Likelihood INference for Discretely Observed Non-linear Diffusions

By Ola Elerian, Siddhartha Chib, N. Shephard. 2001

528 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7b7ade268bed2c8779ad26484ad4e7b8ce3b10b0

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Citations in the corpus

Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey (2004, methodology): “Bayesian analysis of discretely observed diffusions has been discussed by Eraker (2001), Elerian et al. (2001) and Roberts and Stramer (2001).”
Bayesian analysis of single‐molecule experimental data (2005, methodology): “…results of Roberts and Sahu (1997), gave some analytic convergence results; see also the discussion in Jacquier et al. (1994) for empirical results from stochastic volatility models, and for example Elerian et al. (2001) for suggestions on efficient blocking schemes for updating diffusion paths.”
Testing the assumptions behind importance sampling (2009, methodology): “R I This is the case in the stochastic volatility literature; see, e.g., Hendry and Richard (1991), Danielsson and Richard (1993), Sandmann and Koopman (1998), Elerian, Chib, and Shephard (2001), Durham and Gallant (2002), Durham (2006), and Asai and McAleer (2006).”
Simulated Likelihood Estimation of Diffusions with an Application to Exchange Rate Dynamics in Incomplete Markets (2002, unknown): “…the usual problems with nonparametric density estimation: a slower convergence rate (in the number of simulations) and the curse of dimensionality.1 The SML approach relates also to the Markov chain Monte Carlo (MCMC) approach described by Jones (2000a), Elerian et al. (2001), and Eraker (2001).”
Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations (2006, methodology): “Each step is now described in more detail following Elerian et al. (2001).”
A Gaussian approach for continuous time models of the short-term interest rate (2001, background): “Duffie and Singleton (1993), Gallant and Tauchen (1996), Eraker (2001), Elerian et al. (2001) , Durham and Gallant (2002)), some are based on numerical approximations (such as Lo (1988)), while others are based on closed-form approximations (such as A¨ it-Sahalia (1999, 2000)).”
DIAGNOSTIC CHECKING FOR THE ADEQUACY OF NONLINEAR TIME SERIES MODELS (2003, unknown): “…are of interest~e+g+, Brock et al+, 1991; Brock, Dechert, Scheinkman, and LeBaron, 1996, Christoffersen, 1998; Diebold, Gunther, and Tay, 1998; Kim, Shephard, and Chib, 1998; Clement and Smith, 2000; Elerian, Chib, and Shephard, 2001!+ See also an empirical application in Section 8+ Because$et~u0!”
Bayesian inference for irreducible diffusion processes using the pseudo-marginal approach (2011, methodology): “It has been well documented that näıve data augmentation techniques lead to problems of high dependency between the covariance parameters and the diffusion paths (see Elerian et al. 2001; Roberts and Stramer 2001).”
Stochastic Gradient Descent in Continuous Time (2016, unknown): “[14] estimates parameters by a Bayesian approach.”
AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs (2019, methodology): “Elerian et al. (2001) and Eraker (2001) used the Euler-Maruyama discretization to approximate p ( x θ ) on a ﬁxed, ﬁne grid of artiﬁcial observation times later to be leveraged in a MCMC sampling scheme.”
Bayesian semiparametric stochastic volatility modeling (2010, methodology): “Fortunately, less correlated draws of the volatilities can be found by sampling random length blocks of volatilities instead of the entire vector (see Pitt and Shephard, 1997; Elerian et al., 2001; Fleming and Kirby, 2003).”
Econometric analysis of realized volatility and its use in estimating stochastic volatility models (2002, background): “A very incomplete list of references includes Gourieroux et al. (1993), Gallant and Long (1997), Kim et al. (1998), Elerian et al. (2001) and Sørensen (2000).”
On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations * (2003, background): “Since SDEs of type (1) are Markov – see, for example, Jazwinski (l970) – then, for such models, 1Other approaches for estimating the parameters of SDEs have been proposed, see, for example, Aı̈t Sahalia (1996a, 1996b), Pedersen (1995) and Elerian et al. (2001).”