Procedure
The Box-Jenkins strategy is a systematic, iterative approach used to find the most appropriate ARIMA model for a specific time series.
- Model Specification (Identification): Analyze time series plots and statistical properties (like the ACF) to select a candidate model. Follow the principle of parsimony by choosing the simplest model that fits the data.
- Model Fitting: Estimate the unknown parameters of the candidate model. Common estimation methods include Least Squares, Maximum Likelihood, and the Method of Moments.
- Model Diagnostics: Evaluate the quality of the fitted model. Check if the model assumptions are satisfied and verify that the residuals behave like white noise.
- Iteration: If the diagnostics reveal deficiencies in the model, return to Step 1 to specify a different candidate.
Expected Outcome: A statistically sound and parsimonious model ready for high-quality forecasting.
Tip
Troubleshooting: If a model is overly complex with too many parameters, it may “overfit” the training data, leading to poor performance on new data. Always prioritize the simplest model if accuracy remains comparable.