An Empirical Characteristic Function Approach to VaR under a Mixture of Normal Distribution with Time-Varying Volatility
This paper considers Value at Risk measures constructed under a discrete mixture of normal distribution on the innovations with time-varying volatility, or MN-GARCH, model. We adopt an approach based on the continuous empirical characteristic function to estimate the param eters of the model using several daily foreign exchange rates' return data. This approach has several advantages as a method for estimating the MN-GARCH model. In particular, under certain weighting measures, a closed form objective distance function for estimation is obtained. This reduces the computational burden considerably. In addition, the characteristic function, unlike its likelihood function counterpart, is always uniformly bounded over parameter space due to the Fourier transformation. To evaluate the VaR estimates obtained from alternative specifications, we construct several measures, such as the number of violations, the average size of violations, the sum square of violations and the expected size of violations. Based on these measures, we find that the VaR measures obtained from the MN-GARCH model outperform those obtained from other competing models.
|Date of creation:||Dec 2008|
|Date of revision:|
|Contact details of provider:|| Postal: Waterloo, Ontario, N2L 3G1|
Phone: (519) 888-4567 ext 33695
Fax: (519) 725-0530
Web page: http://economics.uwaterloo.ca/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Schwert, G William, 1989.
" Why Does Stock Market Volatility Change over Time?,"
Journal of Finance,
American Finance Association, vol. 44(5), pages 1115-53, December.
- G. William Schwert, 1988. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
- Knight, John & Yu, Jun, 1999.
"Empirical Characteristic Function in Time Series Estimation,"
220, Department of Economics, The University of Auckland.
- Knight, John L. & Yu, Jun, 2002. "Empirical Characteristic Function In Time Series Estimation," Econometric Theory, Cambridge University Press, vol. 18(03), pages 691-721, June.
- Vlaar, Peter J G & Palm, Franz C, 1993. "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 351-60, July.
- Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Markus Haas, 2004.
"Mixed Normal Conditional Heteroskedasticity,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 2(2), pages 211-250.
- Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
- Hamilton, James D. & Susmel, Raul, 1994.
"Autoregressive conditional heteroskedasticity and changes in regime,"
Journal of Econometrics,
Elsevier, vol. 64(1-2), pages 307-333.
- Tom Doan, . "RATS programs to estimate Hamilton-Susmel Markov Switching ARCH model," Statistical Software Components RTZ00083, Boston College Department of Economics.
- BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K., 1999.
"Adaptive polar sampling with an application to a Bayes measure of value-at-risk,"
CORE Discussion Papers
1999057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- K. Van Dijk & Luc Bauwens & Charles Bos, 2000. "Adaptive Polar Sampling With An Application To A Bayes Measure Of Value-At-Risk," Computing in Economics and Finance 2000 145, Society for Computational Economics.
- Luc Bauwens & Charles S. Bos & Herman K. van Dijk, 1999. "Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk," Tinbergen Institute Discussion Papers 99-082/4, Tinbergen Institute.
- Bauwens, L. & Bos, C.S. & van Dijk, H.K., 1999. "Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk," Econometric Institute Research Papers TI 99-082/4, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Jose A. Lopez, 1999.
"Methods for evaluating value-at-risk estimates,"
Federal Reserve Bank of San Francisco, pages 3-17.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
- Gray, Stephen F., 1996.
"Modeling the conditional distribution of interest rates as a regime-switching process,"
Journal of Financial Economics,
Elsevier, vol. 42(1), pages 27-62, September.
- Tom Doan, . "RATS programs to replicate Gray's 1996 Regime Switching GARCH paper," Statistical Software Components RTZ00080, Boston College Department of Economics.
When requesting a correction, please mention this item's handle: RePEc:wat:wpaper:08008. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Pat Gruber)
If references are entirely missing, you can add them using this form.