Autocorrelation: Reading ACF and PACF Plots
Explore how to interpret autocorrelation and partial autocorrelation plots to identify lag dependencies within time series data. Learn to distinguish patterns like white noise, autoregressive, and moving-average signals. Understand the importance of correct data ordering and stationarity transformations before model selection to improve forecasting accuracy.
After differencing removes a changing baseline, consecutive values can still move together. If a daily demand series rises above its usual level today and tends to remain high tomorrow, the series retains information across time. We need to detect that lag dependence before choosing a forecasting model.
The autocorrelation function (ACF) measures the correlation between a series and a shifted copy of itself. A lag of 1 compares each observation with the observation immediately before it. A lag of 7 compares each observation with the value seven time steps earlier.
The partial autocorrelation function (PACF) measures the relationship at one lag after accounting for all shorter lags. For example, a PACF value at lag 3 asks whether today still relates directly to the value three periods ago after lags 1 and 2 have already explained what they can.
ACF and PACF plots diagnose structure. They do not produce forecasts, and a visible spike does not by itself prove that a lag belongs in a model.
Aligning observations by lag
Before reading a plot, we need to see the paired observations that correlation uses. Suppose a short series records daily package counts as 10, 13, 15, 14, and 18. A lag of 1 aligns 13 with 10, 15 with 13, and so ...