[Gretl-users] Re: Gretl User's guide State Space modeling - clarification

On Mon, 18 Mar 2024, Alecos Papadopoulos wrote: > On page 349 of gretl's user guide the state space model is defined as y_t = Z_t \alpha_t + \epsilon_t (36.1) \alpha_{t+1} = T_t \alpha_t + \eta_t (36.2) > Later, when presenting the state-space GUI (p. 369) we read  that it > supports models of the form y_t = Z alpha_t + \epsilon_t (36.6) \alpha_t = T \alpha_{t-1} + R \eta_t (36.7) > My only question is about the time indices on the state vector in the > transition equation. > > In the first model (p. 349), the starting values for the state > variables (alpha) should be for time t, and will also affect the first > time point of the measurement equation. In the second formulation (p. > 369), these starting values should be for time (t-1), they should lead > to alpha values for time t through the transition equation alone, > which will then affect the first time point of the measurement equation. > > Which of the two does gretl do? Gretl does the first of these. The first state value lines up with the first observation in both filtering and simulation. But I'd like to hear from Jack in case I'm missing something.

Besides your point about initial values, it seems to me there's another question here. That is, for the state in any given period, is its disturbance component dated to the prior period (the first case above) or to the current period (the second case)? While this may just be a matter of convention, it could make a difference when interpreting results -- you'd want to know of any given software which convention it's using. I'm looking through the various state-space articles on my HD and the first convention is used in most cases (the doc for SsfPack and KFAS, all de Jong's papers, most articles by Koopman, the Durbin and Koopman book). The second one I'm seeing in a couple of papers that have Koopman and Shephard as co-authors.