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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?

Please also point me to an implementation, ideally in C/C++ or java.

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Your transformation would need to be a bit weird in that it would need to pull the tails in -- preferably in a smooth way. But I'm not convinced of the advantage. What are you doing that you think you need a normal distribution? – Patrick Burns Jan 1 '12 at 16:02
Your question leaves me unclear. You say you have financial data and refer to them as a "series". Are you doing time series analysis, and want a procedure and test to achieve stationarity? That's not quite the same as what you seem to be asking, and while you would need to get a stationary time series, as @PatrickBurns notes, it wouldn't necessarily need to be normally distributed. – gung Jan 1 '12 at 22:09

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It appears that you are just asking for a test for normality. If so, Shapiro-Wilk is hard to beat. This is not, however, the easiest test in the pantheon to implement.

Why not just use R? The shapiro.test function will do the work for you.

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the original poster is asking about how to transform data to normality, not how to test for normality. – Macro Jan 1 '12 at 22:41
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@Macro - "What is the most appropriate statistic and corresponding test to optimize my parameters and determine if the outcome can be considered normally distributed?" This isn't quite asking how to do the transform, it's instead asking how to evaluate whether the transform is effective, i.e., (in this case) a statistic and corresponding test for normality. – jbowman Jan 2 '12 at 1:12
I don't know R :( And I have to do quite a lot of other computations in this program. – Grzenio Jan 2 '12 at 15:04
@Grzenio - I'll try to pull something together for you later today, probably in C/C++. – jbowman Jan 2 '12 at 15:50

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