Student : Becar Iuliana Supervisor: Professor Moisa Altar

DISSERTATION PAPER Modeling and Forecasting the Volatility of the EUR/ROL Exchange Rate Using GARCH Models.

• Student :Becar Iuliana

• Supervisor: Professor Moisa Altar

Table of Contents

• The importance of forecasting exchange rate volatility.

• Data description.

• Model estimates and forecasting performances.

• Concluding remarks.

Why model and forecast volatility?

• Volatility is one of the most important concepts in the whole of finance.

• ARCH models offered new tools for measuring risk, and its impact on return.

• Volatility of exchange rates is of importance because of the uncertainty it creates for prices of exports and imports, for the value of international reserves and for open positions in foreign currency.

Volatility Models.

• ARCH/GARCH models.

• Engle(1982)

• Bollerslev(1986)

• Baillie, Bollerslev and Mikkelsen (1996)

• ARFIMA models.

• Granger (1980)

Data description

• Data series: nominal daily EUR/ROL exchange rates

• Time length: 04:01:1999-11:06:2004

• 1384 nominal percentage returns

Descriptive Statistics for the return series.

Heteroscedasticity

Autocorrelation and Partial Autocorrelation of Squared Returns

Stationarity

• Unit Root Tests for EUR/ROL return series.

Model estimates and forecasting performances.

• Methodology.

• Ox Professional 3.30 G@RCH4.0

• 4.01.1999-30.12.2002 (1018 observations) for model estimation

• 06.01.2003-11.06.2004 (366 observations) for out of sample forecast evaluation.

• The Models.

• Two distributions: Student, Skewed Student, QMLE.

• The Mean Equations:

• 1. A constant mean

• 2. An ARFIMA(1,da,0) mean

• 3. An ARFIMA(0, da,1) mean

The variance equations.

• GARCH(1,1) and FIGARCH(1,d,1) without the constant term and with a non-trading day dummy variable.

• The estimated twelve models.

• Examining the models page 30 to 34 the conclusions are:

• The estimated coefficients are significantly different from zero at the 10% level.
• the ARFIMA coefficient lies between
• which implies stationarity.
• all variance coefficients are positive and

In-sample model evaluation. Residual tests. GARCH models.

In-sample model evaluation. Residual tests. FIGARCH models.

Out-of-sample Forecast Evaluation

• Forecast methodology

• - sample window: 1018 observations

• - at each step, the 1 step ahead dynamic forecast is stored

• for the conditional variance and the conditional mean

• -dynamic forecast is programmed in OxEdit

• G@RCH3.0 package

• Benchmark: ex-post volatility = squared returns.

Measuring Forecast Accuracy.

• The Mincer-Zarnowitz regression:

• The Mean Absolute Error:

• Root Mean Square Error (standard error):

• Theil's inequality coefficient -Theil's U:

One Step Ahead Forecast Evaluation Measures.

2. Forecasting the conditional mean. Loss functions.

3. Forecasting the conditional variance. Loss functions.

Concluding remarks.

• In-sample analysis:

• Residual tests:

• -all models may be appropriate.

• -the Student distribution is better than the Skewed Student.

• Out-of-sample analysis:

• -the FIGARCH models are superior.

• -for the conditional mean the Student distribution is

• superior.

• -the two ARFIMA mean equations don't provide a better

• forecast of the conditional mean.

• - for the conditional variance the Skewed Student

• distribution is superior.

Concluding remarks.

• Model construction problems;

• Further research:

• -option prices, which reflect the market’s expectation

• of volatility over the remaining life span of the option.

• -daily realized volatility can be computed as the sum of

• squared intraday returns

Bibliography

• Alexander, Carol (2001) – Market Models - A Guide to Financial Data Analysis, John Wiley &Sons, Ltd.;

• Andersen, T. G. and T. Bollerslev (1997) - Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts, International Economic Review;

• Andersen, T. G., T. Bollerslev, Francis X. Diebold and Paul Labys (2000)- Modeling and Forecasting Realized Volatility, the June 2000 Meeting of the Western Finance Association.

• Andersen, T. G., T. Bollerslev and Francis X. Diebold (2002)- Parametric and Nonparametric Volatility Measurement, Prepared for Yacine Aït-Sahalia and Lars Peter Hansen (eds.), Handbook of Financial Econometrics, North Holland.

• Andersen, T. G., T. Bollerslev and Peter Christoffersen (2004)-Volatility Forecasting, Rady School of Management at UCSD

• Baillie, R.T., Bollerslev T., Mikkelsen H.O. (1996)- Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, Vol. 74, No.1, pp. 3-30.

• Bollerslev, Tim, Robert F. Engle and Daniel B. Nelson (1994)– ARCH Models, Handbook of Econometrics, Volume 4, Chapter 49, North Holland;

• Diebold, Francis and Marc Nerlove (1989)-The Dynamics of Exchange Rate Volatility: A Multivariate Latent factor Arch Model, Journal of Applied Econometrics, Vol. 4, No.1.

• Diebold, Francis and Jose A. Lopez (1995)- Forecast Evaluation and Combination, Prepared for G.S. Maddala and C.R. Rao (eds.), Handbook of Statistics, North Holland.

• Enders W. (1995)- Applied Econometric Time Series, 1st Edition, New York: Wiley.

Bibliography

• Engle, R.F. (1982) – Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica, 50, pp. 987-1007;

• Engle, R.F. and Victor K. Ng (1993) – Measuring and Testing the Impact of News on Volatility, The Journal of Finance, Vol. XLVIII, No. 5;

• Engle, R. (2001) – Garch 101: The Use of ARCH/GARCH Models in Applied Econometrics, Journal of Economic Perspectives – Volume 15, Number 4 – Fall 2001 – Pages 157-168;

• Engle, R. and A. J. Patton (2001) – What good is a volatility model?, Research Paper, Quantitative Finance, Volume 1, 237-245;

• Engle, R. (2001) – New Frontiers for ARCH Models, prepared for Conference on Volatility Modelling and Forecasting, Perth, Australia, September 2001;

• Hamilton, J.D. (1994) – Time Series Analysis, Princeton University Press;

• Lopez, J.A.(1999) – Evaluating the Predictive Accuracy of Volatility Models, Economic Research Deparment, Federal Reserve Bank of San Francisco;

• Peters, J. and S. Laurent (2001) – A Tutorial for G@RCH 2.3, a Complete Ox Package for Estimating and Forecasting ARCH Models;

• Peters, J. and S. Laurent (2002) – A Tutorial for G@RCH 2.3, a Complete Ox Package for Estimating and Forecasting ARCH Models;

• West, Kenneth and Dongchul Cho (1994)-The Predictive Ability of Several Models of Exchange Rate Volatility, NBER Technical Working Paper #152.

Appendix 1.

Appendix 2

Appendix 3

Appendix 4

Appendix 5

Appendix 6

Appendix 7

Appendix 8

Appendix 9

Appendix 10

Appendix 11

Appendix 12

Appendix 15.Phillips-Perron Test.