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Is there any straight way to know the value of p and q if ACF and PACF plots are both dies down?(d=0) enter image description here 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. enter image description here any suggestion or source recommendation to disproof or back up my guess? sorry for my broken English

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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 enter image description here , 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.

Here is the original acf/pacf enter image description here and the acf of an automatically identified useful model's errors enter image description here along with a plot of the mode; s residuals enter image description here

The initial model here (note an ar(3) without lag 2) enter image description here was tried and iterated via diagnostic checking to the final model enter image description here and here enter image description here .

The cleansed vs actual graph is enlightening enter image description here with the Actual/Fit and Forecast graph here enter image description here

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.

enter image description here

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  • $\begingroup$ Thank you for answering my question sir. Yes indeed this software that I currently use can't compute (3,0,0) and (0,0,0)(1,0,0)3 (* ERROR * Model cannot be estimated with these data.). I'll try another software to be sure as you suggest. I'm sorry I was forgot to put the training datalink. Although i forgot to include the data, your answer is exactly what I need to confirm my view of the plot's pattern and the possible models. now I can continue my work. Once again thank you $\endgroup$ Apr 22 '20 at 13:34

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