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A survey of sequential Monte Carlo methods for economics and finance
, 2009
"... This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in ..."
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Cited by 34 (7 self)
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This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macroeconomics to option pricing. The objective of this paper is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.
Efficient Bayesian Inference for Switching StateSpace Models using Particle Markov Chain Monte Carlo Methods
, 2010
"... Switching statespace models (SSSM) are a popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov chain Monte Carlo (MCMC) techniques. However, even sophisticated ..."
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Cited by 13 (1 self)
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Switching statespace models (SSSM) are a popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov chain Monte Carlo (MCMC) techniques. However, even sophisticated MCMC methods dedicated to SSSM can prove quite inefficient as they update potentially strongly correlated variables oneatatime. Particle Markov chain Monte Carlo (PMCMC) methods are a recently developed class of MCMC algorithms which use particle filters to build efficient proposal distributions in highdimensions [1]. The existing PMCMC methods of [1] are applicable to SSSM, but are restricted to employing standard particle filtering techniques. Yet, in the context of SSSM, much more efficient particle techniques have been developed [22, 23, 24]. In this paper, we extend the PMCMC framework to enable the use of these efficient particle methods within MCMC. We demonstrate the resulting generic methodology on a variety of examples including a multiple changepoints model for welllog data and a model for U.S./U.K. exchange rate data. These new PMCMC algorithms are shown to outperform experimentally stateoftheart MCMC techniques for a fixed computational complexity. Additionally they can be easily parallelized [39] which allows further substantial gains.
On Particle Methods for Parameter Estimation in StateSpace Models
, 2015
"... Nonlinear nonGaussian statespace models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical approximations to the associated state inference problems. However, ..."
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Cited by 6 (1 self)
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Nonlinear nonGaussian statespace models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical approximations to the associated state inference problems. However, in most applications, the statespace model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard particle methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive review of particle methods that have been proposed to perform static parameter estimation in statespace models. We discuss the advantages and limitations of these methods and illustrate their performance on simple models.
Estimating nonlinear economic models using surrogate transitions. Available from https://files.nyu.edu/mes473/public/Smith Surrogate.pdf
, 2011
"... Abstract We propose a novel combination of algorithms for jointly estimating parameters and unobservable states in a nonlinear state space system. We exploit an approximation to the marginal likelihood to guide a Particle Marginal MetropolisHastings algorithm. While this algorithm seemingly target ..."
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Cited by 4 (1 self)
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Abstract We propose a novel combination of algorithms for jointly estimating parameters and unobservable states in a nonlinear state space system. We exploit an approximation to the marginal likelihood to guide a Particle Marginal MetropolisHastings algorithm. While this algorithm seemingly targets reduced dimension marginal distributions, it draws from a joint distribution of much higher dimension. The algorithm is demonstrated on a stochastic volatility model and a Real Business Cycle model with robust preferences.
Martingale unobserved component models
, 2013
"... I discuss models which allow the local level model, which rationalised exponentially weighted moving averages, to have a timevarying signal/noise ratio. I call this a martingale component model. This makes the rate of discounting of data local. I show how to handle such models effectively using an ..."
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Cited by 3 (0 self)
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I discuss models which allow the local level model, which rationalised exponentially weighted moving averages, to have a timevarying signal/noise ratio. I call this a martingale component model. This makes the rate of discounting of data local. I show how to handle such models effectively using an auxiliary particle filter which deploys M Kalman filters run in parallel competing against one another. Here one thinks of M as being 1,000 or more. The model is applied to inflation forecasting. The model generalises to unobserved component models where Gaussian shocks are replaced by martingale difference sequences.
Particle Markov Chain Monte Carlo
, 2009
"... ... have emerged as the two main tools to sample from highdimensional probability distributions. Although asymptotic convergence of MCMC algorithms is ensured under weak assumptions, the performance of these latters is unreliable when the proposal distributions used to explore the space are poorly ..."
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Cited by 3 (0 self)
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... have emerged as the two main tools to sample from highdimensional probability distributions. Although asymptotic convergence of MCMC algorithms is ensured under weak assumptions, the performance of these latters is unreliable when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. In this thesis we propose a new Monte Carlo framework in which we build efficient highdimensional proposal distributions using SMC methods. This allows us to design effective MCMC algorithms in complex scenarios where standard strategies fail. We demonstrate these algorithms on a number of example problems, including simulated tempering, nonlinear nonGaussian statespace model, and protein folding.
Marginal likelihood for Markovswitching and changepoint GARCH models
, 2011
"... GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markovswitching GARCH and changepoint GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issu ..."
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Cited by 3 (0 self)
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GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markovswitching GARCH and changepoint GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is essential for determining the number of regimes or changepoints. We solve the problem by using particle MCMC, a technique proposed by Andrieu, Doucet, and Holenstein (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series.
Generalized Method of Moments with Latent Variables ∗
, 2012
"... The contribution of generalized method of moments (Hansen and Singleton, 1982) was to allow frequentist inference regarding the parameters of a nonlinear structural model without having to solve the model. Provided there were no latent variables. The contribution of this paper is the same. With late ..."
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Cited by 2 (0 self)
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The contribution of generalized method of moments (Hansen and Singleton, 1982) was to allow frequentist inference regarding the parameters of a nonlinear structural model without having to solve the model. Provided there were no latent variables. The contribution of this paper is the same. With latent variables.