Hi there,
merely to straighten out a wee point first of
all, I ask the following by way of trying to help.
Are you aware (for example) that in their books,
P Brockwell and R Shumway pose the
ARIMA equations in different form re the
positive and negative coefficient signage.
Their models are different and the signage
results are different but
when the coefficients are inserted in their
models, the results are the same.
Just asking that you properly know the model
being computed is all I'm asking.
----- Original Message -----
Sent: Sunday, January 09, 2011 10:54
PM
Subject: [Gretl-users] Some questions
about X-12-ARIMA
Dear all:
I make my question clearer. ARIMA and
X-12-ARIMA have almost the same outcomes under most combinations of AR and MA.
For example, Using the same sample, the output of ARIMA(1,1,1)(1,1,0
):
Function evaluations: 22
Evaluations of gradient:
8
Model 5: ARIMA, using observations 1982:03-1989:12 (T = 94)
Estimated
using BHHH method (conditional ML)
Dependent variable: (1-L)(1-Ls)
z
coefficient std. error
z p-value
---------------------------------------------------------
phi_1 0.0386387
0.490287 0.07881 0.9372
Phi_1 -0.547450
0.103980 -5.265 1.40e-07
***
theta_1
0.134454 0.505469
0.2660 0.7902
Mean dependent var
-595.9894 S.D. dependent var 35113.05
Mean of
innovations -657.4065 S.D. of innovations
29171.20
Log-likelihood -1099.788
Akaike criterion 2207.577
Schwarz
criterion 2217.750
Hannan-Quinn
2211.686
Real Imaginary Modulus Frequency
-----------------------------------------------------------
AR
Root
1
25.8808 0.0000
25.8808 0.0000
AR
(seasonal)
Root
1
-1.8266 0.0000
1.8266 0.5000
MA
Root 1
-7.4375 0.0000
7.4375 0.5000
-----------------------------------------------------------
the
output of X-12-ARIMA(1,1,1)(1,1,0 ):
Model 6: ARIMA, using
observations 1982:03-1989:12 (T = 94)
Estimated using X-12-ARIMA
(conditional ML)
Dependent variable: (1-L)(1-Ls)
z
coefficient std. error
z p-value
---------------------------------------------------------
phi_1 0.0383739
0.602274 0.06371 0.9492
Phi_1
-0.547423 0.0911210
-6.008 1.88e-09 ***
theta_1 0.134554
0.597619 0.2252 0.8219
Mean dependent var -595.9894 S.D. dependent
var 35113.05
Mean of innovations -657.4774 S.D. of
innovations 29171.20
Log-likelihood
-1099.788 Akaike criterion
2207.577
Schwarz criterion 2217.750
Hannan-Quinn
2211.686
Real Imaginary Modulus Frequency
-----------------------------------------------------------
AR
Root
1
26.0594 0.0000
26.0594 0.0000
AR
(seasonal)
Root
1
-1.8267 0.0000
1.8267 0.5000
MA
Root 1
-7.4320 0.0000
7.4320 0.5000
-----------------------------------------------------------
The
outcomes of ARIMA(1,1,1)(1,1,0 ) and X-12-ARIMA(1,1,1)(1,1,0 ) are almost the
same.
But there are a few exceptions. For example, under the same
sample, the output of ARIMA(1,1,2)(2,1,0 ):
Model 7: ARIMA, using
observations 1983:03-1989:12 (T = 82)
Estimated using BHHH method
(conditional ML)
Dependent variable: (1-L)(1-Ls)
z
coefficient std. error
z p-value
-------------------------------------------------------
phi_1 -0.590308
0.200862 -2.939 0.0033
***
Phi_1
-0.683313 0.134247
-5.090 3.58e-07 ***
Phi_2 -0.240713
0.113586 -2.119 0.0341
**
theta_1 0.873512
0.207170 4.216 2.48e-05
***
theta_2 0.361254
0.0966288 3.739 0.0002
***
Mean dependent var -1074.305 S.D. dependent
var 36698.54
Mean of innovations -1019.087 S.D. of
innovations 28580.42
Log-likelihood
-957.7121 Akaike criterion
1927.424
Schwarz criterion 1941.864
Hannan-Quinn
1933.222
Real Imaginary Modulus Frequency
-----------------------------------------------------------
AR
Root
1
-1.6940 0.0000
1.6940 0.5000
AR
(seasonal)
Root
1
-1.4194 -1.4628
2.0382 -0.3726
Root
2
-1.4194 1.4628
2.0382 0.3726
MA
Root 1
-1.2090 -1.1430
1.6638 -0.3795
Root
2
-1.2090 1.1430
1.6638 0.3795
-----------------------------------------------------------
the
output of X-12-ARIMA(1,1,2)(2,1,0 ):
Model 8: ARIMA, using
observations 1983:03-1989:12 (T = 82)
Estimated using X-12-ARIMA
(conditional ML)
Dependent variable: (1-L)(1-Ls)
z
coefficient std. error
z p-value
-------------------------------------------------------
phi_1
0.653709 0.209156
3.125 0.0018 ***
Phi_1 -0.675406
0.113095 -5.972 2.34e-09 ***
Phi_2 -0.244173
0.113191 -2.157 0.0310 **
theta_1 -0.566737
0.220105 -2.575 0.0100 **
theta_2 -0.222901
0.115118 -1.936 0.0528 *
Mean
dependent var -1074.305 S.D. dependent var
36698.54
Mean of innovations -2724.431 S.D. of
innovations 29295.00
Log-likelihood
-959.7371 Akaike criterion
1931.474
Schwarz criterion 1945.914
Hannan-Quinn
1937.272
Real Imaginary Modulus Frequency
-----------------------------------------------------------
AR
Root
1
1.5297 0.0000
1.5297 0.0000
AR
(seasonal)
Root
1
-1.3830 1.4774
2.0237 0.3698
Root
2
-1.3830 -1.4774
2.0237 -0.3698
MA
Root
1
1.1990 0.0000
1.1990 0.0000
Root
2
-3.7416 0.0000
3.7416 0.5000
-----------------------------------------------------------
The
outcomes of ARIMA(1,1,2)(2,1,0 ) and X-12-ARIMA(1,1,2)(2,1,0 ) are hugely
different.
The question above puzzles me.
I also want to know When I
choose the options Model/Time series/ARIMA/Using X-12-ARIMA to run the
X-12-ARIMA model. Is the set of equation of X-12-ARIMA in gretl the same as
RegARIMA(X-12-ARIMA – Reference Manual, Version 0.3. U.S. Census
Bureau):
φ(B)Φ(B)▽^d ▽_s^D[y-Σβ_i x_it]= θ(B)Θ(B)a_t
I can not see the
outcome of any seasonality adjusting regression variables(the part of y-Σβ_i
x_it, such as length-of-month、Trend constant、Trading day、level shift at t_0
and so on).
Thanks a lot
_______________________________________________
Gretl-users mailing
list
Gretl-users@lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users