Given a set of K independent variables
X = (x1, x2, ..., xk) and a dependent variables
y, I try to run the step-wise regression models to find the best set of variables to describe
y. The length of total data points is
n, so the size of
n x 1, while that of
n x k. For example, the best set of variables could be
x1, x3, x6 if
k = 10, so that model could be
y = 0.25 * x1 + 0.30 * x3 + 0.50 * x6 + e.
While the model works using the full data points
(n), I sometimes want to look at how
y is related to the independent variables in different subset of times, because during a sub-period,
x1, x3, x6 may not be the best model. For example, let
n = 60, so the first date is Sept 2015 and the last date is Aug 2020. I want to know if the best set of factors changes during, say Sept 2015 to Aug 2018 or Aug 2018 to Aug 2020.
I want to know what algorithms are out there for this kind of problem.