Suppose that Y and X are two time-series, and that the slope function varies smoothly with time. I want to smooth only in the time dimension. So I guess that, for each value of t, I need to fit locally a simple linear regression of Y on X, using only data points around the time point of interest t0, giving weights to the observations, Xt, according to how close in time they are. So, if I understand correcly, my bandwidth is in this case a proportion of the time index, rather than in the scale of the explanatory variable X. And weights are computed using the time vector instead of X (i.e. (t - t0)/h instead of (x - x0)/h). Is it correct?