What is h in a stochastic process $P(y_{t1+h}, y_{tn+h})$? I am revising lecture slides and came accross this definition but it lacks any further explanation:

Def:A stochastic process ${y_t}_t>=1$ is strictly stationary if for all $t_1, ..., t_n$ and all $h>=0$; $P(y_{t1},...,y_{tn}) = P(y_{t1+h}, \ldots, y_{tn+h})$

What is h here?

$h$ is a number greater than zero.
But conceptually, it's the amount of time that you shift your time series by. The idea this definition is trying to convey is that if the process is stationary, the joint distribution doesn't change if you shift the set of times that you have all by the same amount. So if you have times $\{1, 2, 3\}$, you'd get the same joint distribution as if you had $\{2, 3, 4\}$ or $\{3, 4, 5\}$ or $\{100001, 100002, 100003\}$, etc.
