In the R package forecast, when you run dynamic regression (regression with arima errors), the coefficients and their standard error are output, but there is no significance test available for the coefficients. I am wondering why this is-- does variable significance in the typical sense (t-test) not hold when adding in Arima terms to the model?
An example of this would be
library(fpp2) library(forecast) auto.arima(uschange[, "Consumption"], xreg = uschange[, "Income"]) Series: uschange[, "Consumption"] Regression with ARIMA(1,0,2) errors Coefficients: ar1 ma1 ma2 intercept xreg 0.6922 -0.5758 0.1984 0.5990 0.2028 s.e. 0.1159 0.1301 0.0756 0.0884 0.0461 sigma^2 estimated as 0.3219: log likelihood=-156.95 AIC=325.91 AICc=326.37 BIC=345.29