DE 09 Time Series Analysis 2024

Introduction to Time Series Analysis

Logistics

Timings: Wednesdays and Fridays at 11:00 AM, Tutorials on Tuesday 2:00 PM.

TA for the course: Megana Prabha

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

Most time series courses around the world focus heavily on software applications. In contrast, this course focuses on mathematically investigating all the steps of Box-Jenkins philosophy. The objective of this course is to train the students in rigorous foundations of Time Series Analysis, in the hopes of producing creative economists who are not afraid to build their own models. Another objective was to give a sneak-peek into how mathematical methods are conceived.

In the classroom the students explore creative mathematical questions and in exams/assignments a rigorous understanding of the subject is tested.

Syllabus

Multilinear regression methods (brief review).

  • The theory of difference equations using matrices and lag operators.
  • Stationarity, covariance stationarity, and ergodicity of time series.
  • ARMA processes: stability and invertibility of MA processes, Wold’s theorem.
  • Minimum mean squared error (MMSE) linear forecasts, including forecast updates for ARMA processes, Wiener-Kolmogorov Representations.
  • Maximum likelihood estimation for Gaussian white noise.
  • Box-Jenkins modelling philosophy.
  • Models of non-stationary time series: linear time trends and unit root processes.
  • Akaike’s Information Criteria and its information theoretic motivations.
  • Dickey-Fuller tests and its theory: Derivation of asymptotic distribution using Wiener processes.

I could not find a good resource for studying mathematical time series online. So I created a flashcard website for my course content. The flashcards website may take 3-5 minutes to load when there is sustained period of inactivity.

Assignments

Exams

References

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