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tiko
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Posts: 217
Joined: March 7th, 2003, 11:11 am

Statistics: Distributions Choices

July 22nd, 2003, 12:49 pm

Hi,I was wondering about the choice of distribution that ones might make when for example modelling: 1-The beta2-Correlation3-Variance of volatilityHaving two sets of beta, correlation and volatility, i want to test hypothesis whether or not each variable is statistically different from the other. I believe that we use the F distribution to test whether variance 1 is statiscally different from the variance 2, is that correct??? what about correlation and beta, which distributions do i use, can i assume that they are normally distributed???Best regards, and thx a lot for help
Last edited by tiko on July 21st, 2003, 10:00 pm, edited 1 time in total.
 
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WaaghBakri
Posts: 732
Joined: March 21st, 2002, 4:07 am

Statistics: Distributions Choices

July 22nd, 2003, 2:49 pm

What is distribution of the underlying data? Isn't the choice & distribution of the estimators dependent on the nature of the underlying data? Curious ....
 
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WaaghBakri
Posts: 732
Joined: March 21st, 2002, 4:07 am

Statistics: Distributions Choices

July 22nd, 2003, 4:07 pm

The sample covariance, s_xy = (1/[N-1]) * sum_{i=1,N} (x_i - m_x)*(y_i - m_y)If x & y are normally distributed then the sample correlation is a ML estimator and given by r = s_xy / (s_x * s_y)where all the above statistics are sample statistics. m_x & m_y the sample mean. As it stands the sample correlation, r, is asymmetric, and the following transformation will make it approximately normal, z = 0.5 * ln( [ 1+ r ] / [ 1 - r ] )with mean & variance, m_z = 0.5 * ln( [ 1+ r_ex ] / [ 1 - r_ex ] ) + r_ex / (2*[N-1])[ s_z ]^2 = 1 / [N-3]where r_ex is the "exact" correlation.
 
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tiko
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Posts: 217
Joined: March 7th, 2003, 11:11 am

Statistics: Distributions Choices

July 22nd, 2003, 5:12 pm

Hi thx a lot WaaghBakri for replying back,what i meant is that i have measured the beta of a certian share X and it was equivalent to â=0.15, volatility level 36.6%, and N=180. Can i test whether or not the beta of that share is not statistically different from zero?Ho: beta=0 and H1 : beta<>0. Using a the confidence intervals in order to test the hypothesis using a alpha= 5%, 0-(1.96*(0.366/SQRT(180)))< 0.15< 0+(1.96*(0.366/SQRT(180))), -0.0535 < 0.15< 0.0535, therefore, we reject the null hypothesis, and accept the alternate hypothesis.Is that correct??
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