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I'm learning time series analysis and I'm a little confused as to how the auto-covariance of a time series dataset works.

We define the auto-cov function of a time series as: $\gamma(h) = E[(Y_t - u_t)(Y_s - u_s)] \ \forall \ h = t-s $

Here t and s are different time indeces for a dataset. But this is where I'm confused since aren't the values at t and s deterministic? For example if we're considering Google stock price for the past 2 years, then on day 30 (t) and day 75 (s) Google's stock price had only 1 value if we're using the closing value of of the stock price for the data set. So I'm confused as to where the distribution is in these time intervals of a time series to compute the auto-covariance function?

mathcomp guy
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    You might want to consider the case where the difference is fixed (h=t-s), and average over all data with that difference. For example, you looked at data from day 75 and day 30. How about day 76 and day 31 etc. The difference is 75-30=45 and 76-31=45 in both cases. I hope this helps. – ad2004 Jun 04 '20 at 00:57
  • Ah that is helpful thanks – mathcomp guy Jun 04 '20 at 01:58

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