Acf Pacf interpretation for ARMA modeling

#1
Hi,

I have trouble interpreting acf and pacf of the stationary series depicted.

Could I receive some suggested interpretations, with focus on determining ARMA(p, q) order? Thanks, please let me know if i should give more information.

Edit: I added a spectrum plot. Because if I'm correct the acf is suggesting a seasonal component in my time series?

Kind regards, sander
 
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noetsi

Fortran must die
#2
To me anyhow it does not look like the variance is constant across time so interpretation of the ACF/PACF would be invalid. You might want to log the data and then use the ACF/PACF for that.
 
#4
I tried your suggestion. Log is not changing my situation very much. Acf looks exactly the same.

I included scale location plots, am i right that the variance is reasonably constant?
 

noetsi

Fortran must die
#5
That doesn't look like a logged version of your original data. You should still have one point for every point in the time series, just logged.

I can't figure out which of those is the ACF, although you need both ACF and PACF anyhow to interpret the results.
 
#6
A few comments before selecting the lags:
- the data that you are dealing with have to be stationary. Your first graph seems to indicate stationarity but I would confirm it by running a Dickley-Fuller test. If it is not stationary, you need to differentiate your data one more time.
- You ACF graph display seasonality. You may want to seasonally adjust your data before running your study
- Your ACF and PACF display AR and MA pattern with long persistence (high p and q). It is not recommended, in general, to include a high number of lags as it induces noise.

In order to find the ARMA(p,q) order you need to use the ACF and PACF as well as the AIC and BIC test. The AIC test is more conservative to determine the number of lags. The lowest (absolute) value given by your AIC and BIC test provides the correct number of lags to include in your ARMA model. Then, you need to test the statistical significance of your selected lags with a regression to confirm that your model is correct. Hope this help!
 
#7
Also, I forgot to mention that your threshold that is usually used in the Box-Jenkins procedure is 5% and not 10% as you seem to indicate in your graph. That would reduce by a lot the number of lags to include. Hope this help!