How to interpret seasonality in ACF and pacf?
As you’ve rightly pointed out, the ACF in the first image clearly shows an annual seasonal trend wrt. peaks at yearly lag at about 12, 24, etc. The log-transformed series represents the series scaled to a logarithmic scale.
How to interpret the seasonality of the log differenced plot?
It is obvious that there is still a seasonal component to the data from the ACF plot. I then tried to use differencing to remove the seasonal component. That resulted in me getting the plot below I feel stuck here. How do I proceed from here ? How do I interpret the seasonality of the Log differenced plot and model the data ?
How does differencing help to stabilize a time series?
This is known as differencing. Transformations such as logarithms can help to stabilise the variance of a time series. Differencing can help stabilise the mean of a time series by removing changes in the level of a time series, and therefore eliminating (or reducing) trend and seasonality.
When is a time series not seasonally integrated?
A sign that a series is not seasonally integrated is significant PACF at seasonal lags after seasonal differencing. For a seasonally non-integrated series, taking seasonal differences does not solve a problem but rather creates one (the problem of overdifferencing).
Is there a lag between ACF and pacf plots?
Armed with the Cheatsheet let’s tackle few sample ACF and PACF plots Looking at this you see a significant Lag in ACF at 12 and geometric decay at each Lag 12 i.e. 24, 36, 48 etc in PACF. Right away you know this is the Seasonal component of the ARIMA (because of the 12 Lag intervals).
When to use ACF and pacf in AR models?
The ACF and PACF should be considered together. It can sometimes be tricky going, but a few combined patterns do stand out. (These are listed in Table 3.1 of the book in Section 3.3). AR models have theoretical PACFs with non-zero values at the AR terms in the model and zero values elsewhere.
How are AR and MA determined from ACF plots?
Both the Seasonal and the non-Seasonal AR and MA components can be determined from the ACF and PACF plots. Since this is a Cliff’s Notes edition, let’s start with the Cheatsheet first, and then I will show you how to map the Cheatsheet patterns to the actual ACF and PACF plots.