normal distribution test

i have historic data (daily) of 30 stock from 250 day (i make 30x250 matrix from it), now i want to test whether this data is normally distributed or not, how to do this? and if its not normally distributed how to normalize it?

Answer 1

[Richard Willey]

Statistics Toolbox offers a number of hypothesis tests that you can use to (formally) test whether your data is normally distributed. With this said and done, I strongly recommend starting with some visualization techniques.

Functions like "normplot" will provide you with a much better feel for the nature of your data and why it does/does not match a normal distribution.

[eri]

i know you have good intentions, but your answer and recommendation is confusing me, sorry

right now i want to know how to test data(in the form of matrix) distribution normality and normalize it(if not normal) using matlab

thanks

[Richard Willey]

Probability plots are a very standard way to check whether data is normally distributed. Arguably, these charts provide better information than a formal hypothesis tests.

The following code might prove helpful

% Generate a vector of 500 normally distributed random numbers with mean =

% 10 and standard deviation =5

foo = 10 + 5*randn(500, 1);

% Use a normplot to see whether the sample appears to be normally

% distributed

normplot(foo)

figure

% Generate a vector of 500 random numbers drawn from a gamma distribution

% with aplha = 5 and beta = 3

bar = gamrnd(5,3, 500,1)

% Use a normplot to see whether the sample appears to be normally

% distributed

normplot(bar)

Answer 2

[the cyclist]

Do you have access to the Statistics Toolbox? There are at least two normality tests included there: jbtest() and lillietest().

I don't have the Finance Toolbox, but I am guessing that there may be something there as well.

You can type "docsearch normality" to poke around in the documentation.

I am not sure what you mean by normalizing it, if it is not normally distributed. Sounds like a dangerous game. Maybe you could provide some more details on what you are trying to do.

[eri]

ok, i am going to try that

what i try to do is make a portfolio out of these data

[eri]

can you give me an example on how to do this?

[Richard Willey]

MathWorks provides dedicated functions for portfolio optimization. The best content that I am aware of is the following downloads from MATLAB Central. (There is an associated webinar that you can view to get an introduction to the techniques)

http://www.mathworks.com/matlabcentral/fileexchange/31290-using-matlab-to-optimize-portfolios-with-financial-toolbox

Answer 3

[bym]

for normalization you can try the Box-Cox transformation

or the Johnson transformation

or just fit it with a non-normal distribution

[eri]

can you give the detail of how to use them in matlab?

Answer 4

[Léon]

Are you talking about prices or returns? Or even something different from that? Regarding returns you should be aware of a leptokurtic distribution of your data. Anyway I wouldn't rely on a normal distribution, but I would definitely use some bootstrapping technique to derive an accurate estimator for the moments.

[eri]

price

Answer 5

[Linda Lin]

kstest