Adding drift to an ARIMA(0,1,1) (0,1,1) model in R

Question

I'm trying to add drift to my ARIMA(0,1,1)(0,1,1) model in R, however R is giving me the error message,

Warning message: In Arima(insample, order = c(0, 1, 1), seasonal = c(0, 1, 1), include.drift = TRUE) : No drift term fitted as the order of difference is 2 or more.

I don't understand the intuition behind this, I've tried writing out the ARIMA model using the lag operator:

$(1-\phi_1L)(1-\Phi_1L^4)(1-L)(1-L^4)y_t=\alpha +(1+\theta_1L)(1+\Theta_1L^4)\epsilon_t$

where $\alpha$ is the drift term.

I can't see why adding a drift term to a differenced series would be problematic?

Answer 1

This is to prevent fitting high-order polynomials for the time series in levels (not differenced), something that is only rarely plausible. According to the function's documentation,

<...> if there is more than one difference taken, no constant is included regardless of the value of this argument. This is deliberate as otherwise quadratic and higher order polynomial trends would be induced.

{Emphasis is mine.)