Overview for Topic 1

Introduction

The first topic in the course covers the linear regression model for stationary time series. First, we give an introduction to economic time series, discuss how time-series data differ from cross-sectional data and explore the implications of the concepts stationarity and weak dependence of time series. Second, we consider the linear regression model for stationary time series. We consider how to derive an estimator of the model's parameters using the principles of the method of moments (MM) and maximum likelihood (ML). We discuss the necessary conditions for consistency, unbiasedness, and asymptotic normality of the estimators. Third, we address how to formulate a good model and how we can test if a model is a valid representation of the data.

Learning Goals

Give an account for the important differences between (independent) cross-sectional data and time series data.

Give a precise definition and interpretation of the concept of stationarity of time series data, and explain the consequences of stationarity and weak dependence of a stochastic process.

Evaluate and justify if a time series is stationary based on a graphical analysis.

Give an interpretation of the linear regression model for stationary time series.

Derive the MM estimator and state the assumptions used to derive the estimator.

Give an account of the sufficient conditions for consistency, unbiasedness, and asymptotic normality of the method of moments estimator in the linear regression model.

Construct misspecification tests and analyze to what extent a statistical model is congruent with the data.

Assignment

Assignment 1: To be added.

Schedule and Preparations

You find the schedule and the required preparations for the lectures here: 

Schedule.

Curriculum

Lecture Note 1, Introduction to Time Series Download Lecture Note 1, Introduction to Time Series

(13 pages).

Lecture Note 2, Linear Regression with Time Series Data Download Lecture Note 2, Linear Regression with Time Series Data

(22 pages).

Lecture Note 3, Introduction to Vector and Matrix Differentiation Download Lecture Note 3, Introduction to Vector and Matrix Differentiation

(cursory readings, 6 pages).

Verbeek, M., "A Guide to Econometrics: A Modern Approach", fifth edition.

Lecture Resources

Slides:

Introduction to the Course: To be added.

Introduction to Economic Time Series. To be added.

Linear Regression with Time Series Data. To be added.

Data:

ConsData.in7 and ConsData.bn7.

Ox programs:

Ox simulation program: oxprogram.ox.

Exercises

Problem Set #1: Time Series and Linear Regression. To be added.

Questions

If you have questions for this topic or for Assignment 1, please post them in this post in the Discussion Forum:

Questions for Topic 1 and Assignment 1.