On the distributional properties of GARCH processes

Journal of Time Series Analysis

Volumn 22, Issue 3, 2001, Pages 339-352

  Pawlak, M ^a   Schmid, W ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

ARCH GARCH models; Distribution properties; Lower bounds; Non linear time series; Statistical process control

Indexed keywords

EID: 0040484894     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00227     Document Type: Article

References (20)

1. Cox, D. R., HINKLEY, D. V. and BARNDORFF-NIELSEN, O. E. (1996) Time Series Models in Econometrics, Finance and Other Fields. London: Chapman and Hall.
2. BAILLIE, R. T., BOLLERSLEV, T. and MIKKELSEN, H. O. (1996) Fractionally integrated generalized autoregressive conditional heteroskedasticity. J. Economet. 74, 3-30.
3. BARNDORFF-NIELSEN, O. E. (1997) Normal inverse Gaussian distributions and volatility modeling. Scand. J. Stat. 24, 1-13.
4. BOLLERSLEV, T. (1986) Generalized autoregressive conditional heteroskedasticity. J. Economet. 31, 307-27.
5. _, CHOU, R. Y. and KRONER, K. F. (1992) ARCH modeling in finance: a review of the theory and empirical evidence. J. Economet. 52, 5-59.
6. EBERLEIN, E. and KELLER, U. (1995) Hyperbolic distributions in finance. Bernoulli 1, 281-99.
7. EMBRECHTS, P., KLÜPPELBERG, C. and MIKOSCH, T. (1996) Modeling Extremal Events. New York: Springer.
8. ESARY, I. D., PROSCHAN, F. and WALKUP, D. W. (1967) Association of random variables with applications. Ann. Math. Stat. 38, 1466-74.
9. ENGLE, R. F. (1995) ARCH; Selected Readings. Oxford: Oxford University Press.
10. GOLDIE, C. M. (1991) Implicit renewal theory and tails of solutions of random equations. Ann. App. Probab. 1, 126-66.
11. GOURIEROUX, C. (1997) ARCH Models and Financial Applications. New York: Springer.
12. HOCHBERG, Y. and TAMHANE, A. C. (1987) Multiple Comparison Procedures. New York: Wiley.
13. KESTEN, H. (1973) Random difference equations and renewal theory for products of random matrices. Acta Math. 131, 207-48.
14. MILHØJ, A. (1985) The moment structure of ARCH processes. Scand. J. Stat. 12, 281-92.
15. NELSON, D. B. (1990) Stationarity and persistence in the GARCH(1, 1) model. Economet. Theory 6, 318-34.
16. SCHMID, W. (1995) On the run length of a Shewhart chart for correlated data. Stat. Pap. 36, 111-30.
17. SCHMID, W. and SCHÖNE, A. (1997) Some properties of the EWMA control chart in the presence of data correlation. Ann. Stat. 25, 1277-83.
18. SEVERIN, T. and SCHMID, W. (1999) Monitoring changes in GARCH models. Allg. Stat. Arch., to be published.
19. TONG, Y. L. (1980) Probability Inequalities in Multivariate Distributions. New York: Academic Press.
20. VERVAAT, W. (1979) On a stochastic difference equation and a representation of non-negative infinitely divisible random variables. Adv. Appl. Probab. 11, 750-83.