Normality tests - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T14:45:39Z http://mathoverflow.net/feeds/question/84682 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/84682/normality-tests Normality tests Grzenio 2012-01-01T12:09:34Z 2012-01-28T23:27:46Z <p>We have financial some data (500-1000 samples), which is not normally distributed (well known fact from the literature). I have some ideas to do parametric transformations of this data (using some other data) to produce "adjusted" series. My goal is to find a transformation that makes the series normally distributed (with mean 0 and std deviation 1). What is the most appropriate statistic and corresponding test to optimize my parameters and determine if the outcome can be considered normally distributed?</p> <p>I apologize if this question is too basic for some - I come from financial mathematics and my statistics knowledge is rather limited.</p> http://mathoverflow.net/questions/84682/normality-tests/86485#86485 Answer by Arthur B for Normality tests Arthur B 2012-01-23T20:49:29Z 2012-01-23T20:49:29Z <p>Sort all your data points in increasing value. If you have $n$ point (1 to $n$), transform point $i$ into $\mathcal{N}^{-1}\left( \frac{i-1/2}{n} \right)$. It does exactly what you want but it's dumb because it's not going to have a lot of predictive power. </p> <p>One of the main source of non-normality in financial time series is heteroskedasticity. Model a stochastic variance first, then work on the residuals. </p> http://mathoverflow.net/questions/84682/normality-tests/86934#86934 Answer by Pierre for Normality tests Pierre 2012-01-28T23:27:46Z 2012-01-28T23:27:46Z <p>The Anderson-Darling test is considered one of the best tests for normality, I think.</p>