Definition of Correlation

Definition: 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 s_x and x_y denote the standard devations of x and y. Let s_xy denote the covariance of x and y. The correlation coefficent between x and y, denoted sometimes r_xy, is defined by:

r_xy = s_xy / s_xs_y

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.

Terms related to Correlation:

• Standard devations
• Covariance
• Durbin-Watson Statistic

About.Com Resources on Correlation:

• [link url=http://economics.about.com/od/canada/a/exchange_ooil.htm]Is the Value of the Canadian Dollar related to Oil Prices?
• Does the Superbowl Predict Economic Growth?
• Will the Canadian Dollar Hit Par?

Writing a Term Paper? Here are a few starting points for research on Correlation:

Books on Correlation:

• Volatility and Correlation: The Perfect Hedger and the Fox
• Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences
• Volatility and Correlation: In the Pricing of Equity, FX and Interest-Rate Options

Journal Articles on Correlation:

• Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics
• Subjectivity and correlation in randomized strategies
• Increasing generalized correlation: a definition and some economic consequences