What is the Correlation Coefficient?

This is the definition from Financial Forecast Center (http://www.neatideas.com/cc.htm).

What is the Correlation Coefficient?

The correlation coefficient concept from statistics   is a measure of how well trends in the predicted values follow trends in the actual values in the past.  It is a measure of how well the predicted values from a forecast model "fit" with the real-life data.

The correlation coefficient is a number between 0 and 1.  If there is no relationship between the predicted values and the actual values the correlation coefficient is 0 or very low (the predicted values are no better than random numbers).  As the strength of the relationship between the predicted values and actual values increases so does the correlation coefficient.  A perfect fit gives a coefficient of 1.0.  Thus the higher the correlation coefficient the better.

For practical usage, you should know that:

1 - Means ideal coincidence between some data.

0 - No correlation. Two sets of data are not related.

-1 - This is anti-correlation, which means that the predicted values "mirror" the actual values (or one data set is the "mirror" for another one).

These are examples:

Positive correlation (=0.5); these two curved lines show the same price movement (most of the time). In other words, price goes up or down for both lines:

No correlation (0.07); these two curved lines show totally different movements (if one goes up, the other may go up or down and there is no regularity seen):

Negative correlation (=-0.4); we observe the "mirror" effect (when one curved line goes up, the other one goes down in most cases, and vice versa):

What correlation is good enough? The more the better. Usually, the models that we analyze provide 0.1-0.2 correlation. Sometimes it is more than that, but these results are not stable. To be sure that this result is not accidental, it is necessary to have a sufficient amount of price bars for calculating the correlation.

This table shows the sufficient amount of price bars for different correlation coefficients (Student's t-distribution):