Good afternoon!

I'm trying to model a time series on the following data, which represent a monthly consumption of juices:

>x<-scan()
1: 2859  3613  3930  5193  4523  3226  4280  3436  3235  3379  3517  6022
13:  4465  4604  5441  6575  6092  6607  6390  6150  6488  5912  6228 10196
25:  7612  7270  8617  9535  8449  8520  9148  8077  7824  7991  7660 12130
37:  9135  9512  9631 12642 11369 12140 13953 12421 11081
46: 
Read 45 items

> arima(x,order=c(2,1,2), seasonal=list(order=c(0,1,0), period=12))->l
> acf(l$resid)
> sd(l$resid)
> Box.test(l$resid)

Now, my problem:
1. All the analysis that i have seen regarding ARIMA modeling, had the residuals acf,  within the confidence interval, while my residual acf at first lag is very close to one (and going out of the confidence interval), even if the Box.test can not reject the null hypothesis of a significant acf for all my residuals.
I imagine that i am doing something wrong with my model. Is the acf at lag 1 a sign that my residuals are not white noise, or what is wrong here?

2. What would be the impact of an inappropriate model on the confidence interval for a future prediction? (disregarding the fact  that an inappropriate model would give a bad forecast on future value, could it have also an impact on enlarging the interval?)

3. As a rule of thumb, do you chose your model by selecting the lowest AIC, or by the lowest standard deviation of the residuals ?

Thank you and have  a great day!



       
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