Strong approximation of the empirical process of garch sequences

Annals of Applied Probability

Volumn 11, Issue 3, 2001, Pages 789-809

  Berkes, István ^a   Horváth, Lajos ^b  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

Empirical process; Estimates for increments; Garch(p, q); Rates of convergence; Strong approximation

Indexed keywords

EID: 0035413562     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1015345349     Document Type: Article

References (18)

1. BERKES, I. and PHILIPP, W. (1979). Approximation theorems for independent and weakly dependent random vectors. Ann. Probab. 7 29-54.
2. BHATTACHARYA, R. N. and RAO, R. R. (1976). Normal Approximation and Asymptotic Expansions. Wiley, New York.
3. BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31 307-327.
4. BOUGEROL, P. and PICARD, N. (1992a). Strict stationary of generalized autoregressive processes. Ann. Probab. 20 1714-1730.
5. BOUGEROL, P. and PICARD, N. (1992b). Stationarity of GARCH processes and of some nonnegative time series. J. Econometrics 52 115-127.
6. DAVIS, R. A., MIKOSCH, T. and BASRAK, B. (1999). Sample ACF of multivariate stochastic recurrence equations with applications to GARCH. Preprint.
7. DUDLEY, R. M. (1976). Probabilities and metrics: convergence of laws on metric spaces, with a view to statistical testing. Aarhus Univ. Lecture Notes Ser. 45.
8. ENGLE, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of the United Kingdom inflation. Econometrica 50 987-1008.
9. GOURIÈROUX, C. (1997). ARCH Models and Financial Applications. Springer, Berlin.
10. KINGMAN, J. F. C. (1973). Subadditive ergodic theory. Ann. Probab. 1 883-909.
11. LAI, T. L. (1974). Reproducing kernel Hubert spaces and the law of the iterated logarithm for Gaussian processes. Z. Wahrsch. Verw. Gebiete 29 7-19.
12. LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces. Springer, Berlin.
13. NELSON, D. B. (1990). Stationarity and persistence in GARCH(1, 1) model. Econometric Theory 6 318-334.
14. PETROV, V. V. (1975). Sums of Independent Random Variables. Springer, Berlin.
15. PETROV, V. V. (1995). Limit Theorems of Probability Theory. Clarendon Press, Oxford.
16. PHILIPP, W. (1984). Invariance principles for sums of mixing random elements and the multivariate empirical process. In Limit Theorems in Probability and Statistics (I. Berkes, E. Csáki and P. Révész, eds.) 843-873. North-Holland, Amsterdam.
17. PHILIPP, W. and PINZUR, L. (1980). Almost sure approximation theorems for the multivariate empirical process. Z. Wahrsch. Verw. Gebiete 54 1-13.
18. STRASSEN, V. (1964). An invariance principle for the law of the iterated logarithm. Z. Wahrsch. Verw. Gebiete 3 211-226.