I am wondering which method makes more sense when computing log returns. I am trying to compute log returns for realized variance, and I have the opening and closing prices for every minute.
Since the log return is defined as
$$r_{t+1} = \ln \left(\frac{p_{t+1}}{p_t} \right)$$
should I take the average of the open and closing prices at every point as use that as $p_t$?
Or should I find $r_{t+1}$ at every $t$ by assuming $p_{t+1}$ = closing price and $p_t$ = opening price?