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 teaches the mathematical foundations of the Box–Jenkins approach to time series. Students will learn how time series models are constructed, what assumptions they require, and why the main methods work. The course will not treat ARIMA models as recipes. The goal is to help students build, modify, and critically evaluate models with mathematical clarity.
We will move from concrete examples to abstraction only when needed. Classroom work will combine mathematical reasoning, conceptual discussion, and programming exploration. Assignments and examinations will 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.
Assignments
Exams
References
- “Time series analysis” : James D. Hamilton, 1994, (Princeton University Press, Princeton, NJ).