Replica Conditional Sequential Monte Carlo

We propose a Markov chain Monte Carlo (MCMC) scheme to perform state inference in non-linear non-Gaussian state-space models. Current state-of-the-art methods to address this problem rely on particle MCMC techniques and its variants, such as the iterated conditional Sequential Monte Carlo (cSMC) scheme, which uses a Sequential Monte Carlo (SMC) type proposal within MCMC. A deficiency of standard SMC proposals is that they only use observations up to time $t$ to propose states at time $t$ when an entire observation sequence is available. More sophisticated SMC based on lookahead techniques could be used but they can be difficult to put in practice. We propose here replica cSMC where we build SMC proposals for one replica using information from the entire observation sequence by conditioning on the states of the other replicas. This approach is easily parallelizable and we demonstrate its excellent empirical performance when compared to the standard iterated cSMC scheme at fixed computational complexity.Comment: To appear in Proceedings of ICML '1

Monte Carlo Simulation of Macroeconomic Risk with a Continuum Agents : The General Case

In large random economies with heterogeneous agents, a standard stochastic framework presumes a random macro state, combined with idiosyncratic micro shocks. This can be formally represented by a ran-dom process consisting of a continuum of random variables that are conditionally independent given the macro state. However, this process satisfies a standard joint measurability condition only if there is essentially no idiosyncratic risk at all. Based on iteratively complete product measure spaces, we characterize the validity of the standard stochastic framework via Monte Carlo simulation as well as event-wise measurable conditional probabilities. These general characterizations also allow us to strengthen some earlier results related to exchangeability and independence.large economy ; event-wise measurable conditional probabilities ; ex-changeability ; conditional independence ; Monte Carlo convergence ; Monte Carlo-algebra ; stochastic macro structure

A hyperbolic transformation for a fixed effects logit model

In this paper, a simple transformation is proposed for the fixed effects logit model, using which some valid moment conditions including the first-order condition for one of the conditional MLE proposed by Chamberlain (1980) can be generated. Some Monte Carlo experiments are carried out for the GMM estimator based on the transformation.fixed effects logit; conditional logit estimator; hyperbolic transformation; moment conditions; GMM; Monte Carlo experiments

Parametric Conditional Monte Carlo Density Estimation

In applied density estimation problems, one often has data not only on the target variable, but also on a collection of covariates. In this paper, we study a density estimator that incorporates this additional information by combining parametric estimation and conditional Monte Carlo. We prove an approximate functional asymptotic normality result that illustrates convergence rates and the asymptotic variance of the estimator. Through simulation, we illustrate the strength of its finite sample properties in a number of standard econometric and financial applications.

Exact inference in diagnosing value-at-risk estimates: A Monte Carlo device

In this note a Monte Carlo approach is suggested to determine critical values for diagnostic tests of Value-at-Risk models that rely on binary random variables. Monte Carlo testing offers exact significance levels in finite samples. Conditional on exact critical values the dynamic quantile test suggested by Engle and Manganelli (2004) turns out more powerful than a recently proposed Portmanteau type test (Hurlin and Tokpavi 2006). --Value-at-Risk,Monte Carlo test