What is the significance of the PACF (Partial Autocorrelation Function) in time series analysis?
Instruction: Explain the concept of PACF and how it is used in the context of time series modeling.
Updated
Example Answer
PACF measures the relationship with a lag after accounting for the intervening lags. At lag three, for example, it asks what linear relationship remains after accounting for lags one and two. It is a partial correlation, not proof of a causal effect.
For a stationary pure AR(p) process, the population PACF cuts off after p. A sample plot can suggest candidate orders, but noise, nonstationarity, and mixed ARMA structure make the pattern less clear. I would compare a small set of plausible models, check residuals, and evaluate forecasts on later data. A single significant spike should not be treated as an automatic instruction to add a lag.
Make it your own
Explain one candidate lag order and what would make you reject it after fitting.
Why this works
It separates the theoretical pattern from noisy sample evidence.