How to use ACF to determine seasonality?
Note that the ACF shows an oscillation, indicative of a seasonal series. Note the peaks occur at lags of 12 months, because April 2011 correlates with April 2012, and 24 months, because April 2011 correlates with April 2013, and so on.
Are there any stationary series with ACF patterns?
Many stationary series have recognizable ACF patterns. Most series that we encounter in practice, however, is not stationary. A continual upward trend, for example, is a violation of the requirement that the mean is the same for all t. Distinct seasonal patterns also violate that requirement.
What is the ACF for an AR ( 1 ) model?
A requirement for a stationary AR (1) is that | ϕ 1 | < 1. We’ll see why below. Formulas for the mean, variance, and ACF for a time series process with an AR (1) model follow. This defines the theoretical ACF for a time series variable with an AR (1) model. Note!
How does seasonality affect the log transformed time series?
This represents the size of the seasonal fluctuations and random fluctuations in the log-transformed time series which seem to be roughly constant over the yearly seasonal fluctuation and does not seem to depend on the level of the time series.
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).
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 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.