I wish to better understand the details of ARIMA models and how to interpret ACF and PACF graphs in determining what type of ARIMA model to use.
From my studies so far, I understand that there are three parts to the model, the AR, I and MA.
In order to predict future values from the time series there are a number of requirements on the time series data:
It must be stationary i.e. have the following properties:
- constant variance
- void of seasonality
- no trend
These properties can be achieved by differencing to remove the trend and seasonality and logs can be taken to flatten the variance.
Now that we have a "white noise" signal we can perform our prediction. Before doing so we need to determine the order of the AR and MA components in order to make an accurate prediction.
By taking the ACF and PCF of the "white noise" data we can determine if the ACF or the PCF shut off quickly or decay exponentially as t increases. If the ACF shuts off quickly this is indicative of "white noise" since there is no autocorrelation between serial time points and informs us of the q value/order of the MA model e.g MA(2) whereas if the PACF shuts off after 2 lags, this provides the p value/order of the AR model e.g AR(2).
From my readings I have scribbled together a flow chart of how in my head I think the process flows. I would be very grateful if you could have a look and tell me if I am wildly off target in my approach.
I have been reading Rob Hyndman's book online and using my process in the diagram below, I do not make the correct choice of ARIMA model for Figure 8.9 so clearly my understanding of the approach is incorrect.
In this figure neither the ACF or PACF shuts off quickly and I wouldn't describe them as decaying exponentially either. Is there a more intuitive approach to understanding these plots?