4:58 p.m.
Dear All,
I'm in trouble with state space models, as I find them difficult to implement. I was
able to set up a few with just one time-variant unobservable variable but I'm not sure
on what I'm doing when there are more. Let's say we depart from the example of the
Phillips curve on pages 345-346 of Gretl manual, where the inflation rate (INFQ) depends
on the unemployment rate (URX). In the example, the intercept is time-invariant and the
coefficient for URX follows a random walk.
Let's expand the model such that there is a second independent variable Effective
Exchange Rate (EER) explaining INFQ. Additionally, I want all three coefficients to follow
an AR(1) process. The image attached shows this new model. How hard would that be to
implement these changes on the script depicted on manual page 347 (as follows):
<hansl>
function void at_each_step(bundle *b)
b.obsymat = transp(b.mX[b.t,])
end function
open AWM.gdt --quiet
smpl 1974:1 1994:1
/* parameter initialization */
scalar b0 = mean(INFQ)
scalar s_obs = 0.1
scalar s_state = 0.1
/* bundle setup */
bundle B = ksetup(INFQ, 1, 1, 1)
matrix B.mX = {URX}
matrix B.depvar = {INFQ}
B.timevar_call = "at_each_step"
B.diffuse = 1
/* ML estimation of intercept and the two variances */
mle LL = err ? NA : B.llt
B.obsy = B.depvar - b0
B.obsvar = s_obs^2
B.statevar = s_state^2
err = kfilter(&B)
params b0 s_obs s_state
end mle
/* display the smoothed time-varying slope */
ksmooth(&B)
series tvar_b1hat = B.state[,1]
series tvar_b1se = sqrt(B.stvar[,1])
gnuplot tvar_b1hat --time-series --with-lines --output=display \
--band=tvar_b1hat,tvar_b1se,1.96 --band-style=fill
</hansl>
--
F.R.Costa
6:57 a.m.
Am 07.10.2021 um 18:58 schrieb F.R.Costa:
Dear All,
I'm in trouble with state space models, as I find them difficult to
implement. I was able to set up a few with just one time-variant
unobservable variable but I'm not sure on what I'm doing when there are
more. Let's say we depart from the example of the Phillips curve on
pages 345-346 of Gretl manual, where the inflation rate (INFQ) depends
on the unemployment rate (URX). In the example, the intercept is
time-invariant and the coefficient for URX follows a random walk.
I looked at the example listing 36.4
(http://gretl.sourceforge.net/guidefiles/example-36.4.inp) and at first
I also found it a bit puzzling.
But the trick there is that the unemployment rate URX is _not_ used in
the model as an exogenous regressor in terms of the notation of gretl's
state-space apparaturs. So there is no x, no obsx, and no time-varying
(nor constant) obsxmat. This feels a bit counterintuitive, especially
since in (36.4) (the equation, not the listing) there appears an x_t
which has nothing to do with the notation in that chapter. (So I think
that x should be changed in the doc.)
As explained below equation (36.5), what the listing 36.4 does is to
treat the time-varying coefficent as the latent state, using the
(apparently implicit) default of F == 1 == statemat.
(@jack: It seems that that default for statemat is not documented. If
there is no such default, then I don't know what's going on.)
And then unemployment URX is used as the "coefficient" H (=obsymat) of
that latent state, where that "coefficient" of course doesn't need to be
estimated, since it's an observable variable in reality.
So you could follow that route by expanding both the state vector and
the obsymat, and introducing a non-unit F to capture your wanted AR(1)
dynamics for the states.
cheers
sven
11:44 a.m.
On Fri, 8 Oct 2021, Sven Schreiber wrote:
As explained below equation (36.5), what the listing 36.4 does is to
treat the time-varying coefficent as the latent state, using the
(apparently implicit) default of F == 1 == statemat.
(@jack: It seems that that default for statemat is not documented. If
there is no such default, then I don't know what's going on.)
In that example, F is set to 1 because it is passed as an argument to
ksetup(), and is never changed.
-------------------------------------------------------
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
-------------------------------------------------------
12:07 p.m.
Am 08.10.2021 um 13:44 schrieb Riccardo (Jack) Lucchetti:
On Fri, 8 Oct 2021, Sven Schreiber wrote:
> As explained below equation (36.5), what the listing 36.4 does is to
> treat the time-varying coefficent as the latent state, using the
> (apparently implicit) default of F == 1 == statemat.
> (@jack: It seems that that default for statemat is not documented. If
> there is no such default, then I don't know what's going on.)
In that example, F is set to 1 because it is passed as an argument to
ksetup(), and is never changed.
Ah of course, that makes sense!
(Maybe at some point in the future we could overload ksetup() to accept
an options bundle instead of the positional arguments, but that's a
different topic.)
One follow-up question though: What about the line with B.depvar =
{INFQ}? A search for "depvar" in the state-space chapter doesn't turn up
anything useful. And isn't the first arg to ksetup() already specifying
that?
thanks
sven
12:22 p.m.
On Fri, 8 Oct 2021, Sven Schreiber wrote:
Am 08.10.2021 um 13:44 schrieb Riccardo (Jack) Lucchetti:
> On Fri, 8 Oct 2021, Sven Schreiber wrote:
>
>> As explained below equation (36.5), what the listing 36.4 does is to
>> treat the time-varying coefficent as the latent state, using the
>> (apparently implicit) default of F == 1 == statemat.
>> (@jack: It seems that that default for statemat is not documented. If
>> there is no such default, then I don't know what's going on.)
>
> In that example, F is set to 1 because it is passed as an argument to
> ksetup(), and is never changed.
Ah of course, that makes sense!
(Maybe at some point in the future we could overload ksetup() to accept
an options bundle instead of the positional arguments, but that's a
different topic.)
One follow-up question though: What about the line with B.depvar =
{INFQ}? A search for "depvar" in the state-space chapter doesn't turn up
anything useful. And isn't the first arg to ksetup() already specifying
that?
A Kalman bundle can have extra keys, apart from the "special" ones such as
statevar, obsymat, etc. In that example depvar is used to have an object
you can subtract b0 from, just for convenience.
-------------------------------------------------------
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
-------------------------------------------------------
12:36 p.m.
Am 08.10.2021 um 14:22 schrieb Riccardo (Jack) Lucchetti:
On Fri, 8 Oct 2021, Sven Schreiber wrote:
> Am 08.10.2021 um 13:44 schrieb Riccardo (Jack) Lucchetti:
>> In that example, F is set to 1 because it is passed as an
argument to
>> ksetup(), and is never changed.
>
> Ah of course, that makes sense!
> One follow-up question though: What about the line with B.depvar
=
> {INFQ}? A search for "depvar" in the state-space chapter doesn't turn
up
> anything useful. And isn't the first arg to ksetup() already specifying
> that?
A Kalman bundle can have extra keys, apart from the "special" ones such
as statevar, obsymat, etc. In that example depvar is used to have an
object you can subtract b0 from, just for convenience.
Hm, OK. In that example it's not really needed to store it in the bundle
though, AFAICS, which makes it a little more confusing.
I think ch. 36 should have an encompassing table listing all the
reserved keys for a Kalman bundle. Currently there are at least five
places where some of them are mentioned.
thanks
sven
12:39 p.m.
On Fri, 8 Oct 2021, Sven Schreiber wrote:
Am 08.10.2021 um 14:22 schrieb Riccardo (Jack) Lucchetti:
> On Fri, 8 Oct 2021, Sven Schreiber wrote:
>
>> Am 08.10.2021 um 13:44 schrieb Riccardo (Jack) Lucchetti:
>>> In that example, F is set to 1 because it is passed as an argument to
>>> ksetup(), and is never changed.
>>
>> Ah of course, that makes sense!
>> One follow-up question though: What about the line with B.depvar =
>> {INFQ}? A search for "depvar" in the state-space chapter doesn't
turn up
>> anything useful. And isn't the first arg to ksetup() already specifying
>> that?
>
> A Kalman bundle can have extra keys, apart from the "special" ones such
> as statevar, obsymat, etc. In that example depvar is used to have an
> object you can subtract b0 from, just for convenience.
Hm, OK. In that example it's not really needed to store it in the bundle
though, AFAICS, which makes it a little more confusing.
I think ch. 36 should have an encompassing table listing all the
reserved keys for a Kalman bundle. Currently there are at least five
places where some of them are mentioned.
Excellent idea.
-------------------------------------------------------
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
-------------------------------------------------------
9:49 a.m.
Am 08.10.2021 um 14:39 schrieb Riccardo (Jack) Lucchetti:
On Fri, 8 Oct 2021, Sven Schreiber wrote:
> I think ch. 36 should have an encompassing table listing all the
> reserved keys for a Kalman bundle. Currently there are at least five
> places where some of them are mentioned.
Excellent idea.
OK -- as a first step, I simply printed out the bundle result of the
example script 36.5, and I was surprised how nicely structured and
commented the printout was!
<console>
? LLM.heyho = I(2)
? print LLM
bundle LLM:
Kalman input matrices
obsy: 100 x 1
obsymat: 1 x 1
obsvar: 1 x 1
statemat: 1 x 1
statevar: 1 x 1
Kalman output matrices
prederr: 100 x 1
pevar: 100 x 1
state: 100 x 1
stvar: 100 x 1
gain: 100 x 1
smdist: 100 x 2
smdisterr: 100 x 2
uhat: 1 x 1
Kalman scalars
t: 0
diffuse: 1
cross: 0
s2: 1.00125
lnl: -632.608
r: 1
n: 1
T: 100
p: 0
Other content
heyho (matrix: 2 x 2)
</console>
Are there other possible reserved Kalman keys which do not show up in
this particular example, or is this it?
Thanks
Sven
10:23 a.m.
On Sun, 10 Oct 2021, Sven Schreiber wrote:
Are there other possible reserved Kalman keys which do not show up
in
this particular example, or is this it?
From lib/src/kalman.c:
<C>
struct K_input_mat K_input_mats[] = {
{ K_y, "obsy" },
{ K_H, "obsymat" },
{ K_x, "obsx" },
{ K_A, "obsxmat" },
{ K_R, "obsvar" },
{ K_F, "statemat" },
{ K_Q, "statevar" },
{ K_m, "stconst" },
{ K_S, "inistate" },
{ K_P, "inivar" }
};
</C>
-------------------------------------------------------
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
-------------------------------------------------------
12:58 p.m.
Am 11.10.2021 um 12:23 schrieb Riccardo (Jack) Lucchetti:
On Sun, 10 Oct 2021, Sven Schreiber wrote:
> Are there other possible reserved Kalman keys which do not show up in
> this particular example, or is this it?
From lib/src/kalman.c:
<C>
struct K_input_mat K_input_mats[] = {
{ K_y, "obsy" },
...
OK, thanks, but...
(BTW, two lines above there's the slightly outdated comment /* mapping
to names used in "kalman ... end kalman" block */, given that AFAIK
there's no kalman block anymore.)
... those are just the input matrices, not all reserved names. However,
poking around some more in lib/src/kalman.c, I also see the following:
<c>
static const char *kalman_output_matrix_names[K_N_OUTPUTS] = {
"prederr",
"pevar",
"state",
"stvar",
"gain",
"llt",
"smdist",
"smdisterr",
"uhat"
};
</c>
and:
<c>
static const char *kalman_output_scalar_names[K_N_SCALARS] = {
"t",
"diffuse",
"cross",
"s2",
"lnl",
"r",
"n",
"T",
"p"
};
</c>
This covers matrices and scalars. Plus, I know from the documentation
that another reserved key is "timevar_call".
So I'm asking again, is this all? Or some other reserved keys in the
Kalman bundle for other types?
thanks
sven
11:43 a.m.
On Thu, 7 Oct 2021, F.R.Costa wrote:
Dear All,
I'm in trouble with state space models, as I find them difficult to
implement. I was able to set up a few with just one time-variant
unobservable variable but I'm not sure on what I'm doing when there are
more. Let's say we depart from the example of the Phillips curve on
pages 345-346 of Gretl manual, where the inflation rate (INFQ) depends
on the unemployment rate (URX). In the example, the intercept is
time-invariant and the coefficient for URX follows a random walk.
Let's expand the model such that there is a second independent variable
Effective Exchange Rate (EER) explaining INFQ. Additionally, I want all
three coefficients to follow an AR(1) process. The image attached shows
this new model. How hard would that be to implement these changes on the
script depicted on manual page 347 (as follows):
Speaking from personal experience, the state-space approach to
time-varying parameter models is often difficult in practice because for
large-ish models the identification issues become quite relevant and
maximising the loglikelihood is quite difficult (although the EM algorithm
may help).
There's an interesting non-parametric alternative that I find myself using
quite often recently that was put forward by Giraitis, Kapetanios and
several co-authors and is implemented in the gretl "ketvals" package.
I'm attaching an example script which shows the two alternatives on some
simulated data, where the simulated coefficients are smoothed versions of
AR(1) processes. As you can see, both approaches reconstruct the histories
for both coefficients relatively well, but the non-parametric approach is
much faster.
-------------------------------------------------------
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
-------------------------------------------------------
5:50 p.m.
WOW. That's the only word that occurs to me.
I'm impressed with the "ketvars" package and the Giraitis et al (2020)
model. If I knew about it before I could have saved a lot of trouble... Still need to
learn more about the kernel parameter. I attached an image with a state space with kalman
filter and the result of ketvars with a parameter of 0.1.
Many thanks
--
F.R.Costa
Oct 8, 2021, 12:43 by p002264(a)staff.univpm.it:
On Thu, 7 Oct 2021, F.R.Costa wrote:
> Dear All,
>
> I'm in trouble with state space models, as I find them difficult to implement. I
was able to set up a few with just one time-variant unobservable variable but I'm not
sure on what I'm doing when there are more. Let's say we depart from the example
of the Phillips curve on pages 345-346 of Gretl manual, where the inflation rate (INFQ)
depends on the unemployment rate (URX). In the example, the intercept is time-invariant
and the coefficient for URX follows a random walk.
>
> Let's expand the model such that there is a second independent variable Effective
Exchange Rate (EER) explaining INFQ. Additionally, I want all three coefficients to follow
an AR(1) process. The image attached shows this new model. How hard would that be to
implement these changes on the script depicted on manual page 347 (as follows):
>
Speaking from personal experience, the state-space approach to time-varying parameter
models is often difficult in practice because for large-ish models the identification
issues become quite relevant and maximising the loglikelihood is quite difficult (although
the EM algorithm may help).
There's an interesting non-parametric alternative that I find myself using quite
often recently that was put forward by Giraitis, Kapetanios and several co-authors and is
implemented in the gretl "ketvals" package.
I'm attaching an example script which shows the two alternatives on some simulated
data, where the simulated coefficients are smoothed versions of AR(1) processes. As you
can see, both approaches reconstruct the histories for both coefficients relatively well,
but the non-parametric approach is much faster.
-------------------------------------------------------
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
-------------------------------------------------------
4:10 p.m.
Any idea about whether the ketvals package allows to deal with missing data. I mean, I
have a few series with some missing data points but I would like to still be able to
determine the time-varying coefficients. However, when that's the case, the ketvals
package stops with an error.
--
F.R.Costa
Oct 8, 2021, 12:43 by p002264(a)staff.univpm.it:
On Thu, 7 Oct 2021, F.R.Costa wrote:
> Dear All,
>
> I'm in trouble with state space models, as I find them difficult to implement. I
was able to set up a few with just one time-variant unobservable variable but I'm not
sure on what I'm doing when there are more. Let's say we depart from the example
of the Phillips curve on pages 345-346 of Gretl manual, where the inflation rate (INFQ)
depends on the unemployment rate (URX). In the example, the intercept is time-invariant
and the coefficient for URX follows a random walk.
>
> Let's expand the model such that there is a second independent variable Effective
Exchange Rate (EER) explaining INFQ. Additionally, I want all three coefficients to follow
an AR(1) process. The image attached shows this new model. How hard would that be to
implement these changes on the script depicted on manual page 347 (as follows):
>
Speaking from personal experience, the state-space approach to time-varying parameter
models is often difficult in practice because for large-ish models the identification
issues become quite relevant and maximising the loglikelihood is quite difficult (although
the EM algorithm may help).
There's an interesting non-parametric alternative that I find myself using quite
often recently that was put forward by Giraitis, Kapetanios and several co-authors and is
implemented in the gretl "ketvals" package.
I'm attaching an example script which shows the two alternatives on some simulated
data, where the simulated coefficients are smoothed versions of AR(1) processes. As you
can see, both approaches reconstruct the histories for both coefficients relatively well,
but the non-parametric approach is much faster.
-------------------------------------------------------
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
-------------------------------------------------------
10:22 a.m.
On Fri, 15 Oct 2021, F.R.Costa wrote:
Any idea about whether the ketvals package allows to deal with
missing data.
At present, no. In fact, I'm not even aware of a theoretical solution to
in-sample missing data. Have to think about it.
-------------------------------------------------------
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
-------------------------------------------------------
921
days inactive
931
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13 comments
3 participants
participants (3)
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F.R.Costa -
Riccardo (Jack) Lucchetti -
Sven Schreiber