Spearman Rank Correlation Coefficient

I'm pleased to introduce this script in honor of the new array functions introduced to PineScript version 4.0. This update is a long time coming and opens the door to amazing scripting possibilities!

Definition

Named after Charles Spearman and denoted by the Greek letter ‘ρ’ (rho), the Spearman rank correlation coefficient is the nonparametric version of the Pearson correlation coefficient. Use the Spearman rank correlation when you have two ranked variables, and you want to see whether the two variables covary. That is, as one variable increases/decreases, the other variable tends to increase/decrease respectively.

It is best used to discover if two variables (and in this first version of the indicator, two ticker symbols) increase and decrease together. There are advantages to using this version of correlation vs. the Pearson R.

Interpretation

The value oscillates between +1 and -1.

• A value of +1 means the two variables are perfectly correlated, that is they are increasing and decreasing together in perfect harmony.
  
• A value of -1 means the two variables exhibit a perfect negative correlation, that is they increase and decrease oppositely.
  
• A value of zero means the two variables are not correlated at all (noise).
  

Versionsinformation:

• Removed the 'lookahead = true' parameter from the security function, not needed.
  
• Fixed logic of duplicates to be more straightforward.
  

Versionsinformation:

• Fixed issue with hLines.
  

Versionsinformation:

• Updated symbol input to input.symbol.
  

Versionsinformation:

• Fixed -1 index out of bounds exception.
  

Versionsinformation:

• Removed index out of bound corner cases.
  

Versionsinformation:

• Added primary source option. The source input that is correlated to the selected symbol's closing price. By default the close of the chart's symbol is correlated against the close of the selected symbol below, however an alternate source can be used to correlated against the selected symbol, such as an indicator on the chart.