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Is this procedure correct? $$E[y_{t-1}\epsilon_t]$$ $$= E[E[y_{t-1}\epsilon_t|y_{t-1}]]$$ $$=E[y_{t-1}E[\epsilon_t|y_{t-1}]]$$

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    $\begingroup$ A time index for the expectations operator would help. $\endgroup$
    – BrsG
    Jul 7, 2022 at 17:05
  • $\begingroup$ Unfortunately I don’t know it. $\endgroup$ Jul 8, 2022 at 8:02

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It appears correct to me. The relevant Wikipedia page is here, https://en.wikipedia.org/wiki/Law_of_total_expectation

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