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Volumn 72, Issue 3, 2004, Pages 337-354

Parametric inference for diffusion processes observed at discrete points in time: A survey

Author keywords

Bayesian analysis; Diffusion processes; Discrete time observations; Efficient method of moments (EMM); Estimating functions; Indirect inference; Likelihood approximations

Indexed keywords


EID: 10244220000     PISSN: 03067734     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1751-5823.2004.tb00241.x     Document Type: Review
Times cited : (140)

References (59)
  • 1
    • 0030369366 scopus 로고    scopus 로고
    • Nonparametric pricing of interest rate derivative securities
    • Aït-Sahalia, Y. (1996). Nonparametric pricing of interest rate derivative securities. Econometrica, 64, 527-560.
    • (1996) Econometrica , vol.64 , pp. 527-560
    • Aït-Sahalia, Y.1
  • 2
    • 0040843309 scopus 로고    scopus 로고
    • Transition densities for interest rate and other nonlinear diffusions
    • Aït-Sahalia, Y. (1999). Transition densities for interest rate and other nonlinear diffusions. J. Finance, 54, 1361-1395.
    • (1999) J. Finance , vol.54 , pp. 1361-1395
    • Aït-Sahalia, Y.1
  • 3
    • 33748439404 scopus 로고    scopus 로고
    • Closed-form expansions for multivariate diffusions
    • Department of Economics, Princeton University
    • Aït-Sahalia, Y. (2002a). Closed-form expansions for multivariate diffusions. Working Paper, Department of Economics, Princeton University.
    • (2002) Working Paper
    • Aït-Sahalia, Y.1
  • 4
    • 0036216388 scopus 로고    scopus 로고
    • Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach
    • Aït-Sahalia, Y. (2002b). Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Econometrica, 70, 223-262.
    • (2002) Econometrica , vol.70 , pp. 223-262
    • Aït-Sahalia, Y.1
  • 5
    • 0000309098 scopus 로고    scopus 로고
    • Estimating continuous-time stochastic volatility models of the short-term interest rate
    • Andersen, T.G. & Lund, J. (1997). Estimating continuous-time stochastic volatility models of the short-term interest rate. J. Econometrics, 77, 343-377.
    • (1997) J. Econometrics , vol.77 , pp. 343-377
    • Andersen, T.G.1    Lund, J.2
  • 6
    • 10244256022 scopus 로고    scopus 로고
    • Estimating functions for discretely sampled diffusion-type models
    • Eds. Y. Aït-Sahalia and L.P. Hansen. Amsterdam: North-Holland
    • Bibby, B.M., Jacobsen, M. & Sørensen, M. (2002). Estimating functions for discretely sampled diffusion-type models. In Handbook of Financial Econometrics, Eds. Y. Aït-Sahalia and L.P. Hansen. Amsterdam: North-Holland.
    • (2002) Handbook of Financial Econometrics
    • Bibby, B.M.1    Jacobsen, M.2    Sørensen, M.3
  • 8
    • 84972534141 scopus 로고
    • Martingale estimation functions for discretely observed diffusion processes
    • Bibby, B.M. & Sørensen, M. (1995). Martingale estimation functions for discretely observed diffusion processes. Bernoulli, 1, 17-39.
    • (1995) Bernoulli , vol.1 , pp. 17-39
    • Bibby, B.M.1    Sørensen, M.2
  • 9
    • 0002166622 scopus 로고    scopus 로고
    • On estimation for discretely observed diffusions: A review
    • Bibby, B.M. & Sørensen, M. (1996). On estimation for discretely observed diffusions: A review. Theory of Stochastic Processes, 2, 49-56.
    • (1996) Theory of Stochastic Processes , vol.2 , pp. 49-56
    • Bibby, B.M.1    Sørensen, M.2
  • 10
    • 0002314533 scopus 로고    scopus 로고
    • A hyperbolic diffusion model for stock prices
    • Bibby, B.M. & Sørensen, M. (1997). A hyperbolic diffusion model for stock prices. Finance Stock., 1, 25-41.
    • (1997) Finance Stock. , vol.1 , pp. 25-41
    • Bibby, B.M.1    Sørensen, M.2
  • 11
    • 0035529545 scopus 로고    scopus 로고
    • Simplified estimating functions for diffusion models with a high-dimensional parameter
    • Bibby, B.M. & Sørensen, M. (2001). Simplified estimating functions for diffusion models with a high-dimensional parameter. Scand. J. Statist., 28, 99-112.
    • (2001) Scand. J. Statist. , vol.28 , pp. 99-112
    • Bibby, B.M.1    Sørensen, M.2
  • 12
    • 0001007401 scopus 로고
    • The Lindeberg-Lévy Theorem for martingales
    • Billingsley, P. (1961). The Lindeberg-Lévy Theorem for martingales. Proc. Amer. Math. Soc., 12, 788-792.
    • (1961) Proc. Amer. Math. Soc. , vol.12 , pp. 788-792
    • Billingsley, P.1
  • 13
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654.
    • (1973) Journal of Political Economy , vol.81 , pp. 637-654
    • Black, F.1    Scholes, M.2
  • 14
    • 84977707412 scopus 로고
    • An empirical comparison of alternative models of the short-term interest rate
    • Chan, K.C., Karolyi, G.A., Longstaff, F.A. & Sanders, A.B. (1992). An empirical comparison of alternative models of the short-term interest rate. J. Finance, 47, 1209-1227.
    • (1992) J. Finance , vol.47 , pp. 1209-1227
    • Chan, K.C.1    Karolyi, G.A.2    Longstaff, F.A.3    Sanders, A.B.4
  • 16
    • 0001700428 scopus 로고
    • Estimation of the coefficients of a diffusion from discrete observations
    • Dacunha-Castelle, D. & Florens-Zmirou, D. (1986). Estimation of the coefficients of a diffusion from discrete observations. Stochastics, 19, 263-284.
    • (1986) Stochastics , vol.19 , pp. 263-284
    • Dacunha-Castelle, D.1    Florens-Zmirou, D.2
  • 17
    • 0035539279 scopus 로고    scopus 로고
    • A jump-diffusion model for exchange rates in a target zone
    • De Jong, F., Drost, F.C. & Werker, B.J.M. (2001). A jump-diffusion model for exchange rates in a target zone. Statist. Neerlandica, 55, 270-300.
    • (2001) Statist. Neerlandica , vol.55 , pp. 270-300
    • De Jong, F.1    Drost, F.C.2    Werker, B.J.M.3
  • 18
    • 12244284604 scopus 로고    scopus 로고
    • The fast climate fluctuations during the stadial and interstadial climate states
    • Ditlevsen, P.D., Ditlevsen, S. & Andersen, K.K. (2002). The fast climate fluctuations during the stadial and interstadial climate states. Annals of Glaciology, 35, 457-462.
    • (2002) Annals of Glaciology , vol.35 , pp. 457-462
    • Ditlevsen, P.D.1    Ditlevsen, S.2    Andersen, K.K.3
  • 19
    • 10244253582 scopus 로고    scopus 로고
    • Stochastic vs. deterministic uptake of dodecanedioic acid by isolated rat livers
    • Department of Biostatistics, University of Copenhagen
    • Ditlevsen, S. & De Gaetano, A. (2003). Stochastic vs. deterministic uptake of dodecanedioic acid by isolated rat livers. Research report 03/11, Department of Biostatistics, University of Copenhagen.
    • (2003) Research Report 03/11
    • Ditlevsen, S.1    De Gaetano, A.2
  • 20
    • 0023310925 scopus 로고
    • On estimating the diffusion coefficient
    • Dohnal, G. (1987). On estimating the diffusion coefficient. J. Appl. Probab., 24, 105-114.
    • (1987) J. Appl. Probab. , vol.24 , pp. 105-114
    • Dohnal, G.1
  • 21
    • 0000440935 scopus 로고    scopus 로고
    • Likelihood inference for discretely observed non-linear diffusions
    • Elerian, O., Chib, S. & Shephard, N. (2001). Likelihood inference for discretely observed non-linear diffusions. Econometrica, 69, 959-993.
    • (2001) Econometrica , vol.69 , pp. 959-993
    • Elerian, O.1    Chib, S.2    Shephard, N.3
  • 22
    • 0035586814 scopus 로고    scopus 로고
    • MCMC analysis of diffusion models with application to finance
    • Eraker, B. (2001). MCMC analysis of diffusion models with application to finance. J. Bus. and Econom. Statist., 19, 177-191.
    • (2001) J. Bus. and Econom. Statist. , vol.19 , pp. 177-191
    • Eraker, B.1
  • 23
    • 84881079791 scopus 로고
    • Approximate discrete-time schemes for statistics of diffusion processes
    • Florens-Zmirou, D. (1989). Approximate discrete-time schemes for statistics of diffusion processes. Statistics, 20, 547-557.
    • (1989) Statistics , vol.20 , pp. 547-557
    • Florens-Zmirou, D.1
  • 24
    • 21344487770 scopus 로고
    • On estimating the diffusion coefficient from discrete observations
    • Florens-Zmirou, D. (1993). On estimating the diffusion coefficient from discrete observations. J. Appl. Probab., 30, 790-804.
    • (1993) J. Appl. Probab. , vol.30 , pp. 790-804
    • Florens-Zmirou, D.1
  • 25
    • 33746404294 scopus 로고    scopus 로고
    • Estimating stochastic differential equations efficiently by minimum chi-squared
    • Gallant, A.R. & Long, J.R. (1997). Estimating stochastic differential equations efficiently by minimum chi-squared. Biometrika, 84, 125-141.
    • (1997) Biometrika , vol.84 , pp. 125-141
    • Gallant, A.R.1    Long, J.R.2
  • 27
    • 0000871426 scopus 로고
    • Estimation of the diffusion coefficient for diffusion processes: Random sampling
    • Genon-Catalot, V. & Jacod, J. (1994). Estimation of the diffusion coefficient for diffusion processes: random sampling. Scand. J. Statist., 21, 193-221.
    • (1994) Scand. J. Statist. , vol.21 , pp. 193-221
    • Genon-Catalot, V.1    Jacod, J.2
  • 28
    • 0001662487 scopus 로고
    • Non-parametric estimation of the diffusion coefficient by wavelets methods
    • Genon-Catalot, V., Laredo, C. & Picard, D. (1992). Non-parametric estimation of the diffusion coefficient by wavelets methods. Scand. J. Statist., 19, 317-335.
    • (1992) Scand. J. Statist. , vol.19 , pp. 317-335
    • Genon-Catalot, V.1    Laredo, C.2    Picard, D.3
  • 30
    • 0000414660 scopus 로고
    • Large sample properties of generalized method of moments estimators
    • Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50, 1029-1054.
    • (1982) Econometrica , vol.50 , pp. 1029-1054
    • Hansen, L.P.1
  • 31
    • 0029182376 scopus 로고
    • Back to the future: Generating moment implications for continuous-time Markov processes
    • Hansen, L.P. & Scheinkman, J.A. (1995). Back to the future: generating moment implications for continuous-time Markov processes. Econometrica, 63, 767-804.
    • (1995) Econometrica , vol.63 , pp. 767-804
    • Hansen, L.P.1    Scheinkman, J.A.2
  • 33
    • 0002144640 scopus 로고    scopus 로고
    • Adaptive estimation in diffusion processes
    • Hoffmann, M. (1999). Adaptive estimation in diffusion processes. Stochastic Process. Appl., 79, 135-163.
    • (1999) Stochastic Process. Appl. , vol.79 , pp. 135-163
    • Hoffmann, M.1
  • 34
    • 10244224932 scopus 로고    scopus 로고
    • Maximum likelihood estimation of non-linear continuous-time term-structure models
    • Department of Finance, Aarhus School of Business
    • Honoré, P. (1997). Maximum likelihood estimation of non-linear continuous-time term-structure models. Working paper 1997-7, Department of Finance, Aarhus School of Business.
    • (1997) Working Paper 1997-7
    • Honoré, P.1
  • 35
    • 0035285979 scopus 로고    scopus 로고
    • Discretely observed diffusions: Classes of estimating functions and small Δ-optimality
    • Jacobsen, M. (2001). Discretely observed diffusions: classes of estimating functions and small Δ-optimality. Scand. J. Statist., 28, 123-149.
    • (2001) Scand. J. Statist. , vol.28 , pp. 123-149
    • Jacobsen, M.1
  • 36
    • 10244230564 scopus 로고    scopus 로고
    • Optimality and small Δ-optimality of martingale estimating functions
    • Jacobsen, M. (2002). Optimality and small Δ-optimality of martingale estimating functions. Bernoulli, 8, 643-668.
    • (2002) Bernoulli , vol.8 , pp. 643-668
    • Jacobsen, M.1
  • 37
    • 0034340752 scopus 로고    scopus 로고
    • Non-parametric kernel estimation of the coefficient of a diffusion
    • Jacod, J. (2000). Non-parametric kernel estimation of the coefficient of a diffusion. Scand. J. Statist., 27, 83-96.
    • (2000) Scand. J. Statist. , vol.27 , pp. 83-96
    • Jacod, J.1
  • 38
    • 85016660810 scopus 로고    scopus 로고
    • Transition densities of diffusion processes: Numerical comparison of approximation techniques
    • Jensen, B. & Poulsen, R. (2002). Transition densities of diffusion processes: numerical comparison of approximation techniques. J. Derivatives, 9, 18-32.
    • (2002) J. Derivatives , vol.9 , pp. 18-32
    • Jensen, B.1    Poulsen, R.2
  • 41
    • 0034340736 scopus 로고    scopus 로고
    • Simple and explicit estimating functions for a discretely observed diffusion process
    • Kessler, M. (2000). Simple and explicit estimating functions for a discretely observed diffusion process. Scand. J. Statist., 27, 65-82.
    • (2000) Scand. J. Statist. , vol.27 , pp. 65-82
    • Kessler, M.1
  • 42
    • 0035995078 scopus 로고    scopus 로고
    • Computational aspects related to martingale estimating functions for a discretely observed diffusion
    • Kessler, M. & Paredes, S. (2002). Computational aspects related to martingale estimating functions for a discretely observed diffusion. Scand. J. Statist., 29, 425-440.
    • (2002) Scand. J. Statist. , vol.29 , pp. 425-440
    • Kessler, M.1    Paredes, S.2
  • 43
    • 0000647626 scopus 로고    scopus 로고
    • Estimating equations based on eigenfunctions for a discretely observed diffusion process
    • Kessler, M. & Sørensen, M. (1999). Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli, 5, 299-314.
    • (1999) Bernoulli , vol.5 , pp. 299-314
    • Kessler, M.1    Sørensen, M.2
  • 46
    • 84974325324 scopus 로고
    • Maximum likelihood estimation of generalized Itô processes with discretely sampled data
    • Lo, A.W. (1988). Maximum likelihood estimation of generalized Itô processes with discretely sampled data. Econometric Theory, 4, 231-247.
    • (1988) Econometric Theory , vol.4 , pp. 231-247
    • Lo, A.W.1
  • 47
    • 84972530323 scopus 로고
    • Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes
    • Pedersen, A.R. (1995a). Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes. Bernoulli, 1(3), 257-279.
    • (1995) Bernoulli , vol.1 , Issue.3 , pp. 257-279
    • Pedersen, A.R.1
  • 48
    • 0002841968 scopus 로고
    • A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations
    • Pedersen, A.R. (1995b). A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scand. J. Statist., 22, 55-71.
    • (1995) Scand. J. Statist. , vol.22 , pp. 55-71
    • Pedersen, A.R.1
  • 49
    • 0034336052 scopus 로고    scopus 로고
    • Estimating the nitrous oxide emission rate from the soil surface by means of a diffusion model
    • Pedersen, A.R. (2000). Estimating the nitrous oxide emission rate from the soil surface by means of a diffusion model. Scand. J. Statist., 27, 385-403.
    • (2000) Scand. J. Statist. , vol.27 , pp. 385-403
    • Pedersen, A.R.1
  • 50
    • 16344386417 scopus 로고    scopus 로고
    • Approximate maximum likelihood estimation of discretely observed diffusion processes
    • Centre for Analytical Finance, Aarhus
    • Poulsen, R. (1999). Approximate maximum likelihood estimation of discretely observed diffusion processes. Working paper 29. Centre for Analytical Finance, Aarhus.
    • (1999) Working Paper 29
    • Poulsen, R.1
  • 51
    • 10244252366 scopus 로고    scopus 로고
    • On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm
    • Roberts, G.O. & Strainer, O. (2001). On inference for partially observed nonlinear diffusion models using the Metropolis- Hastings algorithm. Biometrika, 88, 603-621.
    • (2001) Biometrika , vol.88 , pp. 603-621
    • Roberts, G.O.1    Strainer, O.2
  • 53
    • 0001790102 scopus 로고    scopus 로고
    • Statistical aspects of ARCH and stochastic volatility
    • Eds. D.R. Cox, D.V. Hinkley and O.E. Barndorff-Nielsen, London: Chapman & Hall
    • Shephard, N. (1996). Statistical aspects of ARCH and stochastic volatility. In Time Series Models in Econometrics, Finance and Other Fields. Eds. D.R. Cox, D.V. Hinkley and O.E. Barndorff-Nielsen, pp. 1-67. London: Chapman & Hall.
    • (1996) Time Series Models in Econometrics, Finance and Other Fields , pp. 1-67
    • Shephard, N.1
  • 55
    • 0035285792 scopus 로고    scopus 로고
    • Discretely observed diffusions: Approximation of the continuous-time score function
    • Sørensen, H. (2001). Discretely observed diffusions: approximation of the continuous-time score function. Scand. J. Statist., 28, 113-121.
    • (2001) Scand. J. Statist. , vol.28 , pp. 113-121
    • Sørensen, H.1
  • 56
    • 0037840573 scopus 로고    scopus 로고
    • Simulated likelihood approximations for stochastic volatility models
    • Sørensen, H. (2003). Simulated likelihood approximations for stochastic volatility models. Scand. J. Statist., 30, 257-276.
    • (2003) Scand. J. Statist. , vol.30 , pp. 257-276
    • Sørensen, H.1
  • 57
    • 0000475705 scopus 로고    scopus 로고
    • Estimating functions for discretely observed diffusions: A review
    • Eds. I.V. Basawa, V.P. Godambe and R.L. Taylor, IMS Lecture notes
    • Sørensen, M. (1997). Estimating functions for discretely observed diffusions: A review. In Selected Proceedings of the Symposium on Estimating Functions, Eds. I.V. Basawa, V.P. Godambe and R.L. Taylor, IMS Lecture notes, 32, 305-325.
    • (1997) Selected Proceedings of the Symposium on Estimating Functions , vol.32 , pp. 305-325
    • Sørensen, M.1
  • 58
    • 0011425031 scopus 로고    scopus 로고
    • On asymptotics of estimating functions
    • Sørensen, M. (1999). On asymptotics of estimating functions. Braz. J. Probab. Statist., 13, 111-136.
    • (1999) Braz. J. Probab. Statist. , vol.13 , pp. 111-136
    • Sørensen, M.1
  • 59
    • 0000953249 scopus 로고    scopus 로고
    • Prediction-based estimating functions
    • Sørensen, M. (2000b). Prediction-based estimating functions. Econometrics J., 3, 123-147.
    • (2000) Econometrics J. , vol.3 , pp. 123-147
    • Sørensen, M.1


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