it is time to talk a little more about stochastic processes. In this post, I am going to briefly talk about Stationary processes.
Strict Stationarity
We know that i.i.d. random variables have same probability distributions. We can write such a random variable as:
Xi ~ Fx where Fx denotes probability distribution function and Xi denotes ith normal random variable.
Similarly, in a strictly stationary process,
Strict Stationarity
We know that i.i.d. random variables have same probability distributions. We can write such a random variable as:
Xi ~ Fx where Fx denotes probability distribution function and Xi denotes ith normal random variable.
Similarly, in a strictly stationary process,
- All random variables have same marginal distribution.
- Joint distribution of random variables is time invariant.
- The above two points imply, they all have the same mean and variance.
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