Abstract
A class of martingale estimating functions based on the first two moments of the observed process provides a convenient framework for estimating the parameters of diffusion processes [1]. In the Bayesian set up, combined estimating functions had been studied for diffusion processes in [2] with filtering applications. However, when the conditional mean and the conditional variance are functions of parameters of interest in a diffusion process model, the basic martingales generating components of quadratic estimating functions are such that one is an absolute continuous function with respect to the other [3, p. 94]. Hence, the combined martingale estimating functions cannot be constructed for continuous-time diffusion processes. In this paper, a general framework for parameter estimation of discretely observed interest rate models is developed by using the Milstein approximation and closed form expressions for the information gain are also obtained. The method is used to study the estimates of the parameters for an extended version of the CoxIngersoll-Ross interest rate model.
Highlights
Inference for discrete-time stochastic processes using estimating functions was discussed in [4]
A class of martingale estimating functions based on the first two moments of the observed process provides a convenient framework for estimating the parameters of diffusion processes [1]
In the Bayesian set up, combined estimating functions had been studied for diffusion processes in [2] with filtering applications
Summary
Inference for discrete-time stochastic processes using estimating functions was discussed in [4]. In [8], among others, the estimating functions approach was used to study the estimation problems for some discretely observed interest rate models These methods involve the closed form expressions for the first four conditional moments, obtained by Ito’s approximations, and these are not available for general time-homogeneous diffusion process models and in particular for an extended CIR interest rate model. We study combined martingale estimating functions for interest rate models and show that the combined estimating functions are more informative when the conditional mean and variance of the observed process depend on the parameter of interest. It follows from [11, p. 916] that if we solve an unbiased estimating equation gn 0 to get an estimator, the asymptotic variance of theresulting estimator is the inverse tained of the from ainmfoormreatiinofnormIgant.ivHe eensctiemtahteingesteiqmuaattoior nobisasymptotically more efficient
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
