Time Series Analysis: Lecture Notes

Welcome!

These are the lecture notes for EN.553.439/639 Time Series Analysis, based on the Cryer and Chen textbook Time Series Analysis: With Applications in R and Time Series Lecture notes of Dr Torcaso.

The notes are typed by Yue Wu. The notes are authored and maintained by Sergey Kushnarev, and include:

• Topic summaries
• Mathematical derivations
• R notebooks with code and data examples
• Figures and simulation results

Think of these notes as a companion to our lectures and discussions, not a substitute. You’ll likely spot some typos and errors, so always double-check with the textbook and other course materials. If you catch an issue or have a question, please don’t hesitate to reach out to me via email or during office hours.

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📚 Lecture Notes

• Lecture 1: Introduction to Time Series Analysis
• Lecture 2: Stationarity
• Lecture 3: Q-dependent CLT. MA(q), General Linear Process. Causality
• Lecture 4: AR(1), Yule-Walker method, AR-polynomial
• Lecture 5: AR(p): causality, YW method, GLP representation,
• Lecture 6: Recursive equations, ACVF for AR(2), AR(p), Invertibility
• Lecture 7: ARMA(1,1), ARMA(p,q): GLP representation, YW method, ACVF.
  • Rnotebook: Visualizing Time Series
• Lecture 8: Trends, Estimation of the mean Yt, Rnotebook: regression approach, residual analysis
  • Rnotebook: Regression Methods in Time Series
• Lecture 9: Residual Analysis. Sample ACF
• Lecture 10: ARIMA(\(p,d,q\)), Overdifferencing, GLP-like representation
• Lecture 11: Transformations of TS, sample ACF, Bartletts Theorem, Hypothesis test for MA(q)
• Lecture 12: PACF, sample PACF, Durbin-Levinson recursion
• Lecture 13: EACF, Specification of some TS, Unit Root test.
• Lecture 14: Parameter Estimation: method of moments
  • Rnotebook: Model Specification
• Lecture 15: Parameter Estimation: Method of Moments, conditional least squares
• Lecture 16: Parameter Estimation: MLE, unconditional least squares
  • Rnotebook: Parameter Estimation
• Lecture 17: Diagnostics: residuals, overfitting
  • Rnotebook: Model Diagnostics
• Lecture 18: Forecasting
• Lecture 19: Forecasting: RW, ARMA(1,1), ARIMA, EWMA
  • Rnotebook: Forecasting
• Lecture 20: SARIMA = Seasonal ARIMA
  • Rnotebook: SARIMA = Seasonal ARIMA
• Lecture 21: Cross-Correlation Function, Spurious Regression
• Lecture 22: Spurious Regression, Prewhitening
  • Rnotebook: Spurious Regression
• Lecture 23: ARCH/GARCH Models
  • Rnotebook: ARCH/GARCH

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🔗 Resources

• [Course Syllabus (PDF)] TBD
• RStudio Cloud Project