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ARIMA comparison results between Matlab and Eviews

Nick 님이 질문을 제출함. 15 Sep 2019
최근 활동 Gaurav Garg 님이 답변함. 18 Sep 2019
Hi all,
I have only started looking at time series regression analysis so maybe my question is relatively simple, but here it goes:
I have the following quarterly time series, for which I'm trying to run a simple AR(1) model as per below:
Y = [ 20 24 24 23 23 23 24 25 25 27 28 31 40 40 43 48 48 51 53 55 57 61 63 64 64 62 63 64 ...
67 66 69 69 78 73 75 72 70 71 71 76 80 81 78 75 74 75 75 76 77 78 78 79 80 83 83 86]' ;
Mdl = arima(1,0,0);
Results = estimate(Mdl,Y)
ARIMA(1,0,0) Model:
--------------------
Conditional Probability Distribution: Gaussian
Standard t
Parameter Value Error Statistic
----------- ----------- ------------ -----------
Constant 1.88484 0.907647 2.07662
AR{1} 0.986253 0.0146277 67.4238
Variance 6.15792 0.924064 6.66395
Also, then I tried the regARIMA function:
Alt_Mdl = regARIMA('ARLags',1);
Alt_Results = estimate(Alt_Mdl,Y)
ARIMA(1,0,0) Error Model:
--------------------------
Conditional Probability Distribution: Gaussian
Standard t
Parameter Value Error Statistic
----------- ----------- ------------ -----------
Intercept 70.4571 13.8459 5.08866
AR{1} 0.966818 0.0154338 62.6431
Variance 6.76639 1.09355 6.18751
The results between arima and regARIMA differ. Why is this the case?
At this stage, I'm not really interested on whether the results and the model selection are the appropriate ones, or for stationarity etc.
Consequently, when I run the same time series in Eviews the results are also different, but closer to regARIMA.
See below. I understand that the programmes have different calculation methods etc however, the results are completely different (e.g. see the constant) so I was hoping for some clarity for anyone that knows especially on the difference between regARIMA and arima. Am I writing something wrong in the codes?
Many thanks!
Eviews steps:
  1. Load the same vector as y
  2. Go to Quick--> Estimate Equation --> Type: y c ar(1) (using Least Squares)
Dependent Variable: Y
Method: ARMA Maximum Likelihood (OPG - BHHH)
Date: 09/15/19 Time: 13:33
Sample: 1 56
Included observations: 56
Convergence achieved after 12 iterations
Coefficient covariance computed using outer product of gradients
Variable Coefficient Std. Error t-Statistic Prob.
C 53.57297 29.24125 1.832102 0.0726
AR(1) 0.996036 0.018536 53.73544 0.0000
SIGMASQ 7.702169 1.043955 7.377876 0.0000
R-squared 0.981990 Mean dependent var 58.71429
Adjusted R-squared 0.981311 S.D. dependent var 20.86730
S.E. of regression 2.852743 Akaike info criterion 5.072937
Sum squared resid 431.3215 Schwarz criterion 5.181438
Log likelihood -139.0422 Hannan-Quinn criter. 5.115003
F-statistic 1444.931 Durbin-Watson stat 1.746115
Prob(F-statistic) 0.000000

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Gaurav Garg 님의 답변 18 Sep 2019
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Hi,
The ARIMA model and regARIMA model are completely different. ARIMA model is a linear time series model for a univariate response process. The arima object allows you to create an auto-regressive moving average model. However, regARIMA model creates a regression model with ARIMA time series errors.
The way the models work is different. regARIMA is an alternative ARIMA model representation. The errors in regARIMA model can have an autocorrelation structure and models can be specified for them. These models include -
  • Moving Average
  • Autoregressive
  • Mixed autoregressive and Moving average
  • Integrated
Hence, error models can be specified containing known coefficients to -
  • Simulate responses using simulate
  • Explore impulse responses using impulse
  • Forecast future observations using forecast
  • Estimate unknown coefficients with data using estimate
For even better understanding, the following documents may be helpful -
You may further investigate how estimate function works for both the models.

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