I don't know which model to fit to these ACF and PACF. Is it an AR(3) or something else? This is the ACF plot that I am getting.

And here is the PACF plot.

  • $\begingroup$ could you provide more background information on what you were doing to generate these? $\endgroup$
    – ReneBt
    Apr 29, 2019 at 8:03

2 Answers 2


There are suspicious peaks at lag 12. I suspect you have monthly data, and these peaks come from yearly seasonality. Consider taking seasonal differences, then plotting the ACF and PACF plots for these differences. Here are some hints on using (P)ACF to determine ARIMA orders.

In general, the Box-Jenkins approach is outdated. Consider using a more modern approach like choosing models based on AIC, as implemented in auto.arima() in the forecast package for R.


The ACF and the PACF are summary statistics and trying to parse the appropriate model is nigh impossible unless you restrict yourself to very simple (pure arima models) and even then it is a daunting task. Fitting a set of presumptive models using a list based approach seldomly is satisfactory except in the rare case of no latent deterministic structure..

Your data may need auto-regressive or moving-average structure along with regular differencing , seasonal differencing, and deterministic structure like level/step shifts , local time trends, pulses , seasonal pulses. Additionally there may be the need for the data to be partitioned due to changes in parameters over time or error variance changes over time or error variance-expected value linkages. Only your data knows for sure ... which is why I ask you to post your data and I will try and help further.

You might want to follow my guidance here Significant lags at ACF and PACF plots in GLM: what should I do? regarding the ways to match asc/pacf to simple arima models.

The more comprehensive/modern way to identify models is to integreate arima with deterministic structure as outlined here https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf reflecting an iterative approach not a one-step approach as is often suggested here.

If the data is deemed confidential simply scale it by subtracting a constant and dividing it by another constant


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