Does it make sense to build a $SARIMA(1,0,0)(2,0,0)$ when $\Phi_1$ is not significant and $\phi_1$ and $\Phi_2$ are? I have this case, here is the plot:
Here are the data:
data<-ts(c(5.8,5.4,5.3,5.4,5.7,5.7,5.6,5.6,6.0, 5.2,4.9,4.9,5.2,5.0,4.9,4.4,4.5,3.7,4.0,4.3,5.0,5.3,5.7,5.3, 5.2,4.9,4.8,4.4,5.1,4.4,4.0,4.8,4.7,4.8,5.1,4.9,5.7,5.0,5.3, 5.4,6.0,5.4,5.6,5.6,5.8,5.8,5.6,5.7,6.3,6.1,6.1,5.6,6.0,5.4), start=c(2004,1), end=c(2017,2), frequency=4)
I'm assuming that the Data Generating Process has a high AR component (so I'm refusing to treat this with a unit root inside).
Here are the ACF and PACF: The first model I choose is an $AR(1)$, but then I would reject the Ljung-Box test of on the residuals. It seems to be a seasonal component like $SARIMA(1,0,0)(1,0,0)$ or $(1,0,0)(2,0,0)$.
I try, but the first gives the seasonal coefficient not significant, and the second, as I mentioned before, gives only the second seasonal coefficient signficant (plus $\phi_1$).
Then residuals are ok, but I'm wondering if this identification is good and could someone suggest to me how to improve it in another way.
This question originated from this nother question here.