Empirical Dynamic Asset Pricing: Model Specification and Econometric Assessment

By Kenneth J. Singleton | Go to book overview

6
Simulation-Based Estimators of DAPMs

6.1. Introduction

For several reasons, the implementation of GMM and ML estimators in the analysis of DAPMs may be computationally demanding, if not essentially infeasible. One such circumstance is when there are unobserved state variables. For instance, the stochastic volatility model of the instantaneous return (Example 2.3) has

where the volatility process v(t) is assumed to be unobserved by the econometrician. Consequently, discretely sampled returns, {rt}, are not Markov conditioned on their own history and the functional form of the conditional distribution of rt is unknown. Moreover, apart from a few special cases, the moments of rt, expressed as functions of the unknown parameters, are unknown.1 The preceding estimation problem is, of course, rendered even more challenging by the presence of jumps in returns or volatility, possibly with state-dependent arrival intensities.

This chapter discusses two possible solutions to the problem of estimating DAPMs in the presence of jumps and latent time series: the simulated moments estimator (SME) and the Markov chain Monte Carlo (MCMC) estimator. Both of these estimators are applicable to DAPMs without latent variables. However, it is especially in situations where one or more variables are latent or the processes involve complex specifications of jumps that

1For this particular example approximate ML estimators have been developed, some of which were discussed in Chapter 5.

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