Simulation-based Estimation Methods for Financial Time Series Models

This paper overviews some recent advances on simulation-based methods of estimating time series models and asset pricing models that are widely used in finance. The simulation based methods have proven to be particularly useful when the likelihood function and moments do not have tractable forms and hence the maximum likelihood method (MLE) and the generalized method of moments (GMM) are difficult to use. They can also be useful for improving the finite sample performance of the traditional methods when financial time series are highly persistent and when the quantity of interest is a highly nonlinear function of system parameters. The simulation-based methods are classified in this paper, based on the frequentist/Bayesian split. Frequentist’s simulation-based methods cover simulated generalized method of moments (SMM), efficient method of moments (EMM), indirect inference (II), various forms of simulated maximum likelihood methods (SMLE). Asymptotic properties of these methods are discussed and asymptotic efficiency is compared. Bayesian simulation-based methods cover various MCMC algorithms. Each simulation-based method is discussed in the context of a specific financial time series model as a motivating example. The list of discussed financial time series models cover continuous time diffusion models, latent variable models, term structure models, asset pricing models, and structural models for credit risk. Finite sample problems of the exact maximum likelihood method, such as finite sample bias, are also discussed. Simulation-based bias correction methods, such as indirect inference, simulation-based median unbiased estimation, and bootstrap methods are reviewed. A nice property about these simulation-based bias correction methods is that they retains the good asymptotic properties of maximum likelihood estimation while reducing finite sample bias. ∗Yu gratefully acknowledge financial support from the Ministry of Education AcRF fund under Grant No. T206B4301-RS. †School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903; email: [email protected].