Is there any straight way to know the value of p and q if ACF and PACF plots are both dies down?(d=0) I have tried ARIMA(3,0,3) because of the third lag that significant on both. I also tried ARIMA(2,0,3) because the one of the P-value shown after final estimates of parameters of ARIMA(3,0,3) are more than 0.05. any suggestion or source recommendation to disproof or back up my guess? sorry for my broken English
without having the actual data I can only surmise .. If you wish to post your data I will give you a definitive statement/conclusion . ..otherwise here is my guess
Given that there is not a seasonal/quarterly effect in the data , I would think that a model of the form (0,0,0)(1,0,0)3 might be appropriate .. this is the same as a model (3,0,0) WITHOUT the first two ar lags BUT probably your software doesn't allow that as this one does ...
Whereas the acf and pacf SEEM similar there is more "chatter" in the ACF thus ties go to the AR side. If the obverse was true then the conclusion would be an ma model.
EDITED AFTER RECEIPT OF 36 MONTHLY VALUES:
Model identification guidelines are "rules of thumb" and often are naive when data has "complications" . Your data , typical of national account series has a very significant quarterly effect AND a monthly deterministic Christmas effect (month 12) AND two data points that are anomalies. As I had previously reflected (before receiving the data) these complications/opportunities can obfuscate/confuse simple approaches/algorithms designed to identify a useful model.
If you look "closely" at the within year pattern you can now "see" the quarterly effect more clearly.
I used AUTOBOX a time series package that I have helped to develop precisely because simple rules work seldomly , if at all. In closing "all models are wrong" but this model seems useful .
Anomalies , particularly the significant ones that you have ) tend to suppress the acf as the model error variance is bloated by them creating an "Alice in Wonderland Effect" aptly reflected by my friend and colleague Prof. Keith Ord of Georgetown University.
As to why your software returned an ERROR when you specified a seasonality of "3" , you should address that question to the author who perhaps didn't anticipate data like yours.