Questions about ARIMA

by Carlos N   Last Updated October 16, 2018 18:19 PM

I am estimating this model:

enter image description here

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: enter image description here

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:

enter image description here

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? 4) 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? 5)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? 6) Finally, should I repeat that for every variable in the model or not? Why?

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