Economics 408 
Time Series Econometrics

Spring 2023

This is an introduction to modeling time series data. The prerequisites are mathematical economics (Econ 331), or math through multivariable calculus, and econometrics or mathematical statistics.



James D. Hamilton, Time Series Analysis (QA 280.H264 1994)
David F. Hendry, Dynamic Econometrics (HB 141.H458 1995)

These are the sources of my course notes. I do not recommend buying either book.

Other readings are available from the Blackboard site:
Johnston and DiNardo, Econometric Methods, Fourth Edition (J&D).
Maddala, G.S., Introduction to Econometrics, Second Edition (M).
Moody, Basic Econometrics with Stata (BES)


Forecasting test




Modeling test


Term paper


There is no final exam.


All homework assignments must be completed on time.

Grading scale: A 90-100, B 80-89, C 70-79, D 60-69. Numerical grades are rounded up.

Introduction and Review

Matrix derivatives

Least squares

Assignment 1: matrix algebra, write a Stata multiple regression program

Gauss-Markov theorem

Trigonometry (Hamilton 704-711)

Complex numbers
Circular functions
DeMoivre's Theorem

Difference Equations (Hamilton ch. 1)

Dynamic multipliers (P&R 413-431)
Eigenvalues (Johnston, J. "The Eigenvalue Problem")
Stability conditions: roots inside the unit circle

Lag Operators (Hamilton ch. 2)

Lag polynomials
Stability conditions: roots outside the unit circle

Stationary Time Series Models

Univariate Time Series Models and ARMA's 
(P&R 463-601; Hamilton ch. 3, 4; J&D 204--215)

Stationary ARMA processes
White noise
Covariance stationarity
MA(q) processes
AR(p) processes

Digression: nonstationary processes and ARIMA

Box-Jenkins forecasting philosophy (M, 542-549;J&D 228-234)

a. Identification
b. Estimation
c. Forecasting

Assignment: forecasting

Multi-Equation models: VAR's 
(P&R 399-407,431-435; M, 578-80, 592-7; Hamilton ch. 11;J&D 287-301)

VAR's and reduced form equations
Matrix notation
Stability conditions
Impulse response functions
Hypothesis tests
Granger causality tests (P&R 216-7; M, 393-4)
Assignment: VAR (crime and punishment)

Models of Nonstationary Time Series

Unit Roots (Hamilton ch. 15, 17)

Trend Stationary vs Difference Stationary Models (M, 258-264)
Persistence of shocks
Dickey-Fuller tests (P&R 507-513; M 582-588; J&D 215-228; BES Ch. 15, 16)
Assignment: Diebold and Senhadh, "The Uncertain Unit Root in Real GNP: Comment," American Economic Review, 86, 1996, 1291-98.
Assignment: Lothian and Taylor "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy 104, 1996, 488-509.

Unit root tests and structural breaks

Is Crime a Random Walk?

Multivariate Time Series Models: Cointegration (Hamilton ch. 19)

Cointegration and long term equilibria
    (Granger, "Introduction." from Engle, R.F. and Granger, C.W.J., Long Run Economic Relationships,
    Oxford University Press, 1991.)
Tests for cointegration (P&R 513-516; M, 588-600; J&D 301-305)
    Enders, W. "Characteristic Roots, Rank, and Cointegration." 385-405.
Estimating the cointegration vector (dynamic ordinary least squares)
Assignment: Warner, "Does world investment demand determine U.S. imports?" American Economic Review, 84, 1994, 1409-1422.
Assignment: Demand for money in the US, Stock and Watson, "A simple Extimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, 61, 783-820, 1993. Read section 7 (Stock&Watson.pdf).


Modeling Time Series Data: David Hendry and the British School 
(Hendry, Dynamic Econometrics)

Levels of knowledge (ch 1)
Econometric Concepts (ch 2)
Nonsense regressions and spurious detrending (ch 4)
Exogeneity (ch 5)
Typology of linear dynamic models (ch 7)
Dynamic systems (ch 8)
Theory of reduction (ch 9)
Simultaneous equations (ch 11)
Encompassing (ch 14)
Modeling issues (ch 15)
Example: demand for money in the U.K.(ch 16)

Hendry and Ericsson, "An econometric analysis of U.K. money demand in monetary trends in the
    United States and theUnited Kingdom by Milton Friedman and Anna J. Schwartz."
    American Economic Review 81, March 1991, 8-49.
Granger, C.W.J. "Where are the Controversies in Econometric Methodology?"
    (From Granger, C.W.J. Modelling Economic Time Series, Oxford: Oxord University Press, 1990.
Pagan, A.R. "Three Econometric Methodologies: A Critical Appraisal."
    (From Granger, C.W.J. Modelling Economic Time Series, Oxford: Oxord University Press, 1990.
"Professor Hendry's Econometric Methodology."
    (From Granger, C.W.J. Modelling Economic Time Series, Oxford: Oxord University Press, 1990.
Review and integration with mainstream econometrics: Johnston & Dinardo, 244-265.

Panel Data (BES Ch. 17)

Fixed effects model
Panel unit root tests
Panel cointegration tests