Dear all:

I have three questions.

1: Why is the outcome of X-12-ARIMA model almost the same as Seasonal ARIMA. For example, there are two models with the same lags of AR and MA, namely X-12-ARIMA(1,1,0)(1,1,1) and ARIMA(1,1,0)(1,1,1).

The coefficient of AR(1)、SAR(1)、SMA(1) of X-12-ARIMA(1,1,0)(1,1,1) is 0.853261、1.774953、0.114786.

The coefficient of AR(1)、SAR(1)、SMA(1) of Seasonal ARIMA(1,1,0)(1,1,1) is

0.853332、1.774762、0.114335

AIC of X-12-ARIMA(1,1,0)(1,1,1) is 2487.968

AIC of ARIMA(1,1,0)(1,1,1) is 2487.942

MAPE of out of sample of X-12-ARIMA(1,1,0)(1,1,1) is 4.7894

MAPE of out of sample of Seasonal ARIMA(1,1,0)(1,1,1) is 4.7326

This two models are almost the same. Other lags of AR and MA have the same situation. But there is a few exceptions. For example,  X-12-ARIMA(1,1,2)(2,1,0) and Seasonal ARIMA(1,1,2)(2,1,0) may have different outcome.

2: I choose the options of 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 general model of RegARIMA in X-12-ARIMA – Reference Manual, Version 0.3. (U.S. Census Bureau)?

I can not see the outcome of any seasonality adjusting regression variables(such as length-of-month、level shift and so on).

3. Is there any relationship between the option of Model/Time series/ARIMA/Include a constant and trend constant in regARIMA? Can I not choose the option of Model/Time series/ARIMA/Include a constant when runing X-12-ARIMA?

Thanks a lot