* Background *
Currently working on a year long Masters thesis in Finance. My
supervisors nor any of the econometrics professors were able to help
me with this question. It will require knowledge of
econometrics/statistics to answer, rather than a web search.
* Question *
I have 30 years of monthly time series returns data for stockmarket
indices of two countries, a total of 360 observations. Breaking the
data into two samples, 1972-1987, and 1988-2002 I find - as I expected
a priori - that the sample correlation between the markets is higher
in the second period.
I want to implement a test of whether the difference between the
sample correlation coefficients is statistically significant. If the
difference between two sample correlations followed some known
distribution, I could do this myself but I don't know if it does.
As my supervisor said "This sounds like a standard sort of a problem,
surely there must be a test for that." But I asked around and no-one
seemed to know. It?s a little bit different to the usual, as the
econometrics of testing a correlation coefficient are not like testing
a slope coefficient.
I have an econometrics major but only at undergraduate level so an
answer I can understand understandable would be an advantageous -
though not essential as I have my supervisors to help interpret any
answer, and also another Professor I have already spoken to with a PhD
in financial statistics and option modelling. I have econometrics
text books. Unfortunately, he could only find a test for whether a
single sample correlation was zero. That's not really appropriate
here ? as I am testing whether the difference between two sample
correlation coefficients is zero. I?m not at all confident that the
distribution of a single sample correlation coefficient under the null
that the population coefficient equals zero, is therefore appropriate.
You can assume
A1) the returns from the two countries are jointly normally
distributed, with equal variance for all countries and time periods
A2) the true population correlation stays the same within each of the
sample periods, except for the single change at some known date ? in
this case Jan 1988.
Thanks in advance.
* Extras *
NOT required to satisfactorily answer this question. If you have an
answer to the base question - please do post it.
Comments on any of these issues will be appreciated and remunerated by
an extra tip. The answerer can also post anything further which
springs to mind later as a Clarification of Answer if they wish ? I
will wait a few days after an answer is posted before rating it and
deciding on a tip.
1) I actually want to use this test more than once, applying it
separately to several pairs of countries. While most have similar
sample variances, and i'm willing to assume therefore identical
population variances, a couple are a bit different. The lowest sample
standard deviation was about 4% per month, and the highest % per
month. So a test relying on the assumption of identical variance
might not be quite spot on for these countries.
2) Similarly to above, one countries sample variance decreased quite a
bit between the two periods.
3) In practice, I have found that across the top 5 countries, the
correlation increases in all 12 of them. At the moment I am thinking
I probably will have to just test consider each "pairing"
individually. I doubt very much there is a way of getting an
increased power of test by aggregating the data, though I would be
very interested to know if there is.
4) I might leave out the final quarter of 1987 from my analysis, as
it's a bit of an outlier due to the October 1987 stockmarket crash and
the reverbarations that followed. I don't think this should
invalidate my test or be problematic, just reduce the sample size
marginally.
5) Perhaps there are other ways of testing whether markets tend to
move together rather than correlation.
Thank you! |
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