# a simpler test for normality given skewness, kurtosis and autocorrelation and size of time series

I typically do a JB (Jarque Bera) test and DW (Durbin Watson) tests for check for normality given skewness, kurtosis and autocorrelation of the data. However this requires a CHI distribution table lookup and some calculation. I was wondering if there is a simple less accurate test that I can do on the data to check if it is normal or not?

Secondly How do I numerically test for I.I.D ?

There are simple visual tests for normality and i.i.d.

To test for nomality, simply look at the distribution of the observations and overlay the normal density function as in the following chart:

The blue line represents the normal distribution. The black bars are from the histogram representing the empirical distribution. Clearly the data is leptokurtotic is skewed to the right.

To test whether the data is i.i.d., simply partition the data set into different periods and plot the frequency distribution:

Notice the distribution has shifted from Period 1 to Period 2 -- therefore this data is not i.i.d.

• To visually compare distributions, it is often easier (for the untrained eye) to look at the quantile-quantile plots: the sample data versus a gaussian distribution to test for normality, the first half of the sample versus the second half to test if the distributions are identical. Mar 22 '12 at 1:06
• True - a comparison of the univariate statistics as you suggest would be the simplest way in my view Mar 22 '12 at 1:08
• I do the Q-Q plot for visual testing. But I was asking for a numerical routine which is simpler than JB test. Actually I found something here wilmott.com/messageview.cfm?catid=34&threadid=79342. A simpler test. Thanks, nice charts btw! Mar 22 '12 at 1:54