ARIMA equation intercept interpretation

I get an ARIMA equation in a form like below:

ARIMA ({1,-6.88479117532726E-02,-0.41430691637436},0,{1,4.42986549117398E-03}) X ({1,-0.473450289323228},0,{1,0.013772719862356,-2.14724317829266E-02,-4.80711350511344E-02,-1.15173259713497E-02,-9.86142925337024E-03,1.06803677786174})(6) Intercept:18561.1721123981

I do understand the coefficients part and the seasonal part as well, however, I have trouble deciphering what exactly is the intercept here. Initially, I thought it would be equivalent to the value of mu in the original Box-Jenkins equation (so indicate a level), then I thought it's an intercept for the AR terms. It seems that none of these interpretations is good. The only official explanation I found at msdn was:

"Normally, the intercept (VALUETYPE = 11) or residual in a regression equation tells you the value of the predictable attribute, at the point where the input attribute, is 0. In many cases, this might not happen, and could lead to counterintuitive results.

For example, in a model that predicts income based on age, it is useless to learn the income at age 0. In real-life, it is typically more useful to know about the behavior of the line with respect to average values. Therefore, SQL Server Analysis Services modifies the intercept to express each regressor in a relationship with the mean.

This adjustment is difficult to see in the mining model content, but is apparent if you view the completed equation in the Mining Legend of the Microsoft Tree Viewer. The regression formula is shifted away from the 0 point to the point that represents the mean. This presents a view that is more intuitive given the current data.

Therefore, assuming that the mean age is around 45, the intercept (VALUETYPE = 11) for the regression formula tells you the mean income."

But I don't think it applies to ARIMA equations as well. I am lost, can anyone explain to me how do I make sense of the intercept in these equations?

September 6th, 2015 9:18am

Hi piotr.m,

I am trying to involve someone more familiar with this topic for a further look at this issue. Sometime delay might be expected from the job transferring. Your patience is greatly appreciated.

Thank you for your understanding and support.

Regards,
Katherine Xiong

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September 7th, 2015 4:02am

intercept = Mean * (SUM OF AR Polynomial Coefficients)
September 8th, 2015 1:52am

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