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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

MichelleX
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1 Answers1

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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,

enter image description here

Rob Hyndman
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  • I want to convert the above three equations into the form y_t and x_t, same form as equations 2.12a and 2.12b in your book <>. In your book, you give examples for additive trend (state vector multiplied by matrix). But if I use the same vector (l_t, b_t)' multiplied by a matrix, l_t and b_t would be added together. – MichelleX Jun 12 '15 at 07:22
  • The functions are not linear. I've updated my answer to give more of the details. – Rob Hyndman Jun 12 '15 at 09:56
  • Thanks a lot for your help! – MichelleX Jun 12 '15 at 10:30