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I'm recently been trying to understand time series better,and would really appreciate if someone can show me this:

I found this online under a lecture slide by J. McJames of Portland Univ., and I was curious why (how) this is true. Where gamma-hat is the biased ACVF Where gamma-hat is the biased ACVF.

The slide asked the students to show the equation is true for a fixed h ≥ 0. It provided a hint: enter image description here

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  • $\begingroup$ Could you please define your variables or copy-paste relevant sections from the lecture? I'm also a little unsure why you provided the second image; that's just the definition of variance and doesn't provide any additional information. $\endgroup$
    – Chris C
    Commented Dec 1, 2015 at 2:49
  • $\begingroup$ I found another slide with the same equation. It appears gamma-hat is the based autocovariance function, where h is the lag operator. I'm not sure if the updated hint provides additional help, bc I don't know the problem 2 it's referencing. However, it sounds like a standard proof question, and I'm really curious to see why this is the case. $\endgroup$
    – pikachumonster
    Commented Dec 1, 2015 at 3:09

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