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I am working on a commodity-exchange rate model as part of my thesis. My dependent variable is log of first difference of exchange rate of Colombia and my independent variable is log of first difference of crude petroleum price.

I have daily data for last 20 years for both the variable. I am interested in looking whether the relationship (i.e. the effect of crude petroleum prices on Colombia's exchange rate) between the two variables changes over time.

So let say i want to check whether effect of crude petroleum prices on Colombia's exchange rate in the last 5 years ( 2012-2017) is different from that in 2007-2012.

I was thinking of creating dummy variables for 5 years ( 1 if the data is from 2012-2017, 0 otherwise) and then creating an interaction variable of the dummy and crude petroleum prices.

I am not sure whether this is the right thing to do. also can i use any other model or test for the same. Any advice is appreciated. Please let me know if my question is unclear. I can try to modify it.

Thanks in advance.

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One way is to check their (linear) dependency with Pearson's correlation coefficient. If you rather want to check for sign dependency, you can use Spearman's correlation coefficient.

You could for example take the yearly data, calculate the correlation coefficient between the two data sets for every year and then check, whether the coefficient changed substantially.
Before comparing the values, I would firstly test for their significance, though, to test whether there is any dependency to speak of.

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