Re: [Gretl-devel] Arima problem
by Allin Cottrell

On Tue, 2 Nov 2010, Allin Cottrell wrote:
> On Tue, 2 Nov 2010, [iso-8859-1] G�staf Steingr�msson wrote...
Apologies for the empty message. A proper reply should also be on
the way.
Allin Cottrell
14 years

Re: [Gretl-devel] Arima problem
by Allin Cottrell

On Tue, 2 Nov 2010, [iso-8859-1] G�staf Steingr�msson wrote:
> I posted a question few days ago but wasn't clear about my
> problem so I didn't receive the answer I was looking for.
Also you are not subscribed to the gretl-devel list under the
email address you're using, which may explain communication
difficulties.
> That is why I present my problem again. I was using standard
> non-seasonal ARIMA(1,1,1) model which should be on the form:
>
> Y^(t) = c + Y(t-1) + Phi*(Y(t-1)-Y(t-2)) + theta*e(t-1)
>
> I got parameters from Gretl for c, Phi and theta. I also got
> time series for Y(t) and Y^(t) for many values of t's.
>
> I assumed that e(t-1) = Y(t) - Y^(t-1) in order to compare
> values of Y^(t) that the model got and what I should get on the
> spreadsheet by using the values for above parameters and the
> above equation. The values didnt match at all...
The first point is that when gretl estimates an ARMA model with
mean term \mu via exact ML, the model is in fact
\phi(L) (y - \mu) = \theta(L) e_t
This is explained in the Gretl User's Guide, chapter 21 (see
equations (21.4) and (21.5) in particular. This means that in your
forecasting equation you need to replace c with (1 - \phi)c on the
right-hand side.
This will produce forecast values that are close to those given by
gretl. But they will not be identical, for this reason: what gretl
produces as the ARMA residual, available via the accessor $uhat,
is the one-step ahead forecast error,
y_t - E_{t-1} y_t
where E_{t-1} y_t is the optimal forecast of y_t as of date t-1,
produced by the Kalman filter. Now the point is that this value is
not exactly the one that is needed for "e(t-1)" in the forecasting
equation you cite. To make that equation valid you need the
optimal estimate of the (t-1)-dated innovation based on all
information up to t - 1. This is implicitly produced by the Kalman
filter, but it is not the same as gretl's reported $uhat. The
difference arises because observation of y at t allows revision of
the optimal estimates of the underlying innovations at t-1 and t.
For example, consider a Gaussian ARMA(1,1) process with an
unconditional mean of zero. Let the first observation, y_1, equal
1.5. Then the first forecast error ($uhat[1]) is also 1.5. But
this does not mean that the optimal estimate of e_1 is 1.5, once
y_1 is observed. Rather, the positive value of y_1 suggests that
the pre-sample value e_0 was positive, and the optimal estimate
of e_1 (which we need for forecasting y_2) will be < 1.5.
Allin Cottrell
14 years

Re: [Gretl-devel] Arima problem
by Allin Cottrell

On Tue, 2 Nov 2010, [iso-8859-1] G�staf Steingr�msson wrote:
> Hi
>
>
>
> I posted a question few days ago but wasn't clear about my problem so I didn't receive the answer I was looking for. That is why I present my problem again. I was using standard non-seasonal ARIMA(1,1,1) model which should be on the form:
>
>
>
> Y^(t) = c + Y(t-1) + Phi*(Y(t-1)-Y(t-2)) + theta*e(t-1)
>
>
>
> I got parameters from Gretl for c, Phi and theta. I also got time series for Y(t) and Y^(t) for many values of t's.
>
>
>
> I assumed that e(t-1) = Y(t) - Y^(t-1) in order to compare values of Y^(t) that the model got and what I should get on the spreadsheet by using the values for above parameters and the above equation. The values didnt match at all. There seemed to be no systemic explanation for the difference between Y^(t) that the model got and what I got. I did this several times for various time series but wasnt able to set up the calculations right so that I would get the same results as the forecasted values.
>
>
>
> Much thanks in advance
>
> Gustaf
>
>
>
>
> Kve�ja / With regards
> G�staf Steingr�msson
> Landsbankinn
> S�rfr��ingur / Analyst
> �h�ttust�ring / Risk Management
> S�mi / Tel.: (+354) 410 6993
> Fars�mi / Mobile: (+354) 820 2646
> Fax: (+354) 410 3010
> www.landsbanki.is<http://www.landsbanki.is/>
>
>
> Landsbankinn (NBI hf.), kt. 471008-0280, Austurstr�ti 11, 155 Reykjav�k, er skr�� hlutaf�lag og starfar samkv�mt heimild og undir eftirliti Fj�rm�laeftirlitsins.
> Landsbankinn (NBI hf.), Austurstr�ti 11, 155 Reykjav�k. is incorporated in Iceland with limited liability (Reg. No: 471008-0280) and is authorised and regulated by the Financial Supervisory Authority in Iceland (Fj�rm�laeftirliti�).
>
> Fyrirvari/Disclaimer: http://www.landsbankinn.is/disclaimer
>
--
Allin Cottrell
Department of Economics
Wake Forest University
14 years

Arima problem
by Gústaf Steingrímsson

Hi
I posted a question few days ago but wasn't clear about my problem so I didn't receive the answer I was looking for. That is why I present my problem again. I was using standard non-seasonal ARIMA(1,1,1) model which should be on the form:
Y^(t) = c + Y(t-1) + Phi*(Y(t-1)-Y(t-2)) + theta*e(t-1)
I got parameters from Gretl for c, Phi and theta. I also got time series for Y(t) and Y^(t) for many values of t's.
I assumed that e(t-1) = Y(t) - Y^(t-1) in order to compare values of Y^(t) that the model got and what I should get on the spreadsheet by using the values for above parameters and the above equation. The values didnt match at all. There seemed to be no systemic explanation for the difference between Y^(t) that the model got and what I got. I did this several times for various time series but wasnt able to set up the calculations right so that I would get the same results as the forecasted values.
Much thanks in advance
Gustaf
Kveðja / With regards
Gústaf Steingrímsson
Landsbankinn
Sérfræðingur / Analyst
Áhættustýring / Risk Management
Sími / Tel.: (+354) 410 6993
Farsími / Mobile: (+354) 820 2646
Fax: (+354) 410 3010
www.landsbanki.is<http://www.landsbanki.is/>
Landsbankinn (NBI hf.), kt. 471008-0280, Austurstræti 11, 155 Reykjavík, er skráð hlutafélag og starfar samkvæmt heimild og undir eftirliti Fjármálaeftirlitsins.
Landsbankinn (NBI hf.), Austurstræti 11, 155 Reykjavík. is incorporated in Iceland with limited liability (Reg. No: 471008-0280) and is authorised and regulated by the Financial Supervisory Authority in Iceland (Fjármálaeftirlitið).
Fyrirvari/Disclaimer: http://www.landsbankinn.is/disclaimer
14 years

GARCH with Exogenous Variables
by Henrique Andrade

Dear Developers,
I would like to make a feature request regarding ARCH and GARCH
modelling. Today we can estimate a variance equation like that:
h(t) = a0 + a1*e^2(t-1) + b*h(t-1)
But we can't do this:
h(t) = a0 + a1*e^2(t-1) + b*h(t-1) + c*dummy
I know I could perform this kind of estimation using commercial
econometric packages, but I would like to use Gretl most of the
time (I'm addicted to Gretl :)).
Thanks in advance,
Henrique C. de Andrade
Doutorando em Economia Aplicada
Universidade Federal do Rio Grande do Sul
www.ufrgs.br/ppge
14 years