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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?

wzbillings
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OLGJ
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    a spacing between data points, so $y_{t},y_{t+3}$ is an example where $h=3$ – David Veitch Oct 20 '22 at 15:21
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    Either you are not correctly transcribing what the lecture slides say, or there are typos in the slides. Your equation should read $$P(y_{t_1}, y_{t_2}, \ldots, y_{t_n}) = Py_{t_1+h}, y_{t_2+h}, \ldots, y_{t_n+h})$$ – Dilip Sarwate Oct 20 '22 at 15:49
  • This is explained and used in my post at https://stats.stackexchange.com/a/566582/919. – whuber Oct 20 '22 at 19:13

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$h$ 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.

wzbillings
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