Testing for a t-distribution into how changes in share prices are distributed

[Key-J]

Hi!
I'm currently doing an investigation into how changes in share prices are distributed. I've collected some data, and have the end of day share prices for 20 different companies since 25th November 2002. I've taken the log of the ratio of the newer share to the previous share price and want to see how this data is distributed. So basically I have 1112 pieces of information and want to see if a distribution is followed.
In my research I have found two arguments; one that share price changes follow a normal distribution and the other that they follow a t-distribution,. I want to test for the existence if these two distributions in my data. How do I do it? :S For the t-distribution, do I need to calculate the degrees of freedom? Because I can't quite remember what to do.

Any help would be much appreciated.
Thanks!

[BradM]

Hello! Welcome to the Cove!

With 1100 data points, I would think the data would approximately represent a normal distribution.

When you say a normal distribution, are you saying the magnitude of the change in a year? I would think that you would pick a specific time-frame to compare all the stocks (month/week/year/10 year), as all of them will increase over the years.

For a rough estimate only, you can always perform a rough analysis of the data to see what the distribution looks like.

Is this anywhere near what you are formulating:

Null hypthosis:
Data follows a normal distribution
Alternative hypothesis
Data does not follow a normal distribution.

I'm curious: what is leading you towards performing a log transformation?

[Key-J]

Hey! Thank you! Thanks for your very quick response. The log transformation is preformed with a share price never being able to be negative.
In minitab I've produced a probability plot and the data fits normal quite well except there are quite a few anomolies at the extremes of the data.
Is it possible to test the data for the existense of a t-distribution using Minitab? In an article in a journal I've read they take a similar situation to what I have except they look at 17 companies and they calculate the Chi-squared results for the scaled t-distribution and the normal distribution for each company and show that the t-distribution is a better fit. Only they don't really explain how to calculate the chi-squared values, is this possible in Minitab?
Thanks again.

[Statistical Steven]

Originally Posted by Key-J

Hey! Thank you! Thanks for your very quick response. The log transformation is preformed with a share price never being able to be negative.
In minitab I've produced a probability plot and the data fits normal quite well except there are quite a few anomolies at the extremes of the data.
Is it possible to test the data for the existense of a t-distribution using Minitab? In an article in a journal I've read they take a similar situation to what I have except they look at 17 companies and they calculate the Chi-squared results for the scaled t-distribution and the normal distribution for each company and show that the t-distribution is a better fit. Only they don't really explain how to calculate the chi-squared values, is this possible in Minitab?
Thanks again.

The Chi-Square test is based on testing the (observed value - expected value)^2 dividied by the expected. Here is the link from the NIST handbook.
http://www.itl.nist.gov/div898/handb...on3/eda35f.htm

The t-distribution is asymptotically normal as n approaches infinity.