Discuss the role of information criteria in time series model selection.
Instruction: Explain what information criteria are and how they are used in the selection of time series models.
Updated
Example Answer
Information criteria compare fitted models by balancing likelihood and parameter count. AIC is minus twice the maximized log likelihood plus twice the number of estimated parameters. BIC uses a parameter penalty based on the log of sample size. AICc adds a small-sample correction; ordinary AIC is not that corrected formula.
I would use them only where the likelihoods and observations are comparable. In ARIMA selection, changing the differencing order changes the data used in the likelihood, so a raw comparison across those orders can be misleading. Lower values help screen candidates; they do not prove good forecasts. I would check residuals, stability, and rolling-origin accuracy before choosing the model, and explain which criterion guided which part of the selection.
Make it your own
Identify the candidate family, what is held comparable, and the final forecasting check.
Why this works
It gives the formulas' meaning and their comparison boundary.
Follow-up to practice
Why might AIC values be incomparable across differencing orders?