Deviance Information Criterion for Comparing Stochastic Volatility Models

Journal of Business and Economic Statistics

Volumn 22, Issue 1, 2004, Pages 107-120

  Berg, Andreas ^a   Meyer, Renate ^a   Yu, Jun ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Bayesian deviance; Jumps; Leverage effect; Markov chain Monte Carlo; Model complexity; Model selection

Indexed keywords

EID: 0742271637     PISSN: 07350015     EISSN: None     Source Type: Journal    
DOI: 10.1198/073500103288619430     Document Type: Article

References (62)

1. Akaike, H. (1973), "Information Theory and an Extension of the Maximum Likelihood Principle," in Proceedings of the Second International Symposium on Information Theory, eds. B. N. Petrov and F. Csaki, Budapest: Akademiai Kiado, pp. 267-281.
2. Andersen, T. G., Chung, H.-J., and Sørensen, B. E. (1999), "Efficient Method of Moments Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Econometrics, 91, 61-87.
3. Andersen, T. G., and Sørensen, B. E. (1996), "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, 14, 329-352.
4. Andrews, D. F., and Mallows, C. L. (1974), "Scale Mixtures of Normal Distributions," Journal of the Royal Statistical Society, Ser. B, 36, 99-102.
5. Berger, J. O., and Pericchi, L. R. (1996), "The Intrinsic Bayes Factor for Model Selection and Prediction," Journal of the American Statistical Association, 91, 109-122.
6. Best, N., Cowles, M. K., and Vines, K. (1995), "CODA Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output Version 0.30," Cambridge, U.K.: MRC Biostatistics Unit.
7. Black, F. (1976), "Studies of Stock Market Volatility Changes, " Proceedings of the American Statistical Association, Business and Economic Statistics Section, 177-181.
8. Blair, B. J., Poon, S.-H., and Taylor, S. J. (2001a), "Modelling S&P 100 Volatility: The Information Content of Stock Returns," Journal of Banking and Finance, 25, 1665-1679.
9. _ (2001b), "Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High Frequency Returns," Journal of Econometrics, 105, 5-26.
10. Bollerslev, T. (1986), "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 31, 307-327.
11. Brenner, R. J., Harjes, R. H., and Kroner, K. F. (1996), "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, 31, 85-107.
12. Carlin, B. P., and Louis, T. A. (1996), Bayes and Empirical Bayes Methods for Data Analysis, Monographs on Statistics and Applied Probability, 69.
13. Chacko, G., and Viceira, L. M. (2003), "Spectral GMM Estimation of Continuous-Time Processes," Journal of Econometrics, 116, 259-292.
14. Chan, K. C., Karolyi, G. A., Longstaff, F. A., and Sanders, A. B. (1992), "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," The Journal of Finance, 47, 1209-1227.
15. Chernov, M., Gallant, A. R., Ghysels, E., and Tauchen, G. (2003), "Alternative Models for Stock Price Dynamics," Journal of Econometrics, 116, 225-257.
16. Chib, S. (1995), "Marginal Likelihood from the Gibbs Output," Journal of the American Statistical Association, 90, 1313-1321.
17. Chib, S., Nardari, F., and Shephard, N. (1999), "Analysis of High Dimensional Multivariate Stochastic Volatility Models," unpublished paper.
18. _ (2002), "Markov Chain Monte Carlo Methods Stochastic Volatility Models," Journal of Econometrics, 108, 281-316.
19. Dempster, A. P. (1974), "The Direct Use of Likelihood for Significance Testing," in Proceedings of Conference on Foundational Questions in Statistical Inference, University of Aarhus, pp. 335-352.
20. Doucet, A., de Freitas, N., and Gordon, N. (2001), Sequential Monte Carlo Methods in Practice, New York: Springer-Verlag.
21. Duffie, D., and Singleton, K. J. (1993), "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, 61, 929-952.
22. Engle, R. F. (1982), "Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom Inflation," Econometrica, 50, 987-1007.
23. Engle, R. F., and Ng, V. K. (1993), "Measuring and Testing the Impact of News on Volatility," The Journal of Finance, 48, 1749-1778.
24. Fernandez, C., Ley, E., and Steel, M. F. J. (2001), "Benchmark Priors for Bayesian Model Averaging," Journal of Econometrics, 100, 381-427.
25. Fleming, J., Ostdiek, B., and Whaley, R. E. (1995), "Predicting Stock Market Volatility: A New Measure," Journal of Futures Markets, 15, 265-302.
26. Gallant, A. R., and Tauchen, G. (1996), "Which Moments to Match," Econometric Theory, 12, 657-681.
27. _ (2001), "Efficient Method of Moments," working paper, University of North Carolina, Dept. of Economics. Available at www.unc.edu/arg.
28. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1996), Bayesian Data Analysis, London: Chapman & Hall.
29. George, E. I., and Foster, D. P. (2001), "Calibration and Empirical Bayes Variable Selection," Biometrika, 87, 731-747.
30. Ghysels, E., Harvey, A. C., and Renault, E. (1996), "Stochastic Volatility," in Statistical Models in Finance, eds. C. R. Rao and G. S. Maddala, Amsterdam: North-Holland, pp. 119-191.
31. Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (1996), Markov Chain Monte Carlo in Practice, London: Chapman & Hall.
32. Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993), "On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," The Journal of Finance, 48, 1779-1801.
33. Gordon, N. J., Salmond, D. J., and Smith, A. E. M. (1993), "A Novel Approach to Nonlinear and Non-Gaussian Bayesian State Estimation," IEEE Proceedings F, 140, 107-133.
34. Han, C., and Carlin, B. P. (2001), "Markov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review," Journal of the American Statistical Association, 96, 1122-1132.
35. Harvey, A. C., Ruiz, E., and Shephard, N. (1994), "Multivariate Stochastic Variance Models," Review of Economic Studies, 61, 247-264.
36. Heidelberger, P., and Welch, P. (1983), "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, 31, 1109-1144.
37. Hoeting, J. A., Madigan, A., Raftery, A. E., and Volinsky, C. T. (1999), "Bayesian Model Averaging: A Tutorial," Statistical Science, 14, 383-417.
38. Hol, E., and Koopman, S. J. (2000), "Forecasting the Variability of Stock Index Returns With Stochastic Volatility Models and Implied Volatility," Discussion paper, TI 2000-104/4, Tinbergen Institute.
39. Hull, J., and White, A. (1987), "The Pricing of Options on Asset With Stochastic Volatilities," The Journal of Finance, 42, 281-300.
40. Jacquier, E., Poison, N. G., and Rossi, P. E. (1994), "Bayesian Analysis of Stochastic Volatility Models" (with discussion), Journal of Business & Economic Statistics, 12, 371-417.
41. Kass, R. E., and Raftery, A. E. (1995), "Bayes Factors," The Journal of the American Statistical Association, 90, 773-795.
42. Key, J. T., Pericchi, L. R., and Smith, A. F. M. (1999), "Bayesian Model Choice: What and Why?" in Bayesian Statistics (Vol. 6), eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 343-370.
43. Kim, S., Shephard, N., and Chib, S. (1998), "Stochastic Volatility: Likelihood Inference Comparison With ARCH Models," Review of Economic Studies, 65, 361-393.
44. Kitagawa, G. (1996), "Monte Carlo Filter and Smoother for Gaussian Nonlinear State Space Models," Journal of Computational and Graphical Statistics, 5, 1-25.
45. Knight, J. L., Satchell, S. E., and Yu, J. (2002), "Estimation of Stochastic Volatility Model by the Empirical Characteristic Function Method," Australian and New Zealand Journal of Statistics, 44, 319-335.
46. Lavine, M., and Schervish, M. J. (1999), "Bayes Factors: What They Are and What They Are Not," The American Statistician, 53, 119-122.
47. Melino, A., and Turnbull, S. M. (1990), "Pricing Foreign Currency Options With Stochastic Volatility," Journal of Econometrics, 45, 239-265.
48. Meyer, R., and Yu. J. (2000), "BUGS for a Bayesian Analysis of Stochastic Volatility Models," The Econometrics Journal, 3, 198-215.
49. Newton, M. A., and Raftery, A. E. (1994), "Approximate Bayesian Inference With the Weighted Likelihood Bootstrap" (with discussion), Journal of the Royal Statistical Society, Ser. B, 56, 3-48.
50. O'Hagan, A. (1991), "Contribution to the Discussion of 'Posterior Bayes Factors,'" Journal of the Royal Statistical Society, Ser. B, 53, 136.
51. _ (1994), Kendall's Advanced Theory of Statistics (Vol. 2), London: Edward Arnold.
52. Pitt, M., and Shephard, N. (1999a), "Filtering via Simulation: Auxiliary Particle Filter," Journal of the American Statistical Association, 94, 590-599.
53. _ (1999b), "Time Varying Covariances: A Factor Stochastic Volatility Approach" (with discussion), in Bayesian Statistics (Vol. 6), eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 547-570.
54. Sandmann, G., and Koopman, S. J. (1998), "Estimation of Stochastic Volatility Models via Monte Carlo Maximum Likelihood," Journal of Econometrics, 87, 271-301.
55. Schwarz, G. (1978), "Estimating the Dimension of a Model," Annals of Statistics, 6, 461-464.
56. Shephard, N. (1996), "Statistical Aspects of ARCH and Stochastic Volatility," in Time Series Models in Econometrics, Finance and Other Fields, eds. D. R. Cox, D. V. Hinkley, and O. E. Barndoff-Nielson, London: Chapman and Hall, pp. 1-67.
57. Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman & Hall.
58. Singleton, K. J. (2001), "Estimation of Affine Asset Pricing Models Using the Empirical Characteristic Function," Journal of Econometrics, 102, 111-141.
59. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and van der Linde, A. (2002), "Bayesian Measures of Model Complexity and Fit" (with discussion), Journal of the Royal Statistical Society, Ser. B, 64, 583-639.
60. Spiegelhalter, D. J., Thomas, A., Best, N. G., and Gilks, W. R. (1996), BUGS 0.5, Bayesian Inference Using Gibbs Sampling, Manual (Version II), Cambridge, U.K.: MRC Biostatistics Unit.
61. Taylor, S. J. (1982), "Financial Returns Modelled by the Product of Two Stochastic Processes - A Study of the Daily Sugar Prices 1961-75," in Time Series Analysis: Theory and Practice (Vol. 1), ed. O. D. Anderson, Amsterdam: North-Holland, pp. 203-226.
62. Zhu, L., and Carlin, B. P. (2000), "Comparing Hierarchical Models for Spatio-Temporally Misaligned Data Using the Deviance Information Criterion," Statistics in Medicine, 19, 2265-2278.