Suppose I'm considering several independent variables for possible inclusion in an ARIMAX model I'm developing. Before fitting different variables, I'd like to screen out variables that exhibit reverse causality by using a Granger test (I'm using the
granger.test function from the
MSBVAR package in R, although, I believe other implimentations work similarly). How do I determine how many lags should be tested?
The R function is:
granger.test(y, p), where
y is a data frame or matrix, and
p is the lags.
The null hypothesis is that the past $p$ values of $X$ do not help in predicting the value of $Y$.
Is there any reason not to select a very high lag here (other than the loss of observations)?
Note that I have already differenced every time series in my data frame, based on the order of integration of my dependent time series. (E.g., differencing my dependent time series once made it stationary. Therefore, I also differenced all "independent" time series once.)