A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models

Journal of Business and Economic Statistics

Volumn 23, Issue 3, 2005, Pages 346-354

  Bauwens, Luc ^a   Laurent, Sébastien ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Multivariate generalized autoregressive conditional heteroscedasticity models; Multivariate skew density; Multivariate Student density; Value at risk

Indexed keywords

EID: 22544468534     PISSN: 07350015     EISSN: None     Source Type: Journal    
DOI: 10.1198/073500104000000523     Document Type: Article

References (47)

1. Alexander, C. O. (2001), A Practitioners Guide to Financial Data Analysis, New York: Wiley.
2. Alexander, C. O., and Lazar, E. (2003), "Symmetric Normal Mixture GARCH," Discussion Papers in Finance 2003-09, ISMA Center.
3. Andersen, T. G., Bollerslev, T., Diebold, F. X., and Labys, P. (2003), "Modeling and Forecasting Realized Volatility," Econometrica, 71, 579-626.
4. Azzalini, A., and Dalla Valle, A. (1996), "The Multivariate Skew-Normal Distribution," Biometrika, 83, 715-726.
5. Bauwens, L., and Laurent, S. (2002), "A New Class of Multivariate Skew Densities, With Application to GARCH Models," CORE DP 2002/20.
6. Bauwens, L., Laurent, S., and Rombouts, J. (2003), "Multivariate GARCH Models: A Survey," CORE DP 2003/31; Journal of Applied Econometrics, forthcoming.
7. Bollerslev, T. (1987), "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," Review of Economics and Statistics, 69, 542-547.
8. _ (1990), "Modeling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," Review of Economics and Statistics, 72, 498-505.
9. Branco, M. D., and Dey, D. K. (2001), "A Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, 79, 99-113.
10. Diebold, F. X., and Inoue, A. (2001), "Long Memory and Regime Switching," Journal of Econometrics, 105, 131-159.
11. Doornik, J. A. (2001), Ox: Object-Oriented Matrix Programming, 3.0, London: Timberlake Consultants Ltd.
12. Drèze, J. H. (1978), "Bayesian Regression Analysis Using Poly-t Densities," Journal of Econometrics, 6, 329-354.
13. Engle, R. F. (1982), "Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom Inflation," Econometrica, 50, 987-1007.
14. _ (2002), "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, 20, 339-350.
15. Engle, R. F., and González-Rivera, G. (1991), "Semiparametric ARCH Model," Journal of Business & Economic Statistics, 9, 345-360.
16. Engle, R. F., and Sheppard, K. (2001), "Theorical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," mimeo, University of California at San Diego.
17. Fernandez, C., Osiewalski, J., and Steel, M. F. J. (1995), "Modeling and Inference With v-Spherical Distributions," Journal of the American Statistical Association, 90, 1331-1340.
18. Fernández, C., and Steel, M. F. J. (1998), "On Bayesian Modelling of Fat Tails and Skewness," Journal of the American Statistical Association, 93, 359-371.
19. Ferreira, J. T. A. S., and Steel, M. F. J. (2003), "Bayesian Multivariate Regression Analysis With a New Class of Skewed Distributions," Statistics Research Report 419, University of Warwick.
20. Fiorentini, G., Sentana, E., and Calzolari, G. (2003), "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroskedastic Dynamic Regression Models With Student t Innovations," Journal of Business & Economic Statistics, 21, 532-546.
21. Geweke, J., and Amisano, G. (2001), "Compound Markov Mixture Models With Application in Finance," mimeo, University of Iowa.
22. Giot, P., and Laurent, S. (2003), "Value-at-Risk for Long and Short Positions," Journal of Applied Econometrics, 18, 641-664.
23. _ (2004), "Modelling Daily Value-at-Risk Using Realized Volatility and ARCH-Type Models," Journal of Empirical Finance, 11, 379-398.
24. Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993), "On the Relation Between Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, 48, 1779-1801.
25. Gourieroux, C. (1997), ARCH Models and Financial Applications, New York: Springer-Verlag.
26. Gourieroux, C., and Jasiak, J. (2001), "Memory and Infrequent Breaks," Economics Letters, 70, 2941.
27. Granger, C. W. J., and Hyung, N. (1999), "Occasional Structural Breaks and Long Memory," Discussion Paper 99-14, University of California at San Diego.
28. Haas, M., Mittnik, S., and Paolella, M. (2002), "Mixed Normal Conditional Heteroskedasticity," Working Paper 2002/10, Center for Financial Studies.
29. Jeantheau, T. (1998), "Strong Consistency of Estimators for Multivariate ARCH Models," Econometric Theory, 14, 70-86.
30. Johnson, M. E. (1987), Multivariate Statistical Simulation, New York: Wiley.
31. Jones, M. C. (2001), "Multivariate T and Beta Distributions Associated With the Multivariate F Distribution," Metrika, 54, 215-231.
32. _ (2002), "Marginal Replacement in Multivariate Densities, With Application to Skewing Spherically Symmetric Distributions," Journal of Multivariate Analysis, 81, 85-99.
33. Jorion, P. (2000), Value-at-Risk: The New Benchmark for Managing Financial Risk, New York: McGraw-Hill.
34. Kupiec, P. (1995), "Techniques for Verifying the Accuracy of Risk Measurement Models," Journal of Derivatives, 2, 173-184.
35. Lambert, P., and Laurent, S. (2001), "Modelling Financial Time Series Using GARCH-Type Models and a Skewed Student Density," mimeo, Université de Liège.
36. Laurent, S., and Peters, J.-P. (2002), "G@RCH 2.2: An Ox Package for Estimating and Forecasting Various ARCH Models," Journal of Economic Surveys, 16, 447-485.
37. Lee, S. W., and Hansen, B. E. (1994), "Asymptotic Properties of the Maximum Likelihood Estimator and Test of the Stability of Parameters of the GARCH and IGARCH Models," Econometric Theory, 10, 29-52.
38. Lumsdaine, R. L. (1996), "Asymptotic Properties of the Quasi Maximum Likelihood Estimator in GARCH(1, 1) and IGARCH(1,1) Models," Econometrica, 64, 575-596.
39. Mauleón, I., and Perote, J. (1999), "Estimation of Multivariate Densities With Financial Data: The Performance of the Multivariate Edgeworth-Sargan Density," in Proceedings of the 12th Australian Finance and Banking Conference, Sidney.
40. Mittnik, S., and Paolella, M. S. (2000), "Conditional Density and Value-at-Risk Prediction of Asian Currency Exchange Rates," Journal of Forecasting, 19, 313-333.
41. Peiró, A. (1999), "Skewness in Financial Returns," Journal of Banking and Finance, 23, 847-862.
42. Richard, J.-F, and Tompa, H. (1980), "On the Evaluation of Poly t Density Functions," Journal of Econometrics, 12, 335-351.
43. Ruiz, E., and Pascual, L. (2002), "Bootstrapping Financial Time Series," Journal of Economic Surveys, 16, 271-300.
44. Samorodnitsky, G., and Taqqu, M. S. (1994), Stable Non-Gaussian Random Processes: Stochastic Models With Infinite Variance, London: Chapman & Hall.
45. Sowell, F. (1992), "Maximum Likelihood Estimation of Stationary Univariate Fractionally Integrated Time Series Models," Journal of Econometrics, 53, 165-188.
46. Tse, Y. K., and Tsui, A. K. C. (2002), "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model With Time-Varying Correlations," Journal of Business & Economic Statistics, 20, 351-362.
47. Vlaar, P. J. G., and Palm, F. C. (1993), "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroskedasticity and Jumps," Journal of Business & Economic Statistics, 11, 351-360.