Efficient Likelihood Evaluation of State-Space Representations

DeJong, David N.; Liesenfeld, Roman; Moura, Guilherme V.; Richard, Jean‐François; Dharmarajan, Hariharan

doi:10.1093/restud/rds040

“…This method requires O(N (T + 1) log N ) operations due to the sorting of the particles, but the resulting continuous estimate of ℓ T (θ) can be maximized using standard optimization techniques. Extensions to the multivariate case where X ⊆ R nx (with n x > 1) have been proposed in [59] and [22]. However, the scheme [59] does not guarantee continuity of the likelihood function estimate and only provides log-likelihood estimates which are positively correlated for neighboring values in the parameter space, whereas the scheme in [22] has O(N 2 ) computational complexity and relies on a nonstandard particle filtering scheme.…”

Section: Likelihood Function Evaluationmentioning

confidence: 99%

On Particle Methods for Parameter Estimation in State-Space Models

Kantas¹,

Doucet²,

Singh³

et al. 2015

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Nonlinear non-Gaussian state-space 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 state-space 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 state-space models. We discuss the advantages and limitations of these methods and illustrate their performance on simple models.Comment: Published at http://dx.doi.org/10.1214/14-STS511 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…Recently, a renewed interest in the use of particle filters for computing marginal likelihood (integrating over state variables) for the purpose of parameter estimation has emerged (Fernandez-Villaverde and Rubio-Ramirez, 2007;Andrieu et al, 2010;Kantas et al, 2009;Malik and Pitt, 2011;DeJong et al, 2013). This is also the context of the present paper.…”

Section: Introductionmentioning

confidence: 87%

Bandwidth Selection in Pre-Smoothed Particle Filters

Kleppe

¹

,

Skaug

²

2012

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For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte Carlo error in the estimates of both the posterior density of the states and the marginal density of the observation at each time point. We correct for variance inflation in the smoother, which together with the use of Gaussian kernels, results in a Gaussian (Kalman) update when the amount of smoothing turns to infinity. We propose and study of a criterion for choosing the optimal bandwidth h in the kernel smoother. Finally, we illustrate our approach using examples from econometrics. Our filter is shown to be highly suited for dynamic models with high signal-to-noise ratio, for which the SIR filter has problems.

show abstract

“…Recently, a renewed interest in the use of particle filters for computing marginal likelihood (integrating over state variables) for the purpose of parameter estimation has emerged (FernandezVillaverde and Rubio-Ramirez, 2007;Andrieu et al, 2010;Kantas et al, 2009;Malik and Pitt, 2011;DeJong et al, 2013). This is also the context of the present paper.…”

Section: Introductionmentioning

confidence: 90%

“…A renewed interest in particle filters in the econometric literature have at least partly been driven by the aim of estimating non-linear solutions to dynamic stochastic general equilibrium (DSGE) models (Fernandez-Villaverde and Rubio-Ramirez, 2007;Amisano and Tristani, 2010;Andreasen, 2011;DeJong et al, 2013;Flury and Shephard, 2011;Malik and Pitt, 2011). We consider a simple neoclassical growth DSGE model (King et al, 1988;Schmitt-Grohe and Uribe, 2004), with equilibrium condition given as…”

Section: Dynamic Stochastic General Equilibrium Modelmentioning

confidence: 99%

Bandwidth selection in pre-smoothed particle filters

Kleppe

¹

,

Skaug

²

2015

View full text Add to dashboard Cite

For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte Carlo error in the estimates of both the posterior density of the states and the marginal density of the observation at each time point. We correct for variance inflation in the smoother, which together with the use of Gaussian kernels, results in a Gaussian (Kalman) update when the amount of smoothing turns to infinity. We propose and study of a criterion for choosing the optimal bandwidth h in the kernel smoother. Finally, we illustrate our approach using examples from econometrics. Our filter is shown to be highly suited for dynamic models with high signal-to-noise ratio, for which the SIR filter has problems.

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Efficient Likelihood Evaluation of State-Space Representations

Cited by 31 publications

References 21 publications

On Particle Methods for Parameter Estimation in State-Space Models

On Particle Methods for Parameter Estimation in State-Space Models

Bandwidth Selection in Pre-Smoothed Particle Filters

Bandwidth selection in pre-smoothed particle filters

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