9:48 a.m.
Hello
I simulated the following AR(1) process xt = 5 + 0.4xt-1 + e with e =
N(0,1) 200 observations
Estimation with OLS: xt = 5.047xt + 0.414xt-1
Estimation with gretl ARIMA: xt = 8.57 + 0.43xt-1
I simulated this AR(2) process: xt = 5 + 0.4xt-1 -0.1xt-2 + e
OLS estimation: xt = 4.64 + 0.377x t-1 -0.0075 x t-2
ARIMA estimation: xt = 7.36 + 0.369xt-1 -0.0076xt-2
Why is gretl giving such a bad estimation compared to OLS-estimation?
Thank you
Raul
10:40 a.m.
On Sat, 23 Feb 2019, Raul Gimeno wrote:
Hello
I simulated the following AR(1) process xt = 5 + 0.4xt-1 + e with e =
N(0,1) 200 observations
Estimation with OLS: xt = 5.047xt + 0.414xt-1
Estimation with gretl ARIMA: xt = 8.57 + 0.43xt-1
I simulated this AR(2) process: xt = 5 + 0.4xt-1 -0.1xt-2 + e
OLS estimation: xt = 4.64 + 0.377x t-1 -0.0075 x t-2
ARIMA estimation: xt = 7.36 + 0.369xt-1 -0.0076xt-2
Why is gretl giving such a bad estimation compared to OLS-estimation?
The answer is in the manual, section 28.2, but in short: the constant term
is a special case of a deterministic exogenous part that is treated
differently in full ML estimation (that is what you get with the arima
command) and conditional ML (that is what you get by OLS).
-------------------------------------------------------
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
-------------------------------------------------------
11:56 a.m.
It seems like you are comparing the intercept (5.047) with the mean (8.57):
for ARIMA estimation the right representation is
x_t - 8.57 = 0.45 * (x_{t-1} - 8.57) + e_t
Indeed 5.047 / (1 - 0.414) = 8.61 which is very close to 8.57.
Best,
Matteo
Il 23/02/2019 10:48, Raul Gimeno ha scritto:
Hello
I simulated the following AR(1) process x_t = 5 + 0.4x_t-1 + e with
e = N(0,1) 200 observations
Estimation with OLS: x_t = 5.047x_t + 0.414x_t-1
Estimation with gretl ARIMA: x_t = 8.57 + 0.43x_t-1
I simulated this AR(2) process: x_t = 5 + 0.4x_t-1 -0.1x_t-2 + e
OLS estimation: x_t = 4.64 + 0.377x t-1 -0.0075 x t-2
ARIMA estimation: x_t = 7.36 + 0.369x_t-1 -0.0076x_t-2
Why is gretl giving such a bad estimation compared to OLS-estimation?
Thank you
Raul
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Matteo Pelagatti
Department of Economics, Management and Statistics
University of Milano-Bicocca
Via Bicocca degli Arcimboldi, 8
20126 Milano
Tel +39 02 6448.5834
1:31 p.m.
Am 23.02.2019 um 12:56 schrieb Matteo Pelagatti:
It seems like you are comparing the intercept (5.047) with the mean
(8.57):
for ARIMA estimation the right representation is
x_t - 8.57 = 0.45 * (x_{t-1} - 8.57) + e_t
Indeed 5.047 / (1 - 0.414) = 8.61 which is very close to 8.57.
Thanks for pointing this out. I have to say, however, that I understand
the confusion of the original post. The ARIMA output is presented just
like the equation format. The built-in help (click the button "help" in
the ARIMA specification window) also has a representation of the
constant term that looks like the intercept instead of the mean.
Granted, in the (excellent) user guide things are clearer. But perhaps
something should be done about the way the ARIMA results are presented.
Perhaps a stylized equation formulation like it is done with the ADF
test output.
thanks
sven
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4 participants
participants (4)
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Matteo Pelagatti -
Raul Gimeno -
Riccardo (Jack) Lucchetti -
Sven Schreiber