MAT 3379 - Summer 2022 Introduction to Time Series Analysis
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MAT 3379 - Summer 2022
Introduction to Time Series Analysis
Study Guide for Final Exam
1 Topics
1. Evaluate covariance function in simple models, check if the model is sta- tionary.
2. Check if ARMA model is stationary and causal.
3. Derive the linear representation for AR(1), ARMA(1,q) and calculate co- variance using the linear representation.
4. Calculate autocovariance function for AR(1), AR(2), AR(3), ARMA(1,1) using the recursive approach.
5. Find the best linear predictor for AR(1), AR(2) using the Yule-Walker procedure. Calculate MSPE.
6. Find the best linear predictor for MA(1), MA(2) models using Yule-Walker procedure (for small n).
7. Use the Durbin-Levinson algorithm for AR(1), AR(2), MA(1), MA(2), ARMA(1,1) (small n).
8. Confidence intervals for the mean in ARMA models.
9. Use the Yule-Walker procedure to derive the estimators of parameters in AR(p) models.
10. MLE for AR(p) models.
11. MLE for MA(1) or MA(2) models.
12. ”Practical” question for AR(1) and AR(2): Yule-Walker estimation and prediction from a partial R output.
13. Nonlinear time series.
2022-07-20