How to annualize intra-day volatility on minute data?

Question

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 1

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.

Answer 2

Intraday seasonality is a major factor in comparing volatility at different times of day. Most time series display significantly higher volatility in the morning EST than mid-day. For US exchange-traded products, volatility picks up again just before 4:00 PM EST. This is known as the u-shaped volatility pattern for exchange-traded products. A proper annualization, which puts minutely volatility at one time of day on the same scale as volatility at another time, would require that you take into account all the systematic variation in volatility as a function of time.

This effect is very well known and has been thoroughly researched and described in An Introduction to High Frequency Finance, an excellent textbook written by the Olsen group, which also sells analytics based on the research described in their book. Their chapters 5 and 6 deal explicitly with an approach to your issue.

FYI, this question is tangentially related to some previous questions, How to update an exponential moving average with missing values? and How to generate synthetic FX data for backtesting? This book is also on my favorite list of books to understand the math in quantitative finance.