Fully nonparametric estimation of scalar diffusion models

Econometrica

Volumn 71, Issue 1, 2003, Pages 241-283

  Bandi, Federico M ^a   Phillips, Peter C B ^b,c,d  

^a UNIVERSITY OF CHICAGO   (United States)

^b YALE UNIVERSITY   (United States)

^c UNIVERSITY OF AUCKLAND   (New Zealand)

^d UNIVERSITY OF YORK   (United Kingdom)

Author keywords

Diffusion; Drift; Local time; Martingale; Nonparametric estimation; Semi martingale; Stochastic differential equation

Indexed keywords

DIFFERENTIAL EQUATIONS; ECONOMICS; FINANCE; INVESTMENTS;

NONPARAMETRIC ESTIMATION; SCALAR DIFFUSION MODELS; STOCHASTIC DIFFERENTIAL EQUATION;

ESTIMATION;

EID: 0037273358     PISSN: 00129682     EISSN: None     Source Type: Journal    
DOI: 10.1111/1468-0262.00395     Document Type: Article

References (29)

1. Aït-Sahalia, Y. (1996a): "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, 64, 527-560.
2. ____(1996b): "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, 2, 385-426.
3. Azema, J., M. Kaplan-Duflo, and D. Revuz (1967). "Mesure Invariante sur les Classes Récurrentes des Processus de Markov," Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 8, 157-181.
4. Bandi, F. M. (2002): "Short-Term Interest Rate Dynamics: A Spatial Approach," Journal of Financial Economics, 65, 73-110.
5. Bandi, F. M., and T. Nguyen (2000): "Fully Nonparametric Estimators for Diffusions: a Small Sample Analysis," Unpublished Manuscript, University of Chicago.
6. Baxter, M., and A. Rennie (1996): Financial Calculus. An Introduction to Derivative Pricing. Cambridge, U.K.: Cambridge University Press.
7. Bergstrom, A. R. (1988): "A History of Continuous Time Econometric Models," Econometric Theory, 4, 365-383.
8. Billingsley, P. (1968): Convergence of Probability Measures. New York: Wiley.
9. Bosq, D. (1998): Nonparametric Statistics for Stochastic Processes. New York: Springer-Verlag.
10. Brugière, P. (1993): "Théorèm de Limite Centrale pour un Estimateur Non Paramétrique de la Variance d'un Processus de Diffusion Multidimensionnelle," Annales de l'Institute Henri Poincaré, 29, 357-389.
11. Florens-Zmirou, D. (1993). "On Estimating the Diffusion Coefficient from Discrete Observations," Journal of Applied Probability, 30, 790-804.
12. German, S. A. (1979): "On a Common Sense Estimator for the Drift of a Diffusion," Unpublished Manuscript, Brown University.
13. Hall, P., and C. C. Heyde (1980) Martingale Limit Theory and its Application. New York: Academic Press.
14. Hansen, L. P., and J. Sargent (1983) "The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities," Econometrica, 50, 377-387.
15. Härdle, W. (1990): Applied Nonparametric Regression. Cambridge: Cambridge University Press.
16. Jacod, J. (1997) "Nonparametric Kernel Estimation of the Diffusion Coefficient of a Diffusion," Prépublication N. 405 du Laboratoire de Probabilités de l'Université Paris VI.
17. Jiang, G. J., and J. Knight (1997) "A Nonparametric Approach to the Estimation of Diffusion Processes, with an Application to a Short-Term Interest Rate Model," Econometric Theory, 13, 615-645.
18. Karatzas, I., and S. E. Shreve (1991): Brownian Motion and Stochastic Calculus. New York: Springer-Verlag.
19. Karlin, S., and H. M. Taylor (1981): A Second Course in Stochastic Processes. New York: Academic Press.
20. Knight, F. B. (1971): A Reduction of Continuous Square Integrable Martingales to Brownian Motion. Berlin: Springer-Verlag.
21. Merton, R. C. (1980): "On Estimating the Expected Return on the Market: An Exploratory Investigation," Journal of Financial Economics, 8, 323-361.
22. Øksendal, B. (1995): Stochastic Differential Equations. Berlin: Springer-Verlag.
23. Pagan, A., and A. Ullah (1999) Nonparametric Statistics. Cambridge, U.K.: Cambridge University Press.
24. Phillips, P. C. B. (1973): "The Problem of Identification in Finite Parameter Continuous-Time Models," Journal of Econometrics, 4, 351-362.
25. Phillips, P. C. B., and J. Park (1998). Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Paper, No. 1181, Yale University.
26. Phillips, P. C. B., and W. Ploberger (1996): "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, 64, 381-413.
27. Pollack, M., and D. Siegmund (1985): "A Diffusion Process and its Applications to Detecting a Change in the Drift of Brownian Motion," Biometrika, 72, 267-280.
28. Revuz, D., and M. Yor (1998): Continuous Martingales and Brownian Motion. New York: Springer-Verlag.
29. Yor, M. (1978): "Temps Locaux," Astérisque, 52-53, 17-35.