Unconditional and conditional distributional models for the Nikkei index

Asia-Pacific Financial Markets

Volumn 5, Issue 2, 1998, Pages 99-128

  Mittnik, Stefan ^a   Paolella, Marc S ^a   Rachev, Svetlozar T ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

GARCH; Persistence; Skewness; Stable Paretian distribution; Volatility

Indexed keywords

EID: 54649083115     PISSN: 13872834     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010016831481     Document Type: Article

References (65)

1. Anderson, T. and Darling, D. (1952), Asymptotic theory of certain 'goodness of fit' criteria based on stochastic processes, Ann. Math. Stat. 23, 193-212.
2. Baillie, R.T. and Bollerslev, T. (1989), The message in daily exchange rates: A conditional-variance tale, J. Bus. Econ. Stat. 7 (3), 297-305.
3. Bera, A., Higgins, M., and Lee, S. (1992), Interaction between autocorrelation and conditional heteroskedasticity: A random coefficient approach, J. Bus. Econ. Stat. 10, 133-142.
4. Blattberg, R. and Gonedes, N. (1974), Stable and student distributions for stock prices, J. Bus. 47, 244-280.
5. Bollerslev, T. (1986), Generalized autoregressive conditional heteroskedasticity, J. Econometrics 31, 307-327.
6. Bollerslev, T. (1987), A conditional heteroskedastic time series model for speculative prices and rates of return, Rev. Econ. Stat. 69, 542-547.
7. Bollerslev, T., Chou, R., and Kroner K. (1992), Modeling in finance: A review of the theory and empirical evidence, J. Econometrics 52, 5-59.
8. Bollerslev, T., Engle, R.F., and Nelson, D.B. (1994), ARCH models, in R. Engle and D. McFadden (eds), Handbook of Econometrics, volume 4, chapter 49, Elsevier Science B.V, Amsterdam, The Netherlands.
9. Box, G. and Jenkins, G. (1976), Time Series Analysis: Forecasting and Control, 2nd edn, Holden-Day, San Francisco.
10. Box, G.E.P. and Tiao, G.C. (1962), A further look at robustness via bayes theorem, Biometrika 49, 419-432.
11. Box, G.E.P. and Tiao, G.C. (1973), Bayesian Inference In Statistical Analysis, Addison-Wesley, Reading, Massachusetts.
12. Brockwell, P. and Davis, R. (1991), Time Series: Theory and Methods, 2nd edn, Springer-Verlag, New York.
13. Butler, R.J., McDonald, J.B., Nelson, R.D., and White, S.B. (1990), Robust and partially adaptive estimation of regression models, Rev. Econ. Stat. 72, 321-327.
14. Chobanov, G., Mateev, P., Mittnik, S., and Rachev, S. (1996), Modeling the distribution of highly volatile exchange-rate time series, in P. Robinson and M. Rosenblatt (eds), Athens Conference on Applied Probability and Time Series, volume II: Time Series Analysis, Springer-Verlag, New York.
15. D'Agostino, R. and Stephens, M. (1986), Goodness of Fit Techniques, Marcel Dekker, New York.
16. Davis, R. and Resnick, S. (1986), Limit theory for the sample covariance and correlation functions of moving averages, Ann. Stat. 14, 533-558.
17. Deb, P. and Sefton, M. (1996), The distribution of a lagrange multiplier test of normality, Economics Letters 51, 123-130.
18. DeGroot, M.H. (1986), Probability and Statistics, 2nd edn, Addison-Wesley, Reading, Massachusetts.
19. Diebold, F. (1986), Testing for serial correlation in the presence of ARCH, in Proc. of the Business and Economic Statistics Section, American Statistical Association, pp. 323-328.
20. Diebold, F. and Schuermann, T. (1992), Exact maximum likelihood estimation of ARCH models, unpublished manuscript, University of Pennsylvania.
21. DuMouchel, W. (1973), On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution, Ann. Stat. 1, 948-957.
22. Engle, R. (1982), Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom Inflation, Econometrica 50, 987-1007.
23. Engle, R.F. and Bollerslev, T. (1986), Modelling the persistence of conditional variances, Econometric Reviews 5, 1-50; 81-87.
24. Fama, E. (1965), The behavior of stock market prices, J. Bus. 38, 34-105.
25. Franses, P.H. and van Dijk, D. (1996), Forecasting stock market volatility using (non-linear) GARCH models, J. Forecasting 15, 229-235.
26. González-Rivera, G. (1997), A note on adaptation in GARCH models, Econometric Reviews 16 (1), 55-68.
27. Granger, C. and Ding, Z. (1995), Some properties of absolute return, an alternative measure of risk, Annales d'Economie et de Statistique 40, 67-91.
28. Hsieh, D.A. (1989), Modeling heteroscedasticity in daily foreign-exchange rates, J. Bus. Econ. Stat. 7(3), 307-317.
29. Janicki, A. and Weron, A. (1994), Simulation and Chaotic Behavior of astable Stochastic Processes, Marcel Dekker, New York.
30. Jarque, C.M. and Bera, A.K. (1987), A test for normality of observations and regression residuals, Internat. Stat. Rev. 55 (2), 163-172.
31. Kariya, T., Tsukuda, Y., Maru, J., Matsue, Y., and Omaki, K. (1995), An extensive analysis on the Japanese markets vis S. Taylor's model, Financial Engineering and the Japanese Markets 2, 15-86.
32. Lange, K.L., Little, R.J., and Taylor, J.M.G. (1989), Robust statistical modeling using the t distribution, J Am. Stat. Assoc. 84 (408), 881-896.
33. Liu, S.-M. and Brorsen, B.W. (1995), Maximum likelihood estimation of a GARCH-stable model, J. Appl. Econometrics 10, 273-285.
34. Mandelbrot B. (1963), The variation of certain speculative prices, J. Bus. 36, 391-419.
35. McCulloch, J.H. (1986), Simple consistent estimators of stable distribution parameters, Communications in Statistics - Simulation and Computation 15(4), 1109-1136.
36. McCulloch, J.H. (1996), Toward numerical approximation of the Skew-stable distributions and densities, working paper 96-33, Department of Economics, The Ohio State University.
37. McDonald, J.B. and Newey, W.K. (1988), Partially adaptive estimation of regression models via the generalized t distribution, Econometric Theory 4, 428-457.
38. Mikosch, T., Gadrich T., Klüppelberg, C., and Adler, R.J. (1995), Parameter estimation for ARMA models with infinite variance innovations, Ann. Stat. 23 (1), 305-326.
39. Mittnik, S., Paolella, M.S., and Rachev, S.T. (1997a), Modeling the persistence of conditional volatilities with GARCH-stable processes, working paper, Institute of Statistics and Econometrics, Christian Albrechts University, Kiel, Germany.
40. Mittnik, S. and Rachev, S. (1993), Modeling asset returns with alternative stable models, Econometric Reviews 12, 261-330.
41. Mittnik, S., Rachev, S., and Chenyao, D. (1996a), Distributions of exchange rats: A geometric summation-stable model, in Proc. of the 1996 Internl. Conf. on Data Analysis, Bulgarian Academy of Sciences, Sofia.
42. Mittnik, S. and Rachev, S.T. (1997), Financial Modeling and Option Pricing with Alternative Stable Models, to appear, Wiley & Sons, Chichester.
43. Mittnik, S., Rachev, S.T., Doganoglu, T., and Chenyao, D. (1996b), Maximum likelihood estimation of stable paretian models, unpublished manuscript, Institute of Statistics and Econometrics, Christian Albrechts University, Kiel, Germany.
44. Mittnik, S., Rachev, S.T., and Paolella, M.S. (1997b), Stable paretian modeling in finance, in R.J. Adler, R.E. Feldmann and M.S. Taqqu (eds), A Practical Guide to Heavy Tails: Statistical Techniques for Analyzing Heavy Tailed Distributions, Birkhäuser, Boston, in press.
45. Mood, A., Graybill, F., and Does, D. (1947), Introduction to the Theory of Statistics, 3rd edn, McGraw-Hill, Tokyo.
46. Nelson, D. (1991), Conditional heteroskedasticity in asset returns: A new approach, Econometrica 59, 347-370.
47. Nelson, D.B. and Cao, C.Q (1992), Inequality constraints in the univariate GARCH model, J. Bus. Econ. Stat. 10 (2), 229-235.
48. Panorska, A, Mittnik, S., and Rachev, S. (1995), Stable ARCH models for financial time series, Appl. Math. Letters 8, 33-37.
49. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1991), Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd edn, Cambridge University Press, New York.
50. Rachev, S. (1991), Probability Metrics and the Stability of Stochastic Models, John Wiley & Sons, New York.
51. Rahman, M. and Gokhale, D. (1996), On estimation of parameters of the exponential power family of distributions, Communication in Statistics - Simulation and Computation 25 (2), 291-299.
52. Rozelle, J. and Fielitz, B. (1980), Skewness in common stock returns, Financ. Rev. 15, 1-23.
53. Samorodnitsky, G. and Taqqu, M. (1994), Stable Non-Gaussian Random Processes, Stochastic Models with Infinite Variance, Chapman & Hall, London.
54. Schwert, W.G. (1989), Why does stock market volatility change over time? J. Finance 44, 1115-1153.
55. Silverman, B. (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall.
56. Simkowitz, M. and Beedles, W. (1980), Asymmetric stable distributed security returns, J. Am. Stat. Assoc. 75, 306-312.
57. Singh, R.S. (1988), Estimation of error variance in linear regression models with errors having a multivariate student-f distribution with unknown degrees of freedom, Economic Letters 27, 47-53.
58. St. Pierre, E.F. (1993), The Importance of Skewness and Kurtosis in the Time-Series of Security Returns, PhD Thesis, Florida State University, College of Business.
59. Tanaka, K. (1996), Time Series Analysis, Nonstationary and Noninvertible Distribution Theory, John Wiley & Sons, New York.
60. Taylor, S. (1986), Modeling Financial Time Series, John Wiley & Sons, New York.
61. Teräsvirta, T. (1996), Two stylized facts and the GARCH (1,1) model, working paper 96, Stockholm School of Economics.
62. Wei, W.W. (1990), Time Series Analysis: Univariate and Multivariate Methods, Addison-Wesley, Reading, Massachusetts.
63. Zellner, A. (1971), An Introduction to Bayesian Inference in Econometrics, John Wiley & Sons, New York.
64. Zellner, A. (1976), Bayesian and non-bayesian analysis of the regression model with multivariate student-t error terms, J. Am. Stat. Assoc. 71 (354), 400-405.
65. Zolotarev, V.M. (1996), One-Dimensional Stable Laws, American Mathematical Society, translation of Odnomernye Ustoichivye Raspredeleniia, NAUKA, Moskow, 1983.