For computation of realized volatility, especially range based volatility, deal prices are commonly used. If Level I data available should the deals data still be used or another measures of spot price would be preferable(for example, mid-price)?
Such measures could diminish the impact of bid-ask spread, but what would be the consequences for the volatility measures? Would the assumptions of the process be violated or quite the opposite - the price process would become closer to theoretical one?
Assuming for the ranged based models, price follows Brownian motion with zero drift:
$dp_t = \sigma dW_t$, where $p = ln(P)$.
What would the better price measure for them? Does the answer change if we use different time windows( 1, 5, 30, 60 minutes)?