Generalized moment estimation of stochastic differential equations

• Ait-Sahalia Y (2002) Maximum-likelihood estimation of discretely-sampled diffusions: a closed-form approximation approach. Econometrica 70:223–262

  Article  MathSciNet  MATH  Google Scholar 

• Anatolyev S (2005) Gmm, gel, serial correlation and asymptotic bias. Econometrica 73:983–1002

  Article  MathSciNet  MATH  Google Scholar 

• Anatolyev S, Gospodinov N (2011) Methods for estimation and inference in modern econometrics. Chapman and Hall/CRC, Boca Raton

  MATH  Google Scholar 

• Andrews DWK (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59:817–858

  Article  MathSciNet  MATH  Google Scholar 

• Bachelier L (1900) Theorie de la speculation. English translation by A J Boness. In: Cootner PH (ed) The random character of stock market prices. MIT Press, Cambridge, pp 17–78, 1967

• Bera A, Bilias Y (2002) The mm, me, ml, el, ef and gmm approaches to estimation: a synthesis. J Econom 107:51–86

  Article  MathSciNet  MATH  Google Scholar 

• Bickel P, Klassen C, Ritov Y, Wellner J (1993) Efficient and adaptative estimation for semiparametric models. Johns Hopkins Press, Baltimore

  Google Scholar 

• Bishwal JPN (2007) Parameter estimation in stochastic differential equations. Springer, Berlin

  MATH  Google Scholar 

• Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81(3):637–654

  Article  MATH  Google Scholar 

• Brennan M, Schwartz ES (1980) Analyzing convertible bonds. J Financ Quant Anal 15:907–929

  Article  Google Scholar 

• Chan KG, Karolyi G, Longstaff F, Sanders AB (1992) An empirical comparasion of alternative models of term structure of interest rates. J Finance 47:1209–1227

  Article  Google Scholar 

• Chaussé P (2010) Computing generalized method of moments and generalized empirical likelihood with R. J Stat Softw 34(11):1–35

  Article  Google Scholar 

• Core Team R (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

  Google Scholar 

• Cox J (1975) Notes on option pricing I: constant elasticity of diffusions. Unpublished manuscript, Stanford University

• Cox JC, Ingersoll JE, Ross SA (1980) An analysis of variable rate loan contracts. J Finance 35(2):389–403

  Article  Google Scholar 

• Cox JC, Ingersoll JE, Ross SA (1985) A theory of the term structure of interest rates. Econometrica 53:385–407

  Article  MathSciNet  MATH  Google Scholar 

• Cuchiero C, Keller-Ressel M, Teichmann J (2012) Polynomial processes and their applications in mathematical finance. Finance Stoch 16(4):711–740

  Article  MathSciNet  MATH  Google Scholar 

• DasGupta A (2008) Asymptotic theory of statistics and probability. Springer, Berlin

  MATH  Google Scholar 

• Delbaen F, Schachermayer W (1994) A general version of the fundamental theory of asset pricing. Math Ann 300:463–250

  Article  MathSciNet  MATH  Google Scholar 

• Dothan UL (1978) On the term structure of interest rates. J Financ Econ 6:59–59

  Article  Google Scholar 

• Evdokimov K, Kitamura Y, Otsu T (2009) Robust estimation of moment condition models with weakly dependente data. Unpublished working paper

• Fernholz ER (2002) Stochastic portfolio theory. Springer, New York

  Book  MATH  Google Scholar 

• Fernholz ER, Karatzas I (2006) The implied liquidity premium for equities. Ann Finance 2:87–99

  Article  MATH  Google Scholar 

• Filipovic D, Mayerhofer E, Schneider P (2013) Density approximations for multivariate affine jump-diffusion processes. J Econom 176(2):93–111

  Article  MathSciNet  MATH  Google Scholar 

• Gourieroux C, Monfort A (1995) Statistics and econometric models. Cambridge University Press, Cambridge

  Book  MATH  Google Scholar 

• Gourieroux C, Monfort A (1996) Simulation-based econometric models. Oxford University Press, Oxford

  MATH  Google Scholar 

• Hansen LP (1982) Large sample properties of generalized method of moments estimators. Econometrica 50:1029–1054

  Article  MathSciNet  MATH  Google Scholar 

• Hansen LP, Heaton J, Yaron A (1996) Finite sample properties of some alternative gmm estimators. J Bus Econ Stat 14:262–280

  Google Scholar 

• Harrison JM, Kreps D (1979) Martingales and arbitrage in multiperiod securities markets. J Econ Theory 20:381–408

  Article  MathSciNet  MATH  Google Scholar 

• Harrison JM, Pliska S (1981) Martingales and stochastic integrals in the theory of continous trading. Stochast Process Their Appl 11:215–260

  Article  MathSciNet  MATH  Google Scholar 

• Iacus SM (2008) Simulation and inference for stochastic differential equations with R examples. Springer, Berlin

  Book  MATH  Google Scholar 

• Imbens GW, Spady RH, Johnson P (1998) Information theoretic approaches to inference in moment conditions models. Econometrica 66:333–357

  Article  MathSciNet  MATH  Google Scholar 

• Karatzas I, Shreve SE (1987) Brownian motion and stochastic calculus. Springer, Berlin

  MATH  Google Scholar 

• Kitamura Y (1997) Empirical likelihood methods with weakly dependent processes. Ann Stat 25:2084–2102

  Article  MathSciNet  MATH  Google Scholar 

• Kitamura Y (2006) Empirical likelihood methods in econometrics: theory and practice. Unpublished Working Paper

• Kitamura Y, Stutzer M (1997) An information-theoretic alternative to generalized method of moments estimation. Econometrica 65(5):861–874

  Article  MathSciNet  MATH  Google Scholar 

• Kitamura Y, Otsu T, Evdokimov K (2013) Robustness, infinitesimal neighborhoods, and moment restrictions. Econometrica 81(3):1185–1201

  Article  MathSciNet  MATH  Google Scholar 

• Kloeden P, Platen E (1992) Numerical solution of stochastic differential equations. Springer, Berlin

  Book  MATH  Google Scholar 

• Lo AW (1988) Maximum likelihood estimation of generalized itô process with discretely sampled data. Econom Theory 4:231–247

  Article  Google Scholar 

• Merton R (1971) Optimum consumption and portofolio rules in a continuos time model. J Econ Theory 3:373–413

  Article  MathSciNet  MATH  Google Scholar 

• Merton RC (1973) The theory of rational option pricing. Bell J 4:141–183

  Article  MathSciNet  MATH  Google Scholar 

• Milstein GN (1974) Aproximate integration of stochastic diferential equations. Theory Probab Appl 19:557–562

  MathSciNet  Google Scholar 

• Newey W, McFadden D (1994) Handbook of econometrics, volume 4, chapter large sample estimation and hypothesis testing. Elsevier, Amsterdam

• Newey W, Smith RJ (2004) High-order properties of gmm and generalized empirical likelihood estimators. Econometrica 72:219–255

  Article  MathSciNet  MATH  Google Scholar 

• Newey WK, West KD (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55:703–708

  Article  MathSciNet  MATH  Google Scholar 

• Owen A (1991) Empirical likelihood for linear models. Ann Stat 18(1):1725–1747

  Article  MathSciNet  MATH  Google Scholar 

• Pedersen AR (1995) A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scand J Stat 22:55–71

  MathSciNet  MATH  Google Scholar 

• Prakasa Rao BLS (1999) Statistical inference for diffusion type process. Arnold, London

  Google Scholar 

• Qin J, Lawless J (1994) Empirical likelihood and general estimating equations. Ann Stat 20(1):300–325

  Article  MathSciNet  MATH  Google Scholar 

• Rogers LCG, Williams D (2000) Diffusions, Markov process and Martingales: volume 2 Itô calculus. Cambridge

• Schennach S (2007) Point estimation with exponentially tilted empirical likelihood. Ann Stat 35(2):634–672

  Article  MathSciNet  MATH  Google Scholar 

• Smith RJ (2001) Gel criteria for moment conditions models. Working paper, University of Bristol

• Vasicek O (1977) An equilibrium characterization of the term structure. J Financ Econ 5:177–88

  Article  Google Scholar 

• Xu K (2009) Empirical likelihood-based inference for nonparametric recurrent diffusions. J Econom 153:65–82

  Article  MathSciNet  Google Scholar 

• Zhou H (2003) Itô conditional moment generator and the estimation of short rate processes. J Financ Econom 1:250–271

  Article  Google Scholar 

• Zivot E, Wang J (2006) Modeling financial time series with S-PLUS, 2nd edn. Springer, Berlin

  MATH  Google Scholar 

Download references