I have a data set of stock returns. I am considering the correlation between mean return and volatility within different hours. I want to compare volatility structures across different hours.
e.g: Is there any different in the correlation structure between 1-2 GMT and 2-3 GMT and 3-4 GMT.
Is there any statistical test to test this hypothesis?
For pair-wise comparison of Pearsonian correlation coefficients Fisher's Z-transformation based test can be used. The transformation reduces variability in the data. The distribution of the transformed test-statistic is an issue for small sample size. There are lot of discussions about this in standard text books.
Thank yo very much for the replies. There is another question. Is it necessary to test the Normality of series (X and Y) for the calculation of Pearson correlation coefficient. And can't we use Fisher's Z-transformation to compare Spearman Rank correlation coefficient.
If you have enough data then it is not necessary to check normality, since asymptotically (that means, for large sample size) the test-statistics has a normal distribution. The similar test and the distribution are applicable for Spearman also.
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