I am running auto.arima on part of a time series (training data) using all possible combinations for several external regressors. I then choose the top 5 models according to fit to testing data using RMSE. In some cases, chosen models estimate ARIMA or xreg coefficients equal to zero. Why are these models chosen? Wouldn't coefficients = 0 essentially cancel out that term in the regression equation? How can I avoid this behavior?
Example output for two models below... also, the s.e. = 0 in some cases and NaN in others.
I have started running auto.arima(... stepwise = FALSE, aproximation = FALSE), but that takes 5-10x longer, and I'm not sure if it fixes the behavior (sorry, not all models have finished running).
[] Series: train[, y] Regression with ARIMA(1,0,1)(0,0,2) errors Box Cox transformation: lambda= -0.9010564 Coefficients: ar1 ma1 sma1 sma2 intercept car_prod crude_oil fx_USD_buy gdp 0.9478 -0.6806 0.4932 0.5201 1.1098 0 0 0 0 s.e. NaN 0.0029 NaN NaN 0.0001 0 0 0 0 sigma^2 estimated as 2.538e-14: log likelihood=1124.07 AIC=-2228.14 AICc=-2224.9 BIC=-2204.45 [] Series: train[, y] Regression with ARIMA(1,0,1)(0,0,2) errors Box Cox transformation: lambda= -0.9010564 Coefficients: ar1 ma1 sma1 sma2 intercept gdp import_trade_balance unemployment 0.9467 -0.6344 0.3925 0.4753 1.1098 0 0 0 s.e. NaN 0.0024 NaN NaN NaN NaN NaN NaN sigma^2 estimated as 2.691e-14: log likelihood=1122.11 AIC=-2226.23 AICc=-2223.62 BIC=-2204.9