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I am doing some descriptive statistics of daily returns on stock indexes. I.e. if $P_1$ and $P_2$ are the levels of the index on day 1 and day 2, respectively, then $log_e (\frac{P_2}{P_1})$ is the return I'm using (completely standard in literature).

So the kurtosis is huge in some of these. I'm looking at about 15 years of daily data (so around $260 * 15$ time series observations)

                      means     sds     mins    maxs     skews     kurts
ARGENTINA          -0.00031 0.00965 -0.33647 0.13976 -15.17454 499.20532
AUSTRIA             0.00003 0.00640 -0.03845 0.04621   0.19614   2.36104
CZECH.REPUBLIC      0.00008 0.00800 -0.08289 0.05236  -0.16920   5.73205
FINLAND             0.00005 0.00639 -0.03845 0.04622   0.19038   2.37008
HUNGARY            -0.00019 0.00880 -0.06301 0.05208  -0.10580   4.20463
IRELAND             0.00003 0.00641 -0.03842 0.04621   0.18937   2.35043
ROMANIA            -0.00041 0.00789 -0.14877 0.09353  -1.73314  44.87401
SWEDEN              0.00004 0.00766 -0.03552 0.05537   0.22299   3.52373
UNITED.KINGDOM      0.00001 0.00587 -0.03918 0.04473  -0.03052   4.23236
                   -0.00007 0.00745 -0.09124 0.06405  -1.82381  63.20596
AUSTRALIA           0.00009 0.00861 -0.08831 0.06702  -0.74937  11.80784
CHINA              -0.00002 0.00072 -0.40623 0.02031   6.26896 175.49667
HONG.KONG           0.00000 0.00031 -0.00237 0.00627   2.73415  56.18331
INDIA              -0.00011 0.00336 -0.03613 0.03063  -0.22301  10.12893
INDONESIA          -0.00031 0.01672 -0.24295 0.19268  -2.09577  54.57710
JAPAN               0.00008 0.00709 -0.03563 0.06591   0.57126   5.16182
MALAYSIA           -0.00003 0.00861 -0.35694 0.13379 -16.48773 809.07665

My question is: Is there any problem?

I want to do extensive time series analysis over this data - OLS and Quantile regression analysis, and also Granger Causality.

Both my response (dependent) and predictor (regressor) will have this property of gigantic kurtosis. So i'll have these return processes on either side of the regression equation. If the non-normality spills over into the disturbances that will only make my standard errors high variance right?

(Perhaps I need a skewness robust bootstrap?)

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1) You may want to move this to the quant.stackexchange.com site. 2) What do you mean by problem? There is a whole literature on the impact of outliers on moments. It can often be more of an art than a science. – John Aug 18 '12 at 5:20
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"Is there any problem?" is too vague. What do you want to do with these data? Your huge kurtoses are associated with huge left skew. Since log(p2/p1) = log p2 - log p1, a huge left skew indicates that there were a few times when this was very low, that is, p1 much higher than p2, compared to the usual case. Could be a company going bankrupt or something like that. – Peter Flom Aug 18 '12 at 5:35
Sorry about this - I've amended my OP. – user13253 Aug 18 '12 at 5:44
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log-returns are typically skewed and heavy tailed. For this reasons it is preferred to consider flexible distributions that can capture this behaviour. See for example 1 and 2. – user10525 Aug 18 '12 at 10:45
Nice! \phantom{ } – user13253 Aug 18 '12 at 11:41

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