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. rjfhud(a)powerup.com.au
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To: gretl-users(a)lists.wfu.edu
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
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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.
|
