135
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Parameter estimation for multivariate diffusion processes with the time inhomogeneously positive semidefinite diffusion matrix

ORCID Icon, &
Pages 11010-11025 | Received 31 Jul 2016, Accepted 27 Oct 2016, Published online: 07 Aug 2017

References

  • Aït-Sahalia, Y. (2002). Maximum likelihood estimation of discretely sampled diffusions: A closed-form approximation approach. Econometrica 70:223–262.
  • Aït-Sahalia, Y. (2008). Closed-form likelihood expansions for multivariate diffusions. Ann. Stat. 36:906–937.
  • Aït-Sahalia, Y., Yu, J. (2006). Saddlepoint approximation for continuous-time Markov processes. J. Economet. 134:507–551.
  • Bibby, B.M., SØrensen, M. (1995). Martingale estimation functions for discretely observed diffusion processes. Bernoulli 1:17–39.
  • Bibby, B.M., Jacobsen, M., SØrensen, M. (2002). Estimating Functions for Discretely Sampled Diffusion-Type Models. Amsterdam: Handbook of Financial Econometrics, North-Holland.
  • Brockwell, P.J., Davis, R.A., Yu, Y. (2007). Continuous-time Gaussian autoregression. Stat. Sin. 17:63–80.
  • Brockwell, P.J., Schlemm, E. (2013). Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations. J. Multivariate Anal. 115:217–251.
  • Brockwell, P.J., Kreiss, J.P. (2014). Bootstrapping continuous-time autoregressive processes. Ann. Inst. Stat. Math. 66:75–92.
  • Chacko, G., Viceira, L.M. (2003). Spectral GMM estimation of continuous-time processes. J. Economet. 116:259–292.
  • Choi, S. (2013). Closed-form likelihood expansions for multivariate time-inhomogeneous diffusions. J. Economet. 174:45–65.
  • Du, X.L., Wang, F.Q. (2010). Modal identification based on Gaussian continuous time autoregressive moving average model. J. Sound Vib. 329:4294–4312.
  • Du, X.L., Lin, J.G., Liu, G.X., Zhou, X.Q. (2015). A physical parameter identification method of Lévy-driven vibratory systems based on multipower variation processes. J. Sound Vib. 343:216–229.
  • Hansen, L.P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50:1029–1054.
  • Hurn, A., Jeisman, J., Lindsay, K. (2007). Seeing the wood for the trees: A critical evaluation of methods to estimate the parameters of stochastic differential equations. J. Financial Economet. 5:390–455.
  • Karatzas, I., Shreve, S.E. (1991). Brownian Motion and Stochastic Calculus. New York: Springer.
  • Liptser, R.S., Shiryayev, A.N. (1977). Statistics of Random Processes, Parts I. New York: Springer-Verlag.
  • Liu, Q.F., Nishiyama, Y. (2008). Maximum empirical likelihood estimation of continuous-time models with conditional characteristic functions. Math. Comput. Simul. 78:341–350.
  • Øksendal, B. (1995). Stochastic Differential Equations. New York: Springer-Verlag.
  • Phillips, P.C.B. (1972). The structural estimation of a stochastic differential equation system. Econometrica 6:1021–1041.
  • Preston, S., Wood, A. (2012). Approximation of transition densities of stochastic differential equations by saddlepoint methods applied to small-time Ito-Taylor sample-path expansions. Stat. Comput. 22:205–217.
  • Singleton, K. (2001). Estimation of affine asset pricing models using the empirical characteristic function. J. Ecomomet. 102:111–141.
  • Stramer, O., Bognar, M., Schneider, P. (2010). Bayesian inference for discretely sampled Markov processes with closed-form likelihood expansions. J. Financial Economet. 8:450–480.
  • Varughese, M. (2009). On the accuracy of a diffusion approximation to a discrete state-space Markovian model of a population. Theor. Popul. Biol. 76:241–247.
  • Varughese, M., Fatti, L. (2008). Incorporating environmental stochasticity within a biological population model. Theor. Popul. Biol. 74:115–129.
  • Varughese, M. (2011). A framework for modelling ecological communities and their interactions with the environment. Ecol. Complex 8:105–112.
  • Wang, H., Zhu, Q.X. (2015). Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form. Automatica 54:284–291.
  • Yao, Z.Y., Wang, F.Q. (2003). Method of identification of a structural physical parameters based continuous time model. J. Southeast Univ. (Nat. Sci. Ed.) 33:617–620.
  • Yoshida, N. (1992). Estimation for diffusion processes from discrete observation. J. Multivariate Anal. 41:220–242.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.