Mike: I think the shift invariance is due to the markov assumption in their model. Equation 1 has something like x(t+1) = A*x(t) + v(t), which can be time-shifted and still be valid. For example, shifting t by 2 we get x(t+3) = A*x(t+2) + v(t+2). I don't really know what they mean by transient actions, but perhaps they mean movements that are unpredictable, such as a person spontaneously jumping in the air...