Decreasing smoothing rule $$x_{t+1}:=a_t\,x_t + (1-a_t)\,x_{t-1}$$ where $$a_t:= b\,\left(1-\left(1-\frac{1}{t}\right)^q\right)$$ for some \(0.7\leq b\leq1\) and some \(5\leq q\leq10\).
smooth_dec(x, xt, b, qu)numeric value of the last value of the parameter.
numeric vector of past values of the parameter (time series).
smoothing parameter \(b\).
smoothing parameter \(q\).
A numeric vector of updated parameters.
Other smoothing rules:
smooth_lin()