Goodness-of-fit test for ergodic diffusions by discrete-time observations: an innovation martingale approach

References

• Aït-Sahalia , Y. 1996 . Testing Continuous-Time Models of the Spot Interest Rate . The Review of Financial Studies , 9 : 385 – 426 .
   Web of Science ®Google Scholar
• Aït-Sahalia , Y. 1999 . Transition Densities for Interest Rate and Other Nonlinear Diffusion . Journal of Finance , 54 : 1361 – 1395 .
   Web of Science ®Google Scholar
• Aït-Sahalia , Fan and Peng . 2009 . Nonparametric Transition-Based Tests for Jump Diffusions . Journal of the American Statistical Association , 104 : 1102 – 1116 .
   Web of Science ®Google Scholar
• Banks , H. T. 1975 . Modeling and Control in the Biological Sciences , Vol. 6 , Berlin : Springer-Verlag . Lecture Notes in Biomathematics
   Google Scholar
• Bergstrom , A. R. 1990 . Continuous Time Econometric Modeling , Oxford : Oxford University Press .
   Google Scholar
• Bianchi , A. 2009 . The Normal Approximation Rate for the Drift Estimator of Multidimensional Diffusions . Statistical Inference of Stochastic Processes , 12 : 251 – 268 .
   Google Scholar
• Chen , S. X. , Gao , J. and Tang , C. Y. 2008 . A Test for Model Specification of Diffusion Processes . Annals of Statistics , 36 : 167 – 198 .
   Web of Science ®Google Scholar
• Cobb , L. 1981 . “ Stochastic Differential Equations for the Social Sciences ” . In Mathematical Frontiers of the Social and Policy Sciences , Edited by: Cobb , L. and Thrall , M. 1 – 26 . Boulder, CO : Westview Press .
   Google Scholar
• Dachian , S. and Kutoyants , Yu. A. 2008 . “ On the Goodness-of-Fit Tests for Some Continuous Time Processes ” . In Statistical Models and Methods for Biomedical and Technical Systems , Edited by: Vonta , F. , Nikulin , M. , Limnios , N. and Huber-Carol , C. 395 – 413 . Boston, MA : Birkhuser .
   Google Scholar
• Delgado , M. and Stute , W. 2008 . Distribution-Free Specification Tests of Conditional Model . Journal of Econometrics , 143 : 37 – 55 .
   Web of Science ®Google Scholar
• Dette , H. , Podolskij , M. and Vetter , M. 2006 . Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing . Scandinavian Journal of Statistics , 33 : 259 – 278 .
   Web of Science ®Google Scholar
• Feller , W. 1971 . An Introduction to Probability Theory and Its Applications , 2 , Vol. II , New York : John Wiley & Sons, Inc .
   Google Scholar
• Fournie , E. 1992 . Un test de type Kolmogorov–Smirnov pour processus de diffusion ergodiques . Rapporte de recherche, 1696, INRIA, Sophia-Antipolis
   Google Scholar
• Fournie , E. and Kutoyants , Yu. A. 1993 . Estimateur de la distance maximale pour le processus de diffusion ergodiques . Rapporte de recherche, 1952, INRIA, Sophia-Antipolis
   Google Scholar
• Gobet , E. , Hoffmann , M. and Reiss , M. 2004 . Nonparametric Estimation of Scalar Diffusions Based on Low Frequency Data . Annals of Statistics , 32 : 2223 – 2253 .
   Web of Science ®Google Scholar
• Gutiérrez , R. , Gutiérrez-Sanchez , R. and Nafidi , A. 2009 . Modelling and Forecasting Vehicle Stocks using the Trends of Stochastic Gompertz Diffusion Models: The Case of Spain . Applied Stochastic Models in Business and Industry , 25 : 385 – 405 .
   Web of Science ®Google Scholar
• Hoffmann , M. 1999 . Adaptive Estimation in Diffusion Processes . Stochastic Processes and Their Applications , 79 : 135 – 163 .
   Web of Science ®Google Scholar
• Hong , Y. and Li , H. 2005 . Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates . The Review of Financial Studies , 18 : 37 – 84 .
   Web of Science ®Google Scholar
• Hull , J. 2000 . Options, Futures and Other Derivatives , 4 , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Kessler , M. 1997 . Estimation of an Ergodic Diffusion from Discrete Observations . Scandinavian Journal of Statistics , 24 : 221 – 229 .
   Web of Science ®Google Scholar
• Koul , H. 2002 . Weighted Empirical Processes in Dynamic Nonlinear Models , 2 , New York : Springer .
   Google Scholar
• Koul , H. and Stute , W. 1999 . Nonparametric Model Checks in Time Series . Annals of Statistics , 27 : 204 – 237 .
   Web of Science ®Google Scholar
• Kutoyants , Yu. A. 2004 . Statistical Inference for Ergodic Diffusion Processes , London : Springer .
   Google Scholar
• Lee , S. and Wee , I. 2008 . Residual Empirical Process for Diffusion Processes . Journal of the Korean Mathematical Society , 45 : 683 – 693 .
   Web of Science ®Google Scholar
• Negri , I. 1998 . Stationary Distribution Function Estimation for Ergodic Diffusion Process . Statistical Inference for Stochastic Processes , 1 : 61 – 84 .
   Google Scholar
• Negri , I. and Nishiyama , Y. 2009a . Goodness of Fit Test for Ergodic Diffusion Processes . Annals of the Institute of Statistical Mathematics , 61 : 919 – 928 .
   Web of Science ®Google Scholar
• Negri , I. and Nishiyama , Y. 2009b . Goodness of Fit Test for Small Diffusions by Discrete Time Observations . Annals of the Institute of Statistical Mathematics , doi: 10.1007/s10463-009-0228-2
   Web of Science ®Google Scholar
• Negri , I. and Nishiyama , Y. 2010 . Goodness of Fit Test for Ergodic Diffusions by Tick Time Sampling Scheme . Statistical Inference for Stochastic Processes , 13 : 81 – 95 .
   Google Scholar
• Nishiyama , Y. 1999 . A Maximal Inequality for Continuous Martingales and M-estimation in a Gaussian White Noise Model . Annals of Statistics , 27 : 675 – 696 .
   Web of Science ®Google Scholar
• Nishiyama , Y. 2000 . Entropy Methods for Martingales , Amsterdam : Centrum voor Wiskunde en Informatica . CWI Tract 128
   Google Scholar
• Papanicolaou , G. 1995 . “ Diffusions in Random Media ” . In Surveys in Applied Mathematics , Edited by: Keller , J. B. , McLaughin , D. and Papanicolaou , G. 205 – 255 . New York : Plenum Press .
   Google Scholar
• Papavasiliou , A. , Pavliotis , G. A. and Stuart , A. M. 2009 . Maximum Likelihood Drift Estimation for Multiscale Diffusions . Stochastic Processes and Their Applications , 119 : 3173 – 3210 .
   Web of Science ®Google Scholar
• Ricciardi , L. M. 1977 . Diffusion Processes and Related Topics in Biology , New York : Springer . Lecture Notes in Biomathematics
   Google Scholar
• Shimizu , Y. 2009 . Notes on Drift Estimation for Certain Non-recurrent Diffusion Processes from Sampled Data . Statistics & Probability Letters , 79 : 2200 – 2207 .
   Web of Science ®Google Scholar
• van der Vaart , A. W. and Wellner , J. A. 1996 . Weak Convergence and Empirical Processes: With Applications to Statistics , New York : Springer-Verlag .
   Google Scholar
• van der Vaart , A. W. and van Zanten , H. 2005 . Donsker Theorems for Diffusions: Necessary and Sufficient Conditions . Annals of Probability , 33 : 1422 – 1451 .
   Web of Science ®Google Scholar
• Veretennikov , A. Yu. 1997 . On Polynomial Mixing Bounds for Stochastic Differential Equations . Stochastic Processes and Their Applications , 70 : 115 – 127 .
   Web of Science ®Google Scholar
• Yoshida , N. 1992 . Estimation for Diffusion Processes from Discrete Observations . Journal of Multivariate Analysis , 41 : 220 – 242 .
   Web of Science ®Google Scholar
• van Zanten , H. 2003 . On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators . Statistical Inference for Stochastic Processes , 6 : 199 – 213 .
   Google Scholar