Goodness of fit test for ergodic diffusions by tick time sample scheme

Statistical Inference for Stochastic Processes

Volumn 13, Issue 1, 2010, Pages 81-95

  Negri, Ilia ^a   Nishiyama, Yoichi ^b  

^a UNIVERSITY OF BERGAMO   (Italy)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

Asymptotically distribution free test; Ergodic diffusion process; Invariance principle; Tick time sample

Indexed keywords

EID: 77951622975     PISSN: 13870874     EISSN: 15729311     Source Type: Journal    
DOI: 10.1007/s11203-010-9041-z     Document Type: Article

References (24)

1. Dachian S, Kutoyants YA (2008) On the goodness-of-fit tests for some continuous time processes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems. Birkhuser, Boston, pp 395-413.
2. Delgado M, Stute W (2008) Distribution-free specification tests of conditional models. J Econom 143: 37-55.
3. Feller W (1971) An introduction to probability theory and its applications, vol II. 2. Wiley, New York.
4. Fournie E (1992) Un test de type Kolmogorov-Smirnov pour processus de diffusion ergodiques, Rapporte de recherche, 1696. INRIA, Sophia-Antipolis.
5. Fournie E, Kutoyants YA (1993) Estimateur de la distance maximale pour le processus de diffusion ergodiques, Rapporte de recherche, 1952. INRIA, Sophia-Antipolis.
6. Fukasawa M (2010) Central limit theorem for the realized volatility based on tick time sampling. Finance Stoch 14: 209-233.
7. Genon-Catalot V, Laredo C (1987) Limit theorems for the first hitting times process of a diffusion and statistical applications. Scand J Stat 14(2): 143-160.
8. Genon-Catalot V, Laredo C, Nussbaum M (2002) Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift. Ann Stat 30(3): 731-753.
9. Gobet E, Hoffmann M, Reiss M (2004) Nonparametric estimation of scalar diffusions based on low frequency data. Ann Stat 32: 2223-2253.
10. Griffin JE, Oomen RCA (2008) Sampling returns for realized variance calculations: tick time or transaction time?. Econom Rev 27: 230-253.
11. Koul H (2002) Weighted empirical processes in dynamic nonlinear models. 2. Springer, New York.
12. Koul H, Stute W (1999) Nonparametric model checks in time series. Ann Stat 27: 204-237.
13. Kutoyants YA (2004) Statistical inference for ergodic diffusion processes. Springer, London.
14. Kutoyants YA (2009) On the goodness-of-fit testing for ergodic diffusion processes. Preprint.
15. Laredo C (1990) A sufficient condition for asymptotic sufficiency of incomplete observations of a diffusion process. Ann Stat 18(3): 1158-1171.
16. Masuda H, Negri I, Nishiyama Y (2008) Goodness of fit test for ergodic diffusions by discrete time observations: an innovation martingale approach. Research Memorandum 1069. The Institute of Statistical Mathematics, Tokyo.
17. Negri I (1998) Stationary distribution function estimation for ergodic diffusion process. Stat Inference Stoch Process 1: 61-84.
18. Negri I, Nishiyama Y (2009) Goodness of fit test for ergodic diffusion processes. Ann Inst Stat Math 61(4): 919-928.
19. Nishiyama Y (1999) A maximal inequality for continuous martingales and M-estimation in a Gaussian white noise model. Ann Stat 27: 675-696.
20. Nishiyama Y (2000) Entropy methods for martingales. CWI Tract 128. Centrum voor Wiskunde en Informatica, Amsterdam.
21. Nishiyama Y (2009) Nonparametric goodness of fit tests for ergodic diffusion processes by discrete observations. Research Memorandum 1094. The Institute of Statistical Mathematics, Tokyo.
22. van der Vaart AW, Wellner JA (1996) Weak convergence and empirical processes: with applications to statistics. Springer, New York.
23. van der Vaart AW, van Zanten H (2005) Donsker theorems for diffusions: necessary and sufficient conditions. Ann Probab 33: 1422-1451.
24. van Zanten H (2003) On uniform laws of large numbers for ergodic diffusions and consistency of estimators. Stat Inference Stoch Process 6: 199-213.