Help understanding ARIMA Model and ACF

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I've read a few resources on ARIMA, and I still have a few outstanding questions. Here is what I know, and let me know if I am incorrect:

Given any set of data, before I can do any forecast, I can use ARIMA to assess the model and make it stationary first.

Before I start, I should plot out the ACF and PCF. The ACF shows the correlation lags and also tells me if there is a trend. If my ACF starts high and gradually dies down, then I should take the first difference. I plot the ACF again and see if there is a pattern. If there is, that means my variance is not stationary. Then, I can consider taking the natural log. I plot the ACF of the differenced logs, and my objective is to have my ACF look "random" and below the confidence shade.

I might still see a spike every 12 months (for example), so that means there is a seasonality. In this case, I need to consider the seasonal component to it.


Is this correct so far? I haven't mentioned PCF, because I still don't know what it represents. If someone can explain, that will be great.

Also, to give some context, I've attached some photos of my data: It includes the difference of the log10, and the ACF, PCF.

question:

for the diff(log10), would you say this is stationary? plotting the raw data, it was trended, taking the first difference it was still not stationary in the variance, so I took the diff(log10), which looked much better...but I still can't decide if this is stationary or not.

for the ACF and PCF:
Would you say there is seasonality, since there are still spikes above the blue line? How would you interpret this ACF and PACF in general?

same question with the PCF. what does this mean?
 

Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
EnumaElish
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Your diff log10 plot does not look stationary. In particular variance seems to increase with time. Also it appears to be autocorrelated. Re pcf here is a source you might find useful: http://people.duke.edu/~rnau/411arim3.htm
 

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