State-Observation Sampling and the Econometrics of Learning Models

In nonlinear state-space models, sequential learning about the hidden state can proceed by particle filtering when the density of the observation conditional on the state is available analytically (e.g. Gordon et al., 1993). This condition need not hold in complex environments, such as the incomplete-information equilibrium models considered in financial economics. In this paper, we make two contributions to the learning literature. First, we introduce a new filtering method, the state-observation sampling (SOS) filter, for general state-space models with intractable observation densities. Second, we develop an indirect inference-based estimator for a large class of incomplete-information economies. We demonstrate the good performance of these techniques on an asset pricing model with investor learning applied to over 80 years of daily equity returns

Indirect Robust Estimation of the Short-term interest Rate Process

We introduce Indirect Robust Generalized Method of Moments (IRGMM), a new simulation-based estimation methodology, to model short-term interest rate processes. The primary advantage of IRGMM relative to classical estimators of the continuous-time short-rate diffusion processes is that it corrects both errors due to discretization and the errors due to model misspecification. We apply this new approach to various monthly and weekly Eurocurrency interest rate series.GMM and RGMM estimators; CKLS one factor model; indirect inference

Accurate and robust tests for indirect inference

In this paper we propose accurate parameter and over-identification tests for indirect inference. Under the null hypothesis the new tests are asymptotically χ2-distributed with a relative error of order n−1. They exhibit better finite sample accuracy than classical tests for indirect inference, which have the same asymptotic distribution but an absolute error of order n−1/2. Robust versions of the tests are also provided. We illustrate their accuracy in nonlinear regression, Poisson regression with overdispersion and diffusion model

Indirect Robust Estimation of the Short-term Interest Rate Process;

We introduce Indirect Robust Generalized Method of Moments (IRGMM), a new simulation-based estimation methodology, to model short-term interest rate processes. The primary advantage of IRGMM relative to classical estimators of the continuous-time short-rate diffusion processes is that it corrects both the errors due to discretization and the errors due to model misspecification. We apply this new approach to various monthly and weekly Eurocurrency interest rate series.GMM and RGMM estimators, CKLS one factor model, indirect inference

Asymmetric stochastic volatility models: properties and particle filter-based simulated maximum likelihood estimation

The statistical properties of a general family of asymmetric stochastic volatility (A-SV)models which capture the leverage effect in financial returns are derived providing analyt- ical expressions of moments and autocorrelations of power-transformed absolute returns.The parameters of the A-SV model are estimated by a particle filter-based simulated max- imum likelihood estimator and Monte Carlo simulations are carried out to validate it. Itis shown empirically that standard SV models may significantly underestimate the value- at-risk of weekly S&P 500 returns at dates following negative returns and overestimate itafter positive returns. By contrast, the general specification proposed provide reliable fore- casts at all dates. Furthermore, based on daily S&P 500 returns, it is shown that the mostadequate specification of the asymmetry can change over time.We gratefully acknowledge the financial support from the Spanish Government, contract grants ECO2015-70331-C2-2-R and ECO2015-65701-P (MINECO/FEDER), the computer support from EUROFIDAI, and the FCT grant UID/GES/00315/2013

Approximate maximum likelihood for complex structural models

Indirect Inference (I-I) is a popular technique for estimating complex parametric models whose likelihood function is intractable, however, the statistical efficiency of I-I estimation is questionable. While the efficient method of moments, Gallant and Tauchen (1996), promises efficiency, the price to pay for this efficiency is a loss of parsimony and thereby a potential lack of robustness to model misspecification. This stands in contrast to simpler I-I estimation strategies, which are known to display less sensitivity to model misspecification precisely due to their focus on specific elements of the underlying structural model. In this research, we propose a new simulation-based approach that maintains the parsimony of I-I estimation, which is often critical in empirical applications, but can also deliver estimators that are nearly as efficient as maximum likelihood. This new approach is based on using a constrained approximation to the structural model, which ensures identification and can deliver estimators that are nearly efficient. We demonstrate this approach through several examples, and show that this approach can deliver estimators that are nearly as efficient as maximum likelihood, when feasible, but can be employed in many situations where maximum likelihood is infeasible

State-Observation Sampling and the Econometrics of Learning Models

In nonlinearstate-spacemodels, sequentiallearningaboutthe hidden statecanproceed byparticlefilteringwhen thedensityoftheobservationconditionalonthe stateisavailable analytically (e.g. Gordon et al. 1993). This condition need not hold in complex environments, such as the incomplete-information equilibrium models considered in financial economics. In this paper, we make two contributions to the learning literature. First, we introduce a new filtering method, the state-observation sampling (SOS) filter, for general state-space models with intractable observation densities. Second, we develop an indirect inference-based estimator for a large class of incomplete-information economies. We demonstrate the good performance of these techniques on an asset pricing model with investor learning applied to over 80 years of daily equity returns

Discussion on dynamic models

Non UBCUnreviewedAuthor affiliation: EDHEC LilleFacult