Subsampling the mean of heavy-tailed dependent observations

Journal of Time Series Analysis

Volumn 25, Issue 2, 2004, Pages 217-234

  Kokoszka, Piotr ^a   Wolf, Michael ^b  

^a UTAH STATE UNIVERSITY   (United States)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Estimation of the mean; GARCH; Heavy tails; Subsampling

Indexed keywords

EID: 1642634053     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.0143-9782.2003.00346.x     Document Type: Article

References (30)

1. ANDERSON, P. L. and MEERSCHAERT, M. M. (1997) Periodic moving averages of random variables with regularly varying tails. Annals of Statistics 24, 771-85.
2. ARCONES, M. and GINÉ, E. (1989) The bootstrap of the mean with arbitrary bootstrap sample size. Annals of the Institute Henri Poincaré 22, 457-81.
3. ARCONES, M. and GINÉ. E. (1991) Additions and corrections to 'the bootstrap of the mean with arbitrary bootstrap sample size'. Annals of the Institute Henri Poincaré 27, 583-95.
4. ATHREYA, K. B. (1987) Bootstrap of the mean in the infinite variance case. The Annals of Statistics 15(2), 724-31.
5. BASRAK, B., DAVIS, R. A. and MIKOSCH, T. (2002a) A characterization of regular variation. Annals of Applied Probability 12, 908-20.
6. BASRAK, B., DAVIS, R. A. and MIKOSCH, T. (2002b) Regular variation of GARCH processes. Stochastic Processes and Their Applications 99, 95-115.
7. BERKES, I., HORVÁTH, L. and KOKOSZKA, P. S. (2003) Estimation of the maximal moment exponent of a GARCH(1.1) sequence. Econometric Theory 19, 565-86.
8. BHANSALI, R. J. (1988) Consistent order determination for processes with infinite variance. Journal of the Royal Statistical Society 50, 46-60.
9. BILLINGSLEY, P. (1999) Convergence of Probability Measures (2nd edn). New York: Wiley.
10. BOUSSAMA, F. (1998) Ergodicity, mixing and estimation in GARCH models. PhD Thesis. University of Paris 6 (in French); translated by F. COMTE as "Probabilistic properties of multivariate GARCH processes".
11. BOUSSAMA, F. (1998) Ergodicity, mixing and estimation in GARCH models. PhD Thesis. University of Paris 6 (in French); translated by F. COMTE as "Probabilistic properties of multivariate GARCH processes".
12. BRADLEY, R. C. (1986) Basic properties of strong mixing conditions. In Dependence in Probability and Statistics (eds E. Eberlein and M. S. Taqqu). Boston: Birkhäuser, pp. 165-92.
13. BROCKWELL, P. J. and DAVIS, R. A. (1991) Time Series: Theory and Methods. New York: Springer-Verlag.
14. CARASCO, M. and CHEN, X. (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17-39.
15. CLINE, D. B. H. and BROCKWELL, P. J. (1985) Linear prediction of ARMA processes with infinite variance. Stochastic Processes and their Applications 19, 281-96.
16. DAVIS, R. A. and HSING, T. (1995) Point process and partial sum convergence for weakly dependent random variables'. Annals of Probability 23, 879-917.
17. DAVIS, R. A. and MIKOSCH, T. (1998) Limit theory for the sample acf of stationary process with heavy tails with applications to ARCH. The Annals of Statistics 26, 2049-80.
18. DOUKHAN, P. (1994) Mixing: Properties and Examples. Lecture Notes in Statistics. New Tork: Springer Verlag.
19. DURRETT, R. (1991) Probability: Theory and Examples. Pacific Grove, CA: Wadsworth & Brooks/Cole.
20. ENGLE, R. F. and BOLLERSLEV, T. (1986) Modelling the persistence of conditional variances. Econometric Reviews 5, 1-50.
21. KOKOSZKA, P. S. and TAQQU, M. S. (1994) Infinite variance stable ARMA processes. Journal of Time Series Analysis 115, 203-20.
22. KOKOSZKA, P. S. and TAQQU, M. S. (1996) Parameter estimation for infinite variance fractional ARIMA. The Annals of Statistics 24, 1880-913.
23. KOKOSZKA, P. S. and TAQQU, M. S. (2001) Can one use the Durbin- Levinson algorithm to generate infinite variance fractional ARIMA time series? Journal of Time Series Analysis 22, 317-37.
24. MAERCKER, G. and MOSER, M. (1999) Yule-Walker estimators in GARCH(1.1) models: asymptotic normality and bootstrap. Beiträge zur Statistik 58. Universität Heidelberg. Available at http://www.statlab.uni-heidelberg.de/reports/www.html.
25. MCELROY, T. and POLITIS, D. N. (2002) Robust inference for the mean in the presence of serial correlation and heavy-tailed distributions. Econometric Theory 18, 1019-39.
26. MEERSCHAERT, M. M. and SCHEFFLER, H. P. (2001) Limit Theorems for Sums of Independent Random Vectors. New York: Wiley.
27. MIKOSCH, T., GADRICH, T., KLÜPPELBERG, C. and ADLER, R. J. (1995) Parameter estimation for ARMA models with infinite variance innovations. The Annals of Statistics 23, 305-26.
28. MIKOSCH, T. and STǍRICǍ, C. (2000) Limit theory for the sample autocorrelation and extremes of a GARCH(1.1) process. The Annals of Statistics 28, 1427-51.
29. POLITIS, D. N., ROMANO, J. P. and WOLF, M. (1999) Subsampling. New York: Springer.
30. SAMORODNITSKY, G. and TAQQU, M. S. (1994) Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. London: Chapman & Hall.