equities - Can Gaussianity of returns depend on the time frame?

I would be interested in knowing if the fact that returns are Gaussian is disproved on all time frames, or if, for example, the 5 minute intra-day time frame could exhibits Gaussian returns assuming there are no micro-structure issues (low volume).

More generally is there any relationship between the time frame of equity returns and their generating distribution? Any known research in this direction?

Answer

My main reference will be "Dan Xu, Christian Beck - Transition from lognormal to chi-square superstatistics for financial time series"

Non-equilibrium statistical mechanics (more specifically, superstatistics) gives some ideas of explaining the relation between time frame and its distribution: "...to regard the time series as a superposition of local Gaussian process weighted with a process of a slowly changing variance parameter"

In their article, the authors found out empirically that: "Chi-square superstatistics appears to best suitable for daily price change (assuming independent variation of volatility parameter in each interval), whereas on much smaller time scales of minutes, lognormal superstatistics seems preferrable"

There are couples of related articles on this topic:

1. 
   

   M. Ausloos and K. Ivanova - Dynamical model and nonextensive statistical mechanics of a market index on large time windows

   
   


2. 
   

   Katz, Y.A.; Tian, L. - Superstatistical fluctuations in time series of leverage returns

   
   


3. 
   

   S.M.D. Queirós and C. Tsallis - On the connection between financial processes with stochastic volatility and nonextensive statistical mechanics

   
   


4. 
   
   

   C. Becka, E.G.D. Cohen - Superstatistics

   
   

I'm not expert in this field, but hope the idea may help.