메뉴 건너뛰기




Volumn 35, Issue 3, 2008, Pages 438-465

The Pearson diffusions: A class of statistically tractable diffusion processes

Author keywords

Eigenfunction; Ergodic diffusion; Integrated diffusion; Likelihood inference; Martingale estimating function; Mixing; Optimal estimating function; Pearson system; Prediction based estimating function; Quasi likelihood; Spectral methods

Indexed keywords


EID: 50249097592     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2007.00592.x     Document Type: Article
Times cited : (160)

References (52)
  • 4
    • 0035648379 scopus 로고    scopus 로고
    • Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial econometrics (with discussion)
    • Barndorff-Nielsen, O. E. Shephard, N. (2001). Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial econometrics (with discussion). J. Roy. Statist. Soc. Ser. B 63, 167 241.
    • (2001) J. Roy. Statist. Soc. Ser. B , vol.63 , pp. 167-241
    • Barndorff-Nielsen, O.E.1    Shephard, N.2
  • 6
    • 33646690994 scopus 로고    scopus 로고
    • Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes
    • Beskos, A., Papaspiliopoulos, O., Roberts, G. O. Fearnhead, P. (2006). Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. J. Roy. Statist. Soc. Ser. B 68, 333 382.
    • (2006) J. Roy. Statist. Soc. Ser. B , vol.68 , pp. 333-382
    • Beskos, A.1    Papaspiliopoulos, O.2    Roberts, G.O.3    Fearnhead, P.4
  • 7
    • 10244256022 scopus 로고    scopus 로고
    • Estimating functions for discretely sampled diffusion-type models
    • In. eds. Y. Ait-Sahalia. L. P. Hansen. North-Holland, Amsterdam.
    • Bibby, B. M., Jacobsen, M. Sørensen, M. (2004). Estimating functions for discretely sampled diffusion-type models. In Handbook of financial econometrics (eds Y. Ait-Sahalia L. P. Hansen North-Holland, Amsterdam.
    • (2004) Handbook of Financial Econometrics
    • Bibby, B.M.1    Jacobsen, M.2    Sørensen, M.3
  • 8
    • 22244488845 scopus 로고    scopus 로고
    • Diffusion-type models with given marginals and autocorrelation function
    • Bibby, B. M., Skovgaard, I. M. Sørensen, M. (2005). Diffusion-type models with given marginals and autocorrelation function. Bernoulli 11, 191 220.
    • (2005) Bernoulli , vol.11 , pp. 191-220
    • Bibby, B.M.1    Skovgaard, I.M.2    Sørensen, M.3
  • 9
    • 1542493781 scopus 로고    scopus 로고
    • Hyperbolic processes in finance
    • In. ed. S. Rachev. Elsevier Science, North-Holland, Amsterdam.
    • Bibby, B. M. Sørensen, M. (2003). Hyperbolic processes in finance. In Handbook of heavy tailed distributions in finance (ed. S. Rachev 211 248. Elsevier Science, North-Holland, Amsterdam.
    • (2003) Handbook of Heavy Tailed Distributions in Finance , pp. 211-248
    • Bibby, B.M.1    Sørensen, M.2
  • 10
    • 0142013411 scopus 로고    scopus 로고
    • Estimating stochastic volatility diffusion using conditional moments of integrated volatility
    • Bollerslev, T. Zhou, H. (2002). Estimating stochastic volatility diffusion using conditional moments of integrated volatility. J. Econometrics 109, 33 65.
    • (2002) J. Econometrics , vol.109 , pp. 33-65
    • Bollerslev, T.1    Zhou, H.2
  • 14
    • 0242473436 scopus 로고    scopus 로고
    • Spectral GMM estimation of continuous-time processes
    • Chacko, G. Viceira, L. M. (2003). Spectral GMM estimation of continuous-time processes. J. Econometrics 116, 259 292.
    • (2003) J. Econometrics , vol.116 , pp. 259-292
    • Chacko, G.1    Viceira, L.M.2
  • 16
    • 0001205798 scopus 로고
    • A theory of the term structure of interest rates
    • Cox, Jr., J. C., Ingersoll, J. E. Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica 53, 385 407.
    • (1985) Econometrica , vol.53 , pp. 385-407
    • Cox Jr., C.J.1    Ingersoll, J.E.2    Ross, S.A.3
  • 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. Ann. Glaciology 35, 457 462.
    • (2002) Ann. Glaciology , vol.35 , pp. 457-462
    • Ditlevsen, P.D.1    Ditlevsen, S.2    Andersen, K.K.3
  • 19
    • 4043148626 scopus 로고    scopus 로고
    • Inference for observations of integrated diffusion processes
    • Ditlevsen, S. Sørensen, M. (2004). Inference for observations of integrated diffusion processes. Scand. J. Statist. 31, 417 429.
    • (2004) Scand. J. Statist. , vol.31 , pp. 417-429
    • Ditlevsen, S.1    Sørensen, M.2
  • 23
    • 0003215606 scopus 로고    scopus 로고
    • Stochastic volatility models as hidden Markov models and statistical applications
    • Genon-Catalot, V., Jeantheau, T. Laredo, C. (2000). Stochastic volatility models as hidden Markov models and statistical applications. Bernoulli 6, 1051 1079.
    • (2000) Bernoulli , vol.6 , pp. 1051-1079
    • Genon-Catalot, V.1    Jeantheau, T.2    Laredo, C.3
  • 24
    • 0348238317 scopus 로고    scopus 로고
    • Parameter estimation for a discrete sampling of an integrated Ornstein-Uhlenbeck process
    • Gloter, A. (2000). Parameter estimation for a discrete sampling of an integrated Ornstein-Uhlenbeck process. Statistics 35, 225 243.
    • (2000) Statistics , vol.35 , pp. 225-243
    • Gloter, A.1
  • 25
    • 33645045882 scopus 로고    scopus 로고
    • Parameter estimation for a discretely observed integrated diffusion process
    • Gloter, A. (2006). Parameter estimation for a discretely observed integrated diffusion process. Scand. J. Statist. 33, 83 104.
    • (2006) Scand. J. Statist. , vol.33 , pp. 83-104
    • Gloter, A.1
  • 26
    • 0036334160 scopus 로고    scopus 로고
    • LAN property for ergodic diffusions with discrete observations
    • Gobet, E. (2002). LAN property for ergodic diffusions with discrete observations. Ann. Inst. H. Poincaré Probab. Statist. 38, 711 737.
    • (2002) Ann. Inst. H. Poincaré Probab. Statist. , vol.38 , pp. 711-737
    • Gobet, E.1
  • 27
    • 0000390402 scopus 로고
    • Quasi likelihood and optimal estimation
    • Godambe, V. P. Heyde, C. C. (1987). Quasi likelihood and optimal estimation. Int. Statist. Rev. 55, 231 244.
    • (1987) Int. Statist. Rev. , vol.55 , pp. 231-244
    • Godambe, V.P.1    Heyde, C.C.2
  • 28
    • 33644532586 scopus 로고    scopus 로고
    • Multivariate Jacobi process and with application to smooth transitions
    • Gourieroux, C. Jasiak, J. (2006). Multivariate Jacobi process and with application to smooth transitions. J. Econometrics 131, 475 505.
    • (2006) J. Econometrics , vol.131 , pp. 475-505
    • Gourieroux, C.1    Jasiak, J.2
  • 29
    • 0000414660 scopus 로고
    • Large sample properties of generalized method of moments estimator
    • Hansen, L. P. (1982). Large sample properties of generalized method of moments estimator. Econometrica 50, 1029 1054.
    • (1982) Econometrica , vol.50 , pp. 1029-1054
    • Hansen, L.P.1
  • 30
    • 0010661898 scopus 로고    scopus 로고
    • Spectral methods for identifying scalar diffusions
    • Hansen, L. P., Scheinkman, J. A. Touzi, N. (1998). Spectral methods for identifying scalar diffusions. J. Econometrics 86, 1 32.
    • (1998) J. Econometrics , vol.86 , pp. 1-32
    • Hansen, L.P.1    Scheinkman, J.A.2    Touzi, N.3
  • 32
    • 0000007742 scopus 로고
    • Systems of polynomials connected with the Charlier expansions and the Pearson differential and difference equations
    • Hildebrandt, E. H. (1931). Systems of polynomials connected with the Charlier expansions and the Pearson differential and difference equations. Ann. Math. Statist. 2, 379 439.
    • (1931) Ann. Math. Statist. , vol.2 , pp. 379-439
    • Hildebrandt, E.H.1
  • 36
    • 0000647626 scopus 로고    scopus 로고
    • Estimating equations based on eigenfunctions for a discretely observed diffusion
    • Kessler, M. Sørensen, M. (1999). Estimating equations based on eigenfunctions for a discretely observed diffusion. Bernoulli 5, 299 314.
    • (1999) Bernoulli , vol.5 , pp. 299-314
    • Kessler, M.1    Sørensen, M.2
  • 37
    • 33947315969 scopus 로고    scopus 로고
    • A diffusion model for exchange rates in a target zone
    • Larsen, K. S. Sørensen, M. (2007). A diffusion model for exchange rates in a target zone. Mathem. Finance 17, 285 306.
    • (2007) Mathem. Finance , vol.17 , pp. 285-306
    • Larsen, K.S.1    Sørensen, M.2
  • 40
    • 0036407554 scopus 로고    scopus 로고
    • Theoretical comparison between integrated and realized volatility
    • Meddahi, N. (2002b). Theoretical comparison between integrated and realized volatility. J. Appl. Econometrics 17, 479 508.
    • (2002) J. Appl. Econometrics , vol.17 , pp. 479-508
    • Meddahi, N.1
  • 41
    • 0345980041 scopus 로고    scopus 로고
    • Non-Gaussian distribution for stock returns and related stochastic differential equation
    • Nagahara, Y. (1996). Non-Gaussian distribution for stock returns and related stochastic differential equation. Financial Eng. Japanese Markets 3, 121 149.
    • (1996) Financial Eng. Japanese Markets , vol.3 , pp. 121-149
    • Nagahara, Y.1
  • 42
    • 70350303608 scopus 로고
    • Non-linear time series models and dynamical systems
    • In. Vol. 5 (eds. E. J. Hannan, P. R. Krishnaiah. M. M. Rao. Elsevier Science Publishers.
    • Ozaki, T. (1985). Non-linear time series models and dynamical systems. In Handbook of statistics, Vol. 5 (eds E. J. Hannan, P. R. Krishnaiah M. M. Rao 25 83. Elsevier Science Publishers.
    • (1985) Handbook of Statistics , pp. 25-83
    • Ozaki, T.1
  • 43
    • 0000678972 scopus 로고
    • Contributions to the mathematical theory of evolution II. Skew variation in homogeneous material
    • Pearson, K. (1895). Contributions to the mathematical theory of evolution II. Skew variation in homogeneous material. Philos. Trans. R. Soc. Lond. Ser. A 186, 343 414.
    • (1895) Philos. Trans. R. Soc. Lond. Ser. a , vol.186 , pp. 343-414
    • Pearson, K.1
  • 44
    • 5244272034 scopus 로고
    • Generalization of some types of the frequency curves of Professor Pearson
    • Romanovsky, V. (1924). Generalization of some types of the frequency curves of Professor Pearson. Biometrika 16, 106 117.
    • (1924) Biometrika , vol.16 , pp. 106-117
    • Romanovsky, V.1
  • 45
    • 0000807050 scopus 로고    scopus 로고
    • Estimation of affine asset pricing models using the empirical characteristic function
    • Singleton, K. J. (2001). Estimation of affine asset pricing models using the empirical characteristic function. J. Econometrics 102, 111 141.
    • (2001) J. Econometrics , vol.102 , pp. 111-141
    • Singleton, K.J.1
  • 46
    • 0000475705 scopus 로고    scopus 로고
    • Estimating functions for discretely observed diffusions: A review
    • In. eds. I. V. Basawa, V. P. Godambe. R. L. Taylor. IMS Lecture Notes - Monograph Series, Vol. 32. Institute of Mathematical Statistics. Hayward.
    • 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 R. L. Taylor 305 325. IMS Lecture Notes - Monograph Series, Vol. 32. Institute of Mathematical Statistics. Hayward.
    • (1997) Selected Proceedings of the Symposium on Estimating Functions , pp. 305-325
    • Sørensen, M.1
  • 47
    • 0011425031 scopus 로고    scopus 로고
    • On asymptotics of estimating functions
    • Sørensen, M. (1999). On asymptotics of estimating functions. Braz. J. Probab. Stat. 13, 111 136.
    • (1999) Braz. J. Probab. Stat. , vol.13 , pp. 111-136
    • Sørensen, M.1
  • 48
    • 0000953249 scopus 로고    scopus 로고
    • Prediction-based estimating functions
    • Sørensen, M. (2000). Prediction-based estimating functions. Econometrics J. 3, 123 147.
    • (2000) Econometrics J. , vol.3 , pp. 123-147
    • Sørensen, M.1
  • 50
    • 0001439117 scopus 로고
    • The construction of a class of stationary Markoff processes
    • In. ed. R. Bellman. American Mathematical Society, Rhode Island.
    • Wong, E. (1964). The construction of a class of stationary Markoff processes. In Stochastic processes in mathematical physics and engineering (ed. R. Bellman 264 276. American Mathematical Society, Rhode Island.
    • (1964) Stochastic Processes in Mathematical Physics and Engineering , pp. 264-276
    • Wong, E.1
  • 51
    • 0010660619 scopus 로고    scopus 로고
    • Finite sample properties of EMM, GMM, QMLE and MLE for a square-root interest rate diffusion model
    • Zhou, H. (2001). Finite sample properties of EMM, GMM, QMLE and MLE for a square-root interest rate diffusion model. J. Comp. Finance 5, 89 122.
    • (2001) J. Comp. Finance , vol.5 , pp. 89-122
    • Zhou, H.1
  • 52
    • 50249150576 scopus 로고    scopus 로고
    • Itô conditional moment generator and the estimation of short-rate processes
    • Zhou, H. (2003). Itô conditional moment generator and the estimation of short-rate processes. J. Financial Econometrics 1, 250 271.
    • (2003) J. Financial Econometrics , vol.1 , pp. 250-271
    • Zhou, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.