11:15 p.m.
On page 349 of gretl's user guide the state space model is defined as
Later, when presenting the state-space GUI (p. 369) we read that it
supports models of the form
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?
--
Alecos Papadopoulos PhD
Affiliate Researcher
Dpt of Economics, Athens University of Economics and Business
Foundation for Economic and Industrial Research (IOBE)
web: alecospapadopoulos.wordpress.com/
ORCID:0000-0003-2441-4550
2:14 p.m.
Am 18.03.2024 um 00:15 schrieb Alecos Papadopoulos:
On page 349 of gretl's user guide the state space model is defined as
[Just to be clear for anybody else on this list, this is just the basic
first formulation, not the most general form that gretl supports.]
Later, when presenting the state-space GUI (p. 369) we read that it
supports models of the form
My only question is about the time indices on the state vector in the
transition equation.
Yeah, that's a good question. My guess would be that the latter
representation is shifted relative to gretl's convention, but I'm not
really sure. @jack, can you comment?
cheers
sven
4:25 p.m.
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.
Allin Cottrell
7:44 a.m.
On 04/04/2024 18:25, Allin Cottrell wrote:
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.
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.
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
12:46 p.m.
Am 06.04.2024 um 09:44 schrieb Riccardo (Jack) Lucchetti:
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.
So we need to adjust the guide there, right?
> 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.
As you say, sometimes that
correlation does play a role, however.
cheers
sven
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4 comments
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participants (4)
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Alecos Papadopoulos -
Allin Cottrell -
Riccardo (Jack) Lucchetti -
Sven Schreiber