I'm new to Time Series and could need some help! I'm trying to do a ARIMA forecast for (differentiated) consumption expenditures ("dkonsumtionsutgifter" is the variable called in my data. I'm running a ADF test and got the following results:
> ADF.test(dKonsumtionsutgifter)
# # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # #
Augmented Dickey--Fuller test
# # # # # # # # # # # # # # # # # # # #
type: trend drift none
AR1: -0.98 -0.43 1.03
lags: 12 12 12
# # # # # # # # # # # # # # # # # # # #
statistic 1pct 5pct 10pct
tau3 -4.64 -4.04 -3.45 -3.15
phi3 10.93 8.73 6.49 5.47
tau2 -3.16 -3.51 -2.89 -2.58
phi1 5.05 6.70 4.71 3.86
tau1 0.22 -2.60 -1.95 -1.61
So my first question is what tau1, tau2 and tau3 stands for? My guessing is that: tau1 = intercept only, tau2 = intercept and time trend and tau3 is intercept with time and seasonal trend. Is that correct or have I got it completely wrong?
My other question is if my tau1 higher than the critical value could cause any problem for choosing my order for the ARIMA and do the forecast?