I want to investigate correlation between two financial indices that vary with time, one is S&P 500 stock index and the other is U.S. green municipal bond index. I do not want to use complicated functions, I want it as simple and effective as possible.
tank you for your kind help
Try cross-correlation. Best, D. Booth
BTW simple and effective don't always go together
I think that the most appropriate method is the cross-correlation function of the two time series S&P 500 and municipal bond index, i.e. their correlation coefficient as a function of the time lag.
As an example, I attach the excel file with two sets of data: data 1 and data 2 (columns b2: b22 and c2:c22)).
The overall correlation of these two sets at no shift (time lag 0) is -0.5.
However the cross-correlation as a function of time lag units (say, day or month, etc) reveals a high positive correlation starting at time unit 2 and continues approximately every 6 time units. Similarly for negative correlation.
You may try a similar analysis with your concrete data.
Kearl Pearson's correlation coefficient with the test of significance of the observed correlation coefficient can be one option.
So, go for computing Kearl Pearson's correlation coefficient from the data and apply t test (or equivalently F test) for testing the significance of the observed correlation coefficient.
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