zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An empirical evaluation of fat-tailed distributions in modeling financial time series. (English) Zbl 1148.62316
Summary: There is substantial evidence that many financial time series exhibit leptokurtosis and volatility clustering. We compare the two most commonly used statistical distributions in empirical analysis to capture these features: the t distribution and the generalized error distribution (GED). A Bayesian approach using a reversible-jump Markov chain Monte Carlo method and a forecasting evaluation method are adopted for the comparison. In the Bayesian evaluation of eight daily market returns, we find that the fitted t error distribution outperforms the GED. In terms of volatility forecasting, models with t innovations also demonstrate superior out-of-sample performance.
MSC:
62P05Applications of statistics to actuarial sciences and financial mathematics
62M10Time series, auto-correlation, regression, etc. (statistics)
62F15Bayesian inference
91B84Economic time series analysis
References:
[1]M. Asai, Bayesian analysis of stochastic volatility models with mixture-of-normal distributions, Math. Comput. Simul., in press. · Zbl 1162.91362 · doi:10.1016/j.matcom.2008.12.013
[2]Ballie, R. T.; Bollerslev, T.: The message in daily exchange rates: A conditional-variance tale, J. busi. Econ. stat. 7, 297-305 (1989)
[3]Bauwens, L.; Lubrano, M.: Bayesian inference on GARCH models using the Gibbs sampler, Economet. J. 1, c23-c46 (1998)
[4]Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity, J. economet. 31, 307-327 (1986) · Zbl 0616.62119
[5]Bollerslev, T.: A conditional hetroskedasticity time series model for security prices and rates of return data, Rev. econ. Stat. 69, 542-547 (1987)
[6]Bollerslev, T.; Chou, R. Y.; Kroner, K. F.: ARCH modeling in finance: a review of the theorem and empirical evidence, J. economet. 52, 5-59 (1992) · Zbl 0825.90057 · doi:10.1016/0304-4076(92)90064-X
[7]Box, G. E. P.; Tiao, G. C.: Bayesian inference in statistical analysis, (1973) · Zbl 0271.62044
[8]Chen, C. W. S.; Chiang, T. C.; So, M. K. P.: Asymmetries reacting to the US stock-return news: evidence from major stock markets based on double-threshold model, J. econ. Busi. 55, 487-502 (2003)
[9]Chen, C. W. S.; So, M. K. P.: On a threshold heteroscedastic model, Int. J. Forecast. 22, 73-89 (2006)
[10]Diebold, F. X.; Mariano, R. S.: Comparing predictive accuracy, J. busi. Econ. stat. 13, 253-263 (1995)
[11]Engle, R. F.: Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation, Econometrica 50, 987-1008 (1982) · Zbl 0491.62099 · doi:10.2307/1912773
[12]Engle, R. F.; Gonzalez-Riviera, G.: Semi-parametric GARCH models, J. busi. Econ. stat. 9, 345-359 (1991)
[13]Ernst, M. D.: A multivariate generalized Laplace distribution, Comput. stat. 13, 227-232 (1998) · Zbl 0922.62043
[14]Fernández, C.; Steel, M. F. J.: On Bayesian modeling of fat tails and skewness, J. am. Stat. assoc. 93, 359-371 (1998) · Zbl 0910.62024 · doi:10.2307/2669632
[15]Glosten, L. R.; Jagannathan, R.; Runkle, D. E.: On the relation between the expected value and the volatility of the nominal excess return on stocks, J. finan. 48, 1779-1801 (1993)
[16]Gómez, E.; Gómez-Villegas, M. A.; Marin, J. M.: A multivariate generalization of the power exponential family of distributions, Commun. stat. Theory methods 27, 589-600 (1998) · Zbl 0895.62053 · doi:10.1080/03610929808832115
[17]Green, P. J.: Reversible jump MCMC computation and Bayesian model determination, Biometrika 82, 711-732 (1995) · Zbl 0861.62023 · doi:10.1093/biomet/82.4.711
[18]Jensen, M. B.; Lunde, A.: The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model, Economet. J. 4, 319-342 (2001)
[19]Li, W. K.; Ling, S.; Mcaleer, M.: Recent theoretical results for time series models with GARCH errors, J. econ. Surveys 16, 245-269 (2002)
[20]Ling, S.; Mcaleer, M.: Asymptotic theory for a vector ARMA-GARCH model, Econ. theory 19, 280-310 (2003)
[21]Mcaleer, M.: Automated inference and learning in modeling financial volatility, Econ. theory 21, 232-261 (2005) · Zbl 1072.62104 · doi:10.1017/S0266466605050140
[22]Nakatsuma, T.: Bayesian analysis of ARMA-GARCH models: a Markov chain sampling approach, J. economet. 95, 57-69 (2000) · Zbl 0970.62014 · doi:10.1016/S0304-4076(99)00029-9
[23]Nelson, D. B.: Conditional heteroscedasticity in asset returns: a new approach, Econometrica 59, 347-370 (1991) · Zbl 0722.62069 · doi:10.2307/2938260
[24]So, M. K. P.; Chen, C. W. S.; Chen, M. -T.: A Bayesian threshold nonlinearity test for financial time series, J. forecast. 24, 61-75 (2005)
[25]So, M. K. P.; Li, W. K.; Lam, K.: A threshold stochastic volatility model, J. forecast. 21, 473-500 (2002)
[26]Vrontos, I. D.; Dellaportas, P.; Poltis, D. N.: Full Bayesian inference for GARCH and EGARCH models, J. busi. Econ. stat. 18, 187-198 (2000)
[27]Watanabe, T.: On sampling the degree-of-freedom of student’s-t disturbances, Stat. prob. Lett. 52, 177-181 (2001) · Zbl 1082.62505 · doi:10.1016/S0167-7152(00)00221-2