A: Terrific question! This would be a great topic for an econometrics project. If I were to study it as one, I'd start this way.
First we need some data. For Canadian Data, a good list of resources is available at "Where can I get data on the Canadian economy?". I need two types of data - one on exchange rates and the other on oil prices.
To get the Canadian-American exchange rate I went to The PACIFIC Exchange Rate Service and choice "Canadian" as the base currency and "American" as the target currency. I chose to look at daily data from the time period January 1, 2002 to September 30, 2005. I then downloaded this into Excel format.
To get U.S. dollar oil price data I went to the U.S. Energy Information Administration and downloaded their Crude Oil Prices in Excel format.
In order to use both data sets, I needed to put them on the same Excel page, lined up the start and end dates, and delete any missing data where I had only the price of oil and not the exchange rate, or vice versa. When I finished that, I had 917 daily entries, with the date in Column A, the price of oil in column B, and the exchange rate in column C. A typical entry should look like:
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Dec 13, 2004 41.06 0.81374
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Two random variables are positively correlated if high values of one are
likely to be associated with high values of the other. They are negatively
correlated if high values of one are likely to be associated with low values
of the other.
Formally, a correlation coefficient is defined between the two random
variables (x and y, here). Let sx and xy denote the
standard devations of x and y. Let sxy denote the
covariance of x and y. The correlation coefficent between x and y,
denoted sometimes rxy, is defined by:
rxy = sxy / sxsy
Correlation coefficients are between -1 and 1, inclusive, by definition. They are greater than zero for positive correlation and less than zero for negative correlations.(Econterms)
To calculate the correlation in Excel you use the command CORREL(B2:B918,C2:C918), where B2:B918 are the starting and ending points for the oil price data and C2:C918 are the starting and ending points for the Canadian dollar data.
Much to my surprise the correlation between oil prices and exchange rates for this period was not 0.3. It was 0.8477.
The 0.8477 figure is exceptionally high, denoting that there is a very, very strong positive relationship between movements in oil prices and movements in the value of the Canadian dollar.
In order to investigate the matter further, I decided to plot the data and run a regression. More on that on the next page.
