ETS multiplicative trend model written in state space form

Question

I have an ETS(M,Md,N) model and would like to write it in state space form:

yt=w(x{t-1})+r(x{t-1})ɛt xt=f(x{t-1})+g(x{t-1})ɛt

For additive trend, the state vector xt=(lt,bt)'. But I have no idea how to write the state vector xt for multiplicative trend.

Can anyone help please:D

Answer 1

The state vector is exactly the same in the multiplicative case as in the additive case. All the equations are given here: https://www.otexts.org/fpp/7/7

For the ETS(M,Md,N) model,