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Technical Studies Reference


Covariance

This study calculates and displays the Covariance of the data specified by the Input Array 1 and Input Array 2 Inputs.

Let \(X^{(1)}\) and \(X^{(2)}\) be random variables denoting Input Array 1 and Input Array 2, respectively, and let \(X^{(1)}_t\) and \(X^{(2)}_t\) be their respective values at Index \(t\). Let the Input Length be denoted as \(n\). Then we denote the Covariance at Index \(t\) for the given Inputs as \(Cov_t\left(X^{(1)}, X^{(2)}, n\right)\). We compute it in terms of Simple Moving Averages as follows.

\(\displaystyle{Cov_t\left(X^{(1)}, X^{(2)}, n\right) = SMA_t\left(X^{(1)}X^{(2)},n\right) - SMA_t\left(X^{(1)},n\right)SMA_t\left(X^{(2)},n\right)}\)

This is displayed for all \(t \geq n\).

Note that if \(X^{(2)} = X^{(1)}\), we have \(Cov_t\left(X^{(1)}, X^{(1)}, n\right) = Var_t\left(X^{(1)}, n\right)\), which is the Variance of \(X^{(1)}\).

Inputs

Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through File >> Open Spreadsheet.

Covariance.483.scss


*Last modified Wednesday, 10th February, 2021.