high frequency - How to annualize intra-day volatility on minute data?

I am trying to convert minute based volatility into annualized volatility in such a way that both are comparable. $Vol_{min} * \sqrt(t)$ does not seam to get them into the same scale if I annualize using daily data of minute data. What are the adjustments I can do to make volatility calculated using intra-day data more comparable to volatility calculated using daily data.

Answer

Let allow me to split your question in parts:

1. How to estimate volatility using high frequency data, see this question https://quant.stackexchange.com/a/3264/2299 and note that it rely on a stationnarity assumption of your PFP (Price Formation Process).


2. You will have to add the overnight volatility to the intraday one.


3. You can question the diffusive nature of the PFP, the Hawkes process are a convenient answer since they are not diffusive at small scales and asymptotically diffusive at larger ones.