The below PDF is the one I am working through from a conceptual perspective, but I don't understand enough about matrix notation (or advanced calculus in general) to follow the logic the authors use to find their values to solve the equations on pages 7 and 8. I will attempt to provide context below; my main question is if the matrices on page 8 follow a certain notation that I can learn/research more.
Both n, the day of the week, and t, the hour of the day, are defining characteristics of each value x.
X0 = The increasing set of absolute value deviations from the linear regression for all values x
X1 = The set containing the cumulative sum of the deviations in X0
Z = The set containing the average between each value in set X1
Sets Y and Z are intended to help predict the next value x. In the below first order differential equation, "a" is a function or value describing the increasing speed of numbers in set X, and "u" is an endogenous control coefficient in system.
(dY/dt) + aY = u
I do not know/fully understand the below matrices and notation provided to help determine "a" and "u".
U = [a, u] ^T
U = (B^T B)^-1 B^T Y
Y is a (n-1)x1 matrix and B is a (n-1)x2 matrix.
The values in Y are X(2), X(3)...X(n) in a column.
The values in B are -Z(2), -Z(3)...-Z(n) in the left column and all 1s in the right column.
In addition, there is an unknown value k that appears in the predictive equations; is this a standard constant/coefficient I'm not familiar with?
Thank you very much for any advice/input.