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Course Director: Joann Jasiak

Office: 1062 Vari Hall

Tel: 736-2100 ext. 77045, e-mail: jasiakj@yorku.ca

http://www.jjstats.com

This is a graduate course in time series analysis for students who have already taken courses in intermediate or advanced econometrics. The objective is to provide the students with a solid theoretical background and a selection of advanced econometric methods for later use in independent applied research. The course covers linear and nonlinear time series models with applications to macroeconomics and finance and their estimation methods. The content of the course includes: Part 1 - properties of univariate stationary processes and the Autoregressive Moving Average (ARMA) models. Part 2 - departures from stationarity, which include unit root processes and the Generalized Autoregressive Conditional Heteroskedastic (GARCH) models. Part 3 - multivariate models, such as the Vector Autoregressive (VAR) model and the Error Correction (ECM) model, causality and cointegration. The models and their applications will be illustrated by simulations and examples of time series from economics and finance. Additional examples for empirical analysis, simulations and problems will be provided to students in assignments. Suggested software are TSP, S+ and SAS.

__Requirements, Evaluation and Other Details__

2. Final exam 50% (date to be determined)

3. Assignments 20% three sets of empirical and theoretical questions distributed in class to be handed in on approximately February 7, March 7 and the last day of classes.

__Course
Content__

1. Introduction: time series (examples), objectives of time series analysis, model classification

2. Stochastic Processes: difference and lag operators, difference equations and their solutions, stationarity

3. Autocovariance and autocorrelation functions, Wold theorem

4. Conditional mean dynamics: ARMA models, model selection, estimation and testing, forecasting, seasonality

5. Nonstationary series: deterministic and stochastic trends, unit root tests, switching regimes, spurious regressions

6. Conditional variance dynamics: GARCH models, applications, Quasi Maximum Likelihood, estimation and testing

7. Multivariate Time Series Models: VAR - estimation and tests

8. Causality, exogeneity, impulse response function, variance decomposition

9. Cointegration and common trends

10. Error Correction Models (ECM) - estimation and tests

__Books and Other Reference
Materials__

**Required:**

Enders, W., *Applied Econometric Time
Series* 3rd or 4th ed., Wiley, 2010 or 2015

**Suggested**:

**
Books:**

Martin, V., Hurn, S, Harris, D., *Econometric Modelling with Time
Series*,
Cambridge Unversity Press 2013

Wei, William W.S., *Time Series Analysis*, Pearson, 2006 (2nd ed.).

Brockwell, P.J. and R.A. Davis *Introduction
to Time series and Forecasting*, 2nd ed., 2002, Springer

Brockwell,
P.J. and R.A. Davis, *Time Series, Theory and Methods* , 2nd ed., Springer-Verlag, 1991.

Gourieroux,
C. and A. Monfort, *Time Series and Dynamic Models*, Cambridge University Press, 1998.

**
Early Papers (easy to read) :**

Bollerslev, T., R.F. Engle and D.B. Nelson (1993);
"ARCH
Models," in
*Handbook of Econometrics*, Vol. 4.

Campbell, J.Y. and P. Perron, "Pitfalls and
Opportunities: What Macroeconomists Should Know about Unit Roots,"* NBER Macroeconomics Annual*, 1991,
(O.T. Blanchard and S. Fisher, eds.), MIT Press.

Diebold,F.X. and M. Nerlove (1990); " Unit Roots in Economic Time Series," in
*Advances in Econometrics* Vol 8, pp 3-69.

Nelson, C.R. and C.J. Plosser (1982), "Trends and
Random Walks in Macroeconomic Time Series," *Journal of Monetary Economics* 10, pp. 139-162.

Sims, C.A. (1972), "Money, Income and Causality," *American Economic Review* 62, pp. 540-552.

Sims, C.A. (1980), "Macroeconomics and Reality," *Econometrica* 48, pp. 1-48.

Stock,
J.H. and M.W. Watson (1988), "Testing for Common Trends," * JASA* 83, pp. 1097-1107.

Tiao,
G.C. and G.E.P Box (1981), "Modelling Multiple Time Series with Applications," *JASA* 76, pp.
802-816.