Advanced time series
Graduate · Statistics
Syllabus focus
Standard syllabus · Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Standard syllabus
Linear time series theory
- Stationarity, ergodicity, and autocovariance
- ARMA, ARIMA, and SARIMA models
- Identification, estimation, and diagnostics
- Forecasting theory: optimal linear predictors
- Seasonal and long-memory models (intro)
State space and spectral methods
- State space models and Kalman filter
- Structural time series models
- Spectral representation and periodograms
- Multivariate time series (VAR intro)
- Cointegration and error correction (overview)
Nonlinear and financial time series
- ARCH/GARCH models for volatility
- Threshold and regime-switching models (intro)
- Functional time series (overview)
- High-frequency data challenges (preview)
Theoretical / proof-based
Asymptotic theory for time series
- Asymptotics for ARMA MLE
- CLT for martingale difference sequences
- Spectral estimation consistency
- Unit root asymptotics (introduction)
- Proofs of optimality for BLUP forecasts
- Large-sample theory for GARCH (overview)
Additional applied practice
- Reviewing assumptions with domain experts
- Documenting analysis choices for reproducibility
- Sensitivity analyses for key modeling decisions
- Connecting results to the original research or business question
Notes
Graduate sequel to undergraduate time series. Includes state space models, spectral analysis, and asymptotic theory for ARMA estimators.