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

On 04/04/2024 18:25, Allin Cottrell wrote: > On Mon, 18 Mar 2024, Alecos Papadopoulos wrote: >> 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. I don't think you are.

> 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. The distinction between the two conventions is immaterial as long as the shocks to the two equations (\epsilon_t and \eta_t) are independent, which is true of most state space models I know of. Otherwise, things become a bit more complicated.