Standard syllabus
Advanced time series · Graduate · Math
Learning objectives from the Advanced time series syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Advanced time series — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Linear time series theory
- Stationarity and ergodicity — Stationarity and ergodicity
- Autocovariance — Autocovariance
- ARMA, ARIMA, and SARIMA models — ARMA, ARIMA, and SARIMA models
- Identification and estimation — Identification and estimation
- Diagnostics — Diagnostics
- Forecasting theory: optimal linear predictors — Forecasting theory: optimal linear predictors
- Seasonal — Seasonal
- Long-memory models (intro) — Long-memory models (intro)
State space and spectral methods
- State space models — State space models
- Kalman filter — Kalman filter
- Structural time series models — Structural time series models
- Spectral representation — Spectral representation
- Periodograms — Periodograms
- Multivariate time series (VAR intro) — Multivariate time series (VAR intro)
- Cointegration — Cointegration
- Error correction (overview) — Error correction (overview)
Nonlinear and financial time series
- ARCH/GARCH models for volatility — ARCH/GARCH models for volatility
- Threshold — Threshold
- Regime-switching models (intro) — Regime-switching models (intro)
- Functional time series (overview) — Functional time series (overview)
- High-frequency data challenges (preview) — High-frequency data challenges (preview)
Learning objectives
Click an objective for study materials.
Linear time series theory
- Stationarity and ergodicity — Stationarity and ergodicity
- Autocovariance — Autocovariance
- ARMA, ARIMA, and SARIMA models — ARMA, ARIMA, and SARIMA models
- Identification and estimation — Identification and estimation
- Diagnostics — Diagnostics
- Forecasting theory: optimal linear predictors — Forecasting theory: optimal linear predictors
- Seasonal — Seasonal
- Long-memory models (intro) — Long-memory models (intro)
State space and spectral methods
- State space models — State space models
- Kalman filter — Kalman filter
- Structural time series models — Structural time series models
- Spectral representation — Spectral representation
- Periodograms — Periodograms
- Multivariate time series (VAR intro) — Multivariate time series (VAR intro)
- Cointegration — Cointegration
- Error correction (overview) — Error correction (overview)
Nonlinear and financial time series
- ARCH/GARCH models for volatility — ARCH/GARCH models for volatility
- Threshold — Threshold
- Regime-switching models (intro) — Regime-switching models (intro)
- Functional time series (overview) — Functional time series (overview)
- High-frequency data challenges (preview) — High-frequency data challenges (preview)
Definitions and structure
- Stationarity and ergodicity — Stationarity and ergodicity
- Autocovariance — Autocovariance
- ARMA, ARIMA, and SARIMA models — ARMA, ARIMA, and SARIMA models
- Identification and estimation — Identification and estimation
- Diagnostics — Diagnostics
Proofs and reasoning
- Forecasting theory: optimal linear predictors — Forecasting theory: optimal linear predictors
- Seasonal — Seasonal
- Long-memory models (intro) — Long-memory models (intro)
- State space models — State space models
- Kalman filter — Kalman filter
Abstraction and generalization
- Structural time series models — Structural time series models
- Spectral representation — Spectral representation
- Periodograms — Periodograms
- Multivariate time series (VAR intro) — Multivariate time series (VAR intro)
- Cointegration — Cointegration
Modeling and computation
- Apply stationarity and ergodicity in engineering contexts — Apply stationarity and ergodicity in engineering contexts
- Apply autocovariance in engineering contexts — Apply autocovariance in engineering contexts
- Apply arma, arima, and sarima models in engineering contexts — Apply arma, arima, and sarima models in engineering contexts
- Apply identification and estimation in engineering contexts — Apply identification and estimation in engineering contexts
- Apply diagnostics in engineering contexts — Apply diagnostics in engineering contexts
Data and technology
- Use software to explore advanced time series problems numerically — Use software to explore advanced time series problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- Forecasting theory: optimal linear predictors — Forecasting theory: optimal linear predictors
- Seasonal — Seasonal
- Long-memory models (intro) — Long-memory models (intro)
- State space models — State space models
- Kalman filter — Kalman filter
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Linear time series theory
Stationarity and ergodicity
Coming soon - State space and spectral methods
State space models
Coming soon - Nonlinear and financial time series
ARCH/GARCH models for volatility
Coming soon
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$1,162 · Advanced time series · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.