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136
Estimating Functions for Discretely Sampled DiffusionType Models. Chapter of the Handbook of financial econometrics, AitSahalia and Hansen eds. http://home.uchicago.edu/ lhansen/handbook.htm Birgé
 in Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics
, 2004
"... Estimating functions provide a general framework for finding estimators and studying their properties in many different kinds of statistical models, including stochastic process models. An estimating function is a function of the data as well as of the parameter to be estimated. An estimator is obta ..."
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Cited by 26 (9 self)
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Estimating functions provide a general framework for finding estimators and studying their properties in many different kinds of statistical models, including stochastic process models. An estimating function is a function of the data as well as of the parameter to be estimated. An estimator is obtained by equating the estimating function to zero and solving the resulting
On Bayesian Inference for Stochastic Kinetic Models Using Diffusion Approximations
, 2004
"... This paper is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a di#usion approximation (or stochastic di#erential equation approach) where a white noise t ..."
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Cited by 25 (7 self)
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This paper is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a di#usion approximation (or stochastic di#erential equation approach) where a white noise term models stochastic behaviour and the model is identified using equispaced time course data. The estimation framework involves the introduction of m1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters
Practical Filtering with Sequential Parameter Learning
, 2003
"... In this paper we develop a general simulationbased approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering ..."
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Cited by 25 (7 self)
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In this paper we develop a general simulationbased approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering distribution as a mixture of lagsmoothing distributions and to implement this sequentially. Our approach has a number of advantages over current methodologies. First, it allows for sequential parmeter learning where sequential importance sampling approaches have difficulties. Second
ANOVA FOR DIFFUSIONS AND ITO PROCESSES
 SUBMITTED TO THE ANNALS OF STATISTICS
"... Ito processes are the most common form of continuous semimartingales, and include diffusion processes. The paper is concerned with the nonparametric regression relationship between two such Ito processes. We are interested in the quadratic variation (integrated volatility) of the residual in this re ..."
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Cited by 25 (11 self)
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Ito processes are the most common form of continuous semimartingales, and include diffusion processes. The paper is concerned with the nonparametric regression relationship between two such Ito processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term. The proposed methodology, “ANOVA for diffusions and Ito processes”, can be used to measure the statistical quality of a parametric model, and, nonparametrically, the appropriateness of a oneregressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.
Parametric Inference for Diffusion Processes Observed At Discrete Points in Time: A Survey
"... This paper is a survey of existing estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and socalled simple es ..."
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Cited by 24 (2 self)
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This paper is a survey of existing estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and socalled simple estimating functions; (ii) analytical and numerical approximations of the likelihood which can in principle be made arbitrarily accurate; (iii) Bayesian analysis and MCMC methods; and (iv) indirect inference and EMM which both introduce auxiliary (but wrong) models and correct for the implied bias by simulation
Bayesian sequential inference for stochastic kinetic biochemical network models J Comput Biol
, 2006
"... As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The ..."
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Cited by 22 (6 self)
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As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The underlying model is replaced by a diffusion approximation where a noise term represents intrinsic stochastic behavior and the model is identified using discretetime (and often incomplete) data that is subject to measurement error. Sequential MCMC methods are then used to sample the model parameters online in several datapoor contexts. The methodology is illustrated by applying it to the estimation of parameters in a simple prokaryotic autoregulatory gene network.
Likelihood based inference for diffusion driven models, working paper
 In submission
, 2004
"... This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be nonstationary. Although our method ..."
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Cited by 21 (1 self)
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This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be nonstationary. Although our methods are sampling based, making use of Markov chain Monte Carlo methods to sample the posterior distribution of the relevant unknowns, our general strategies and details are different from previous work along these lines. The methods we develop are simple to implement and simulation efficient. Importantly, unlike previous methods, the performance of our technique is not worsened, in fact it improves, as the degree of latent augmentation is increased to reduce the bias of the Euler approximation. In addition, our method is not subject to a degeneracy that afflicts previous techniques when the degree of latent augmentation is increased. We also discuss issues of model choice, model checking and filtering. The techniques and ideas are applied to both simulated and real data.
Optimal filtering of jump diffusions: extracting latent states from asset prices”, Working Paper, http://wwwstat.wharton.upenn.edu/ stroud/pubs.html
, 2006
"... This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing mo ..."
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Cited by 20 (5 self)
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This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines timediscretization schemes with Monte Carlo methods to compute the optimal filtering distribution. Our approach is very general, applying in multivariate jumpdiffusion models with nonlinear characteristics and even nonanalytic observation equations, such as those that arise when option prices are available. We provide a detailed analysis of the performance of the filter, and analyze four applications: disentangling jumps from stochastic volatility, forecasting realized volatility, likelihood based model comparison, and filtering using both option prices and underlying returns. 2 1
Nonlinear Mean Reversion in the ShortTerm Interest Rate
, 2003
"... Using a new Bayesian method for the analysis of diffusion processes, this article finds that the nonlinear drift in interest rates found in a number of previous studies can be confirmed only under prior distributions that are best described as informative. The assumption of stationarity, which is co ..."
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Cited by 20 (2 self)
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Using a new Bayesian method for the analysis of diffusion processes, this article finds that the nonlinear drift in interest rates found in a number of previous studies can be confirmed only under prior distributions that are best described as informative. The assumption of stationarity, which is common in the literature, represents a nontrivial prior belief about the shape of the drift function. This belief and the use of ``flat'' priors contribute strongly to the finding of nonlinear mean reversion. Implementation of an approximate Jeffreys prior results in virtually no evidence for mean reversion in interest rates unless stationarity is assumed. Finally, the article documents that nonlinear drift is primarily a feature of daily rather than monthly data, and that these data contain a transitory element that is not reflected in the volatility of longermaturity yields.
Markov chain Monte Carlo methods for generalized stochastic volatility models
 Journal of Econometrics
, 1998
"... This paper is concerned with Markov chain Monte Carlo based Bayesian inference in generalized models of stochastic volatility de ned by heavytailed studentt distributions (with unknown degrees of freedom) and covariate e ects in the observation and volatility equations. A simple, fast and highly e ..."
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Cited by 18 (6 self)
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This paper is concerned with Markov chain Monte Carlo based Bayesian inference in generalized models of stochastic volatility de ned by heavytailed studentt distributions (with unknown degrees of freedom) and covariate e ects in the observation and volatility equations. A simple, fast and highly e cient algorithm, that builds on Kim, Shephard and Chib (1998), is developed for estimating these models. Computation of the likelihood function by a particle lter is considered as are methods for constructing diagnostic measures and the model marginal likelihood. The techniques are applied in detail to daily returns on the S&P 500 index and to weekly changes in the shortterm interest rate.