Tamino favors LASSO LOESS and piecewise linear models. I favor splines, especially penalized smoothing splines via the R package pspline, using generalized cross validation to set the smoothing parameter. Tamino looks for breaks in the piecewise linear case to check for and test for significant changes. I use the first and higher derivatives of the spline.

Both methods are sound and good.

I don’t know how you might use a random forest regression for this purpose, but I bet there is a way. I doubt it is as good, though.