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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