Standard error of the ARIMA constant

Question

I am trying to manually calculate the standard error of the constant in an ARIMA model, if it is included. I have referred to Box and Jenkins (1994) text, specially Section 7.2, but my understanding is that the methods mentioned here calculates the variance-covariance matrix for the ARIMA parameters only, not the constant. Tried searching on the Internet, but couldn't find any theory. Software like Minitab, R etc. calculate this, so I was wondering what is the way? Can someone provide any pointer(s) on this topic? Thanks.

Answer 1

arima() will fit a regression model with ARMA errors. The constant is treated as the coefficient of a regression variable consisting only of 1s. So you need the covariance matrix of the regression coefficients which is usually calculated separately from the covariance matrix of the ARMA coefficients. Look at Section 8.3 of Hamilton's "Time series analysis"

Answer 2

One of the nicest things about R is that you can access a lot of the source code to R itself from within the environment. If you simply type arima at the command prompt, you get the high-level source code for the arima() function. I got several pages of code here, when I tried it.

You do miss out on anything implemented internally within the R executable in native code, but often the high-level code tells you everything you want to know.

Answer 3

Perhaps a shift of perspective can solve this problem. Rather than seeing the constant as something special, just consider the problem without constant and with a variable that is a vector of ones.