hello,how would you adjust a 30 min return, calculated from the first 30 minutes of trading day, to a 1 hour return when you know that returns are not normally distributed with time (as it is higher in the first, say, 10 minutes due to obviously larger information inflow and levels off afterwards).thanx

Hi,with larger information, we should expect to have lower volatility. Therefore, it seems to me that for the first minutes of the process, the process is inhomogeneous and the volatility dependent on time. a)Try first to estimate from the autocorrelation the memory of the process with time. b) it sould decrease as the strting time inrease (i.e after 10 min, after 20 min) c) choose the starting time where the memory of the process start to be significantly lowerThe best guest of the one hour return would be only a trend adjustment.CheersXDan.

what i do now is calculate average 5 min returns for each interval -> i therefore scale down returns and make them comparable even if the initial intervals are of different length. makes sense to me and to previous academic literature. some references for people looking for similar stuff:"Scaling in stock market data: stable laws and beyond", Potters, Bouchaud "Autoregressive Conditional Duration: A New Model for Irregularily Spaced Trasaction Data", Engle , Russell"Consistent High-Precision Voaltility from igh Frequency Data", Corsi, Müller, Zumbach, Dacorogna ->Olson Papers"The Econometriccs of Ultra-High-Frequency Data", Engle"Variance Ratio Statistics and High Frequency Data : Testing for Changes in Intraday Volatility Patterns", Andersen, Bollerslev, Dasany other references or methods appreciated,f.