The functional central limit theorem for a family of GARCH observations with applications

Statistics and Probability Letters

Volumn 78, Issue 16, 2008, Pages 2725-2730

  Berkes, István ^a   Hörmann, Siegfried ^b   Horváth, Lajos ^b  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53249127568     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2008.03.021     Document Type: Article

References (29)

1. Ango Nze P., and Doukhan P. Weak dependence: Models and applications to econometrics. Econometric Theory 20 (2004) 995-1045
2. Berkes I., Horváth L., and Kokoszka P. Probabilistic and statistical properties of GARCH processes. Asymptotic Methods in Stochastics. Fields Inst. Commun. vol. 44 (2004), Amer. Math. Soc. 409-429
3. Billingsley P. Convergence of Probability Measures (1968), Wiley, New York
4. Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31 (1986) 307-327
5. Bougerol P., and Picard N. Strict stationarity of generalized autoregressive processes. Ann. Probab. 20 (1992) 1714-1730
6. Bougerol P., and Picard N. Stationarity of GARCH processes and of some nonnegative time series. J. Econometrics 52 (1992) 115-127
7. Bradley R.C. Information regularity and the central limit question. Rocky Mountain J. Math. 13 (1983) 77-97
8. Carrasco M., and Chen X. Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18 (2002) 17-39
9. Csörgo{double acute} M., and Horváth L. Limit Theorems in Change-point Analysis (1997), Wiley, New York
10. Davidson J. Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes. J. Econometrics 106 (2002) 243-269
11. Dedecker J., Doukhan P., Lang G., Léon J.R., Louhichi S., and Prieur C. Weak Dependence, Examples and Applications. Springer Lecture Notes in Statistics vol. 190 (2007)
12. Ding Z., Granger C.W.J., and Engle R. A long memory property of stock market returns and a new model. J. Empirical Finance 1 (1993) 83-106
13. Doukhan P., and Louhichi S. A new weak dependence condition and applications to moment inequalities. Stoch. Process. Appl. 84 (1999) 313-342
14. Doukhan P., and Wintenberger O. An invariance principle for weakly dependent stationary general models. Probab. Math. Statist. 27 (2007) 45-73
15. Duan J.-C. Augmented GARCH (p, q) process and its diffusion limit. J. Econometrics 79 (1997) 97-127
16. Engle R.F. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50 (1982) 987-1007
17. Giraitis L., Leipus R., and Surgailis D. Recent advances in ARCH modelling. Long Memory in Economics (2007), Springer 3-38
18. Giraitis L., Kokoszka P.S., Leipus R., and Teyssiere G. Rescaled variance and related tests for long memory in volatility and levels. J. Econometrics 112 (2003) 265-294
19. Giraitis L., Kokoszka P.S., and Leipus R. Stationary ARCH models: Dependence structure and central limit theorem. Econometric Theory 16 (2000) 3-22
20. Hansen B. GARCH(1,1) processes are near epoch dependent. Econom. Lett. 36 (1991) 181-186
21. Ibragimov I.A. Some limit theorems for stationary processes. Theor. Probab. Appl. 7 (1962) 349-382
22. Kim J. Detection of change in persistence of a linear time series. J. Econometrics 95 (2000) 97-116
23. Kwiatowski D., Phillips P.C.B., Schmidt P., and Shin Y. Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?. J. Econometrics 54 (1992) 159-178
24. Ling S., Li W.K., and McAleer M. Estimation and testing for unit root processes with GARCH(1,1) errors: Theory and Monte Carlo evidence. Econometric Rev. 22 (2003) 179-202
25. Ling S., and McAleer M. Necessary and sufficient moment conditions for GARCH(r, s) and asymmetric power GARCH(r, s) model. Econometric Theory 18 (2002) 722-729
26. Nelson D.B. Stationarity and persistence in the GARCH(1,1) model. Econometric Theory 6 (1990) 318-334
27. Newman C.M., and Wright A.L. An invariance principle for certain dependent sequences. Ann. Probab. 9 (1981) 671-675
28. Taylor A.M.R. Fluctuation tests for a change in persistence. Oxford Bull. Econo. Statist. 67 (2005) 207-230
29. Zeileis A., Leisch F., Kleiber C., and Hornik K. Monitoring structural change in dynamic econometric models. J. Appl. Econometrics 20 (2005) 99-121