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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?

I apologize if this question is too basic for some - I come from financial mathematics and my statistics knowledge is rather limited.

flag	asked Jan 1 2012 at 12:09 Grzenio 339●7

	I think you have much better chances of getting a good answer by posting to <stats.stackexchange.com/>; instead of here. – Angelo Jan 1 2012 at 12:50
	Ah thanks @Angelo, I didn't realise this other site existed! – Grzenio Jan 1 2012 at 13:54

Pierre · Accepted Answer · 2012-01-28 23:27:46Z UTC

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The Anderson-Darling test is considered one of the best tests for normality, I think.

answered Jan 28 2012 at 23:27

Pierre
128●5

Arthur B · Answer 2 · 2012-01-23 20:49:29Z UTC

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.

One of the main source of non-normality in financial time series is heteroskedasticity. Model a stochastic variance first, then work on the residuals.

Normality tests

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