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I’m working on an exercise to check if a difference between two correlation coefficients is significant. However, I have certain doubts after I did some reading about the topic.

My data consists of 2 sets of daily returns on stock indices (relative changes) for a period of about 10 years. There is an event, approximately in the middle of the whole period, which may influence the correlation between the two sets of data. Obviously, the event splits my dataset in two nonequal subsets. I have to check if the difference between the correlation coefficients is statistically significantly. My doubts and questions are as follows:

  1. Is it correct to use the Person Product Moment Correlation Coefficients for my data? I am asking because I read somewhere that the coefficient applies better to cross-sectional data rather to time series. Additionally, I am confused because for instance in Markowitz’s portfolios the coefficient is used despite that fact.
  2. Are there other measures which may be a better option for my case or can I use Person Correlation Coefficients, because even if they are not the best choice, they produce meaningful results? I have seen some works which use them for this kind of data, but I do not know if they were correct.

  3. I plan to use Fisher r-to-z transformation in order to check the significance of the difference between the coefficients. However, I read somewhere that the test should use random sample and it is used with cross-sectional data. Can I use this test to solve my problem?

  4. Do I have to check for the normality of returns for each subset of data in order to apply aforementioned test?
  5. And lastly, should I worry about spurious correlation? Should I transform the data or run some additional tests?

Thank you in advance for your help.

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