计量经济分析 = Econometric analysis

http://www.cirano.qc.ca/pdf/publication/2002s-58.pdf

Alternative models for stock price dynamics

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Mathematical Methods Of Statistics

Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuous-time model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then mean-reverts strongly when far away from the mean. The volatility is higher when away from the mean.

Testing Continuous-Time Models of the Spot Interest Rate

Summary. The objective of the paper is to present a novel methodology for likelihood-based inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation.

/pdf/exact-and-computationally-efficient-likelihood-based-55jy8u1blo.pdf

Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)

Stochastic differential equations often provide a convenient way to describe the dynamics of economic and financial data, and a great deal of effort has been expended searching for efficient ways to estimate models based on them. Maximum likelihood is typically the estimator of choice; however, since the transition density is generally unknown, one is forced to approximate it. The simulation-based approach suggested by Pedersen (1995) has great theoretical appeal, but previously available implementations have been computationally costly. We examine a variety of numerical techniques designed to improve the performance of this approach. Synthetic data generated by a Cox-Ingersoll-Ross model with parameters calibrated to match monthly observations of the U.S. short-term interest rate are used as a test case. Since the likelihood function of this process is known, the quality of the approximations can be easily evaluated. On datasets with 1,000 observations, we are able to approximate the maximum likelihood e...

/pdf/numerical-techniques-for-maximum-likelihood-estimation-of-3kot19bqai.pdf

Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes

https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1016&context=fin_fac

Likelihood-based specification analysis of continuous-time models of the short-term interest rate ☆

https://www.aronaldg.org/courses/compecon/papers/sv.pdf

Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models

https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1014&context=fin_fac

SV mixture models with application to S&P 500 index returns ☆

Massively parallel desktop computing capabilities now well within the reach of individual academics modify the environment for posterior simulation in fundamental and potentially quite advantageous ways. But to fully exploit these benefits algorithms that conform to parallel computing environments are needed. This paper presents a sequential posterior simulator designed to operate efficiently in this context. The simulator makes fewer analytical and programming demands on investigators, and is faster, more reliable, and more complete than conventional posterior simulators. The paper extends existing sequential Monte Carlo methods and theory to provide a thorough and practical foundation for sequential posterior simulation that is well suited to massively parallel computing environments. It provides detailed recommendations on implementation, yielding an algorithm that requires only code for simulation from the prior and evaluation of prior and data densities and works well in a variety of applications representative of serious empirical work in economics and finance. The algorithm facilitates Bayesian model comparison by producing marginal likelihood approximations of unprecedented accuracy as an incidental by-product, is robust to pathological posterior distributions, and provides estimates of numerical standard error and relative numerical efficiency intrinsically. The paper concludes with an application that illustrates the potential of these simulators for applied Bayesian inference.

/pdf/adaptive-sequential-posterior-simulators-for-massively-4zexputtbn.pdf

Garland Durham

Papers

Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes

Likelihood-based specification analysis of continuous-time models of the short-term interest rate ☆

Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models

SV mixture models with application to S&P 500 index returns ☆

Adaptive sequential posterior simulators for massively parallel computing environments