Some questions about intraday returns and volatility figures. It is with the objective of sense checking.
Firstly, for Security A, I am calculating the five minute interval return numbers over 29500 intervals. You can see below some of the results.
Secondly, for another security, I am calculating the Parkinson volatility numbers using five minute intervals. I use the following Parkinson volatility formula
I first calculate the parkinson numbers per each day and take the average of the days over 365 days.
Return Numbers for Security A at 5 minute intervals R_t(%) x 10^2 R_t(%) |R_t| (%) |R_t| (%) R_t^2(%) R_t^2(%) Mean Standard Deviation Mean Standard Deviation Mean Standard Deviation S -0.0083 0.1166 0.0737 0.0903 0.0001 0.0007
Volatility Numbers for Security B at 5 minute intervals
*calculated per day Average Vol (%) Std Dev Minimum (%) Maximum (%) 0.0737582 0.0312347 0.0290989 0.2561527
1) Do these return and volatility numbers make sense from a scale point of view? What source can guide us as to the stylized facts and expected scale of intraday return /volatility figures? Obviously, this will assure whether one's estimations are within reasonable ranges.The volatility numbers seem low to me.
2) The Parkinson volatility calculation as per the attached formula-what time horizon does it correspond to? daily? what is right frequency convention in the statement of intra-day volatility figures?
3) In terms of volatility conversion, how can one convert a 5 minute intraday volatility number into 30-min volatility numbers? Likewise into daily or annualized figures Your prompt response will be appreciated