# Correlation between non normally distributed variables

#### lunamaths

##### New Member
Apologies if any of the following description doesn't sound right as I'm fairly new to this subject. I'm working on a project which involves looking at the correlation between certain financial asset prices. My data set consists of random variables, a set of bond prices recorded over a specified time period but not necessarily recorded at equal increments of time. The size of the data set will vary but it is likely to remain relatively small (<100). The underlying bond prices are distributed with fat tails and hence a normal distribution is not appropriate. This means that most of the available measures such as Pearson Correlation and analysis such as ANOVA cannot be used. Thus, I have two questions-

1\ What is the best way to test the correlation between the prices within the data set? I am looking for a linear association. My initial thoughts would be to use the Spearman's Rank Correlation.

2\ How do I measure the correlation between my data set (bond prices) and then several other independent and non normally distributed variables representing other financial instruments?

Any help would be greatly appreciated!

Thanks

Rob

#### Karabiner

##### TS Contributor
The underlying bond prices are distributed with fat tails and hence a normal distribution is not appropriate. This means that most of the available measures such as Pearson Correlation and analysis such as ANOVA cannot be used. Thus, I have two questions-
Why do you think that? You can very well compute a Pearson correlation. Maybe the statistical test for the coefficient is not appropriate.
And ANOVA not assuming notmally distributed unconditzional variables. It assumes normally distributed residuals.

With kind regards

Karabiner

#### lunamaths

##### New Member
Thanks. The assumption that the underlying variables should be normally distributed to use the Pearson coefficient is cited in several different sources according my research. Are you saying that is incorrect or you will obtain a still correct but less accurate measure if you use it?