I am estimating this model:

But I want to do some analysis of the variables before. In particular, I am interested in fitting some ARIMA models. First, I am doing it for the inflation rate in Mexico.

1. For the ARIMA model, do I need to take into account the other variables or only the values of variation of inflation in previous periods?
2. When I look at the ACF graph it looks like this:

What does it mean to have a lag at 0.5 ? Since I cannot introduce an MA(.5), should I care about it or only take into account lags at t=1 and t=2?

3. When I look at the PACF it looks like this:

Again, what does it mean to have considerable autocorrelation at t=.5 and t=.8? Since I cannot have an AR(.5), should I pay attention to this lags or only to lags at t=1 and t=2? Why?

1. When I use the auto.arima function in R, it produces a model ARIMA(0,0,2), so that is no AR term, but is this not a contradiction with the PACF graph? What should I do? Why?
2. In order to evaluate the goodness of fit I am using Box.test(fit_resid,lag=10,type="Ljung-Box"), but that gives me a p-value of very small, then is that a good fit or not?
3. Finally, should I repeat that for every variable in the model or not? Why?

4. I suggest posting this as a separate question. The implicit role of ACF and PACF in the algorithm of auto.arima is nontrivial (and there is no explicit role for them).
• @CarlosN, the code arima(x,order=c(1,0,1)) would be for ARIMA(1,0,1), so AR(1) and MA(1). Code for ARIMA(12,0,12) would be arima(x,order=c(12,0,12)) and for ARIMA(6,0,6) would be arima(x,order=c(6,0,6)). Some coefficients (e.g. lags between 1 to 5) can be restricted to zero by the argument fixed. – Richard Hardy Oct 18 '18 at 5:18