For this alpha: from any data point such D_i on, we take the last ten data points (e.g. 10 days) from D_i-10 to D_i-1, and do the calculation with rank(D.Open)_i and rank(D.Volume)_i, and the result is a single value. As the data point moves, we will have an array (list) of corrections.

For this alpha: from any data point such D_i on, we take the last ten data points (e.g. 10 days) from D_i-10 to D_i-1, and do the calculation with rank(D.Open)_i and rank(D.Volume)_i, and the result is a single value. As the data point moves, we will have an array (list) of corrections.

"Cross sectional" just means each part of the calculation using data overlapping with each other. A common name for it will be "rolling window" of a data frame.