DE 09 Time Series Analysis 2025

Introduction to Time Series Analysis

Logistics

Timings: Tuesdays and Fridays at 11:30 AM, Tutorials on Wednesday 2:00 PM.

TA for the course: Nikhil Rajan and Hariharasudhan Selvaraj.

Prerequisites

The prerequisites are Statistics for Economics, Econometrics, Linear Algebra.

Our undergraduates have already studied a Macroeconomics course that heavily drew elements from Ender’s Applied Econometric Time Series. They have also studied a rigorous Stochastic Processes course.

Course Objectives

This course develops the mathematical foundations underlying the Box–Jenkins methodology. The primary objective is to train students to reason rigorously about time series models—how they are constructed, when they are valid, and why they work. Rather than treating models as recipes, the course aims to equip students with the conceptual tools needed to build, modify, and critically assess models on their own.

A secondary objective is to expose students to the process by which mathematical methods are developed: starting from concrete problems, introducing abstraction only when necessary, and understanding the trade-offs involved in modeling choices.

Classroom discussions focus on conceptual, mathematical and programming exploration. Examinations and assignments test precision, rigor, and depth of understanding.

Syllabus

  • Difference equations and their analysis using matrices and lag operators.
  • Stationarity, covariance stationarity, and ergodicity.
  • ARMA processes: stability, invertibility, and Wold’s decomposition.
  • Linear minimum mean squared error (MMSE) forecasting.
  • Wiener–Kolmogorov representations and forecast updating.
  • Brief review of multilinear regression.
  • Maximum likelihood estimation for Gaussian time series models.
  • Akaike Information Criteria.
  • Ljung Box test, Normality tests, Dickey-Fuller tests.
  • Box–Jenkins modeling philosophy.

Course Resources

To support the course, I have developed a custom flashcard-based resource:

👉 https://time-series-flashcards.onrender.com

The site may take 3–5 minutes to load after long periods of inactivity. Last years webpage can also be accessed on this site.

Assignments

Exams

References

  • “Time series analysis” : James D. Hamilton, 1994, (Princeton University Press, Princeton, NJ).