Skewness, kurtosis and normality of a time series I have a sample size of $21$ with $496$ observations.Can I presume an approximately normal distribution,and use a $t$-test to compare the difference in means, and difference in various financial features (Financial data daily prices)? 
In addition, sometimes I get insignificant differences on the daily basis, however, if I annualize the mean and the standard error, it becomes highly significant, like a difference between two means per day is $0.10%$ at the end of the year using this formula it will be extremely huge $((1+R)^{240}))-1$, any converting the standard deviation by the formula $\sqrt{240}* SD_{daily}$.
First it was a typo yes, the difference in the daily return is 0.10%, then the data will be auto-correlated for sure, since the market regulations allows the price to fluctuate by 2% only per trading session so the pattern will be there, what I am doing is Mainly constructing indexes in the market, grouping the 21 stocks into two groups, 16 stocks and 5, and then I will be comparing the indexes returns, Sharpe ratio etc, so when I'm using t-test to check statistical difference as this formula (x1-x2) difference in means / SQRt(SE^2+SE^2) the results were not statistically significant but financially 0.10% per day will be at the end of the year 15-17% difference which is MASSIVE!!!!!
and I provided the statistics for the daily data  Kurtosis: the whole market (7.392221073) first group (6.344474009) second group (14.0065786) Skewness the whole market ,(0.930473559), first group    (1.173843213), second group(1.325395262).
So I'm actually taking the whole population which is only 21 firms in the emergent market, so in my research introduction chapter I have to talk about this issue so do you think I have to say by the  central limit theorem, I have more than 20 sample size, and I would use t-test for comparing, if not it is not acceptable,  tell me any other test for comparing the differences between the means and in details please.
Annual stats 
                            market        set1          set2 
Average Annual Return   0.182450075   0.344723515   0.149800603
Standard Deviation      0.134419078   0.202235211   0.138592387

per session stats      market   set1     set2 
Mean                    0.10%   0.18%   0.08%
Standard Deviation      1.05%   1.57%   1.08%

the conversion done by assuming 165.33 session per annum
 A: I'm afraid I don't know much about the analysis of financial features, so I'm limited in what I can tell you, but I can say some general things.  (@JDav sounds pretty authoritative, but I'm not qualified to evaluate it.)  


*

*In general, it doesn't matter if your data are normally distributed, only if your residuals are (which is explained here) this even true for a t-test.  

*No amount of data will turn a non-normal sample into a normally distributed one.  

*With respect to the validity of the t-test (more specifically its p-values), the question is whether the sampling distributions of the means, and the sampling distribution of their difference, is normally distributed.  With so much data, the central limit theorem is likely to cover you unless you have very heavy tails.  

*Given that your data are clustered / ordered in time, I doubt a t-test is appropriate.  You almost certainly need a multilevel / time-series model.  

A: Your formula( scaling by $\sqrt{240}$) works as long as R is close to zero. Both daily and yearly t-stat should be almost equal on that case, if not, that might be an indication of the poor approximation of the scaling formula (remember that it is based on a Taylor expansion at r=0).
Moreover, even if r is close to zero this formula assumes no autocorrelation, which is that your prices today are not correlated with your prices yesterday. Dependng on your data that could be a heavy assumption. To keep your analysis simple, you may try to stay on a daily basis horizon, this will avoid the poor approximation and the non autocorrelation issues.
Nevertheless it's also true that stock returns are well known for being better explained by non autocorrelated process. But this depends on your data and can be easily verified by calculating a regression $r_t=a+\rho r_{t-1}+u_t$ where $\rho$ would be significant in the presence of correlation (of course this can be generalized to higher orders).
