**Overview:** In the course, we study the empirical modeling of the volatility (i.e., the unconditional and conditional variance) of economic variables. In particular, we concentrate on the specification, estimation and interpretation of different univariate generalized conditional heteroskedasticity (GARCH) models. The approach is applied, and the applications are mainly macroeconomic, such as the modeling of growth and inflation uncertainty.

**Prerequisites:** Basic knowledge of macroeconomics, econometrics and statistics is assumed. Moreover, previous experience with time series and knowledge of linear time series models is helpful, although such models are reviewed briefly at the beginning of the course. *Eviews* is the software package that will be used to demonstrate the methods in class, but any available computer program may be used for the assignments and the term paper.

**Textbooks:** The lectures will not directly follow any textbook, but the relevant parts of the following may be useful as supplementary reading.

- Franses & van Dijk: Non-Linear Time Series Models in Empirical Finance, Cambridge University Press.
- Tsay: Analysis of Financial Time Series. Wiley.
- Taylor: Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.

**Lectures:** 24 hours, 16.3. – 4.5.2007 (23.3 and 30.3. excepted) Wednesdays and Fridays 12 – 14, ECONOMICUM SH 1.

Lecture slides as well as links to supplementary material such as programs and data used in class will be posted *here* in advance. Skimming through the slides before the lecture is highly advisable, and you should have the printouts available in class.

**Assignments:** There will be two homework assignments during the course, each consisting of a number of exercises. The assignments and the data sets will be posted on this page, and the solutions should be turned in by the due date for credit (see below). Typically the exercises will involve small-scale empirical analyses employing methods presented in class, but there may be some analytical problems as well. In class, I will demonstrate the practical implementation of econometric methods with Eviews, but you are free to use any software package for the assignments.

Assignment 1 (added 4.4., due 13.4.) | CANrgdp.txt |

Assignment 2 (added 19.4., due 27.4.) | GHOS.xls |

**Term Paper:** 40% of the grade will be based on a term paper (see below) that is an emprical research report written on a given topic, employing the methods covered in the course.

**Grading:** The final grade of the course consists of the final exam (40%), the term paper (40%) and the two homework assignments (10% each). All three parts are separately graded on a scale from 1 to 5, and in order to pass the course you must get at least 1 in each.

**Exams:** Final exam 18.5.2007 (12 – 14, ECONOMICUM SH 3-4), retake exam 30.5.2007 (12 – 14, ECONOMICUM SH 3-4).

**BSCW:** All teaching material will be made available through the BSCW (Basic Support for Cooperative Work) tool. The BSCW folder of the course can be found at https://kampela.it.helsinki.fi/bscw/bscw.cgi/0/2622940. For the access right to this folder, send an e-mail message containing your own e-mail address (of the form firstname.surname@helsinki.fi if you are a student at the University of Helsinki) to the lecturer. Instructions on the BSCW are available at http://ok.helsinki.fi/index.php?page=277&language=1 (in Finnish) and at http://bscw.fit.fraunhofer.de/bscw_help-4.2/english/contents.html (in English).

**Tentative Outline**

Depending on time constraints, the list of topics is subject to change. The articles marked with an asterisk (*) are required reading for the exam.

1. *Introduction*

- Ramey, G., and V.A. Ramey (1995), Cross-Country Evidence on the Link between Volatility and Growth. American Economic Review 85, 1138 – 1151.
- Blanchard, O., and J. Simon (2001), The Long and Large Decline in U.S. Output Volatility. Brookings Papers on Economic Activity 2001, 135 – 164.

2. *Linear Models for Conditional Mean*

3. *Linear GARCH Models*

- Engle, R.F. (1982), Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50, 987 – 1006.
- Bollerslev, T. (1986), Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31, 307 – 327.
- French, M.W., and D.E. Sichel (1993), Cyclical Patterns in the Variance of Economic Activity. Journal of Business & Economic Statistics 11, 113 – 119.
- Fountas, S. (2001)*, The Relationship between Inflation and Inflation Uncertainty in the UK: 1885 – 1998. Economics Letters 74, 77 -83.

4. *Nonlinear GARCH Models*

- Caporale, B., and T. Caporale (2002), Asymmetric Effects of Inflation Shocks on Inflation Uncertainty, Atlantic Economic Journal 30, 385 – 388.
- Engle, R.F., and G.G.J. Lee (1993), A Permanent and Transitory Component Model of Stock Return Volatility. Discussion Paper 92-44R, University of California, San Diego.
- Hamori, S. (2000)*, Volatility of real GDP: Some Evidence from the United States, the United Kingdom and Japan. Japan and the World Economy 12, 143 – 152.
- Ho, K.-Y., and A.K.C. Tsui (2003)*, Asymetric Volatility of Real GDP: Some Evidence from Canada, Japan, the United Kingdom and the United States. Japan and the World Economy 15, 437 – 445.
- Lanne, M., and P. Saikkonen (2005), Non-Linear GARCH Models for Highly Persistent Volatility. Econometrics Journal 8, 251 – 276

5. *Forecasting*

6. *GARCH-in-Mean Model*

- Engle, R.F., D.M. Lilien, and R.P. Robins (1987), Estimating Time-Varying Risk Premia in the Term Structure: the ARCH-M Model. Econometrica 55, 391 – 407.
- Caporale, T., and B. McKiernan (1998), The Fischer Black Hypothesis: Some Time-Series Evidence. Southern Economic Journal 64, 765 – 771.
- Kontonikas, A. (2004)*, Inflation and Inflation Uncertainty in the United Kingdom, Evidence from GARCH Modelling. Economic Modelling 21, 525 – 543.