Simulation-Based Estimation Methods for Financial Time Series Models

Abstract

This chapter overviews some recent advances on simulation-based methods of estimating financial time series models that are widely used in financial economics. 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 (ML) method and the generalized method of moments (GMM) are difficult to use. They are also useful for improving the finite sample performance of the traditional methods. Both frequentist and Bayesian simulation-based methods are reviewed. Frequentist’s simulation-based methods cover various forms of simulated maximum likelihood (SML) methods, simulated generalized method of moments (SGMM), efficient method of moments (EMM), and indirect inference (II) methods. 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. Empirical applications, based on real exchange rates, interest rates and equity data, illustrate how to implement the simulation-based methods. In particular, we apply SML to a discrete time stochastic volatility model, EMM to estimate a continuous time stochastic volatility model, MCMC to a credit risk model, the II method to a term structure model.