### Abstract

Language | English |
---|---|

Journal | Computational Economics |

Volume | 53 |

Issue number | 3 |

Pages | 991-1017 |

Number of pages | 27 |

ISSN | 0927-7099 |

DOIs | |

State | Published - Mar 2019 |

### Keywords

- Finite mixture
- Distance measure
- Gaussian quadrature
- Importance sampling
- Adaptive algorithm
- Stochastic volatility
- Density kernel

### Cite this

*Computational Economics*,

*53*(3), 991-1017. DOI: 10.1007/s10614-017-9777-2

}

*Computational Economics*, vol. 53, no. 3, pp. 991-1017. DOI: 10.1007/s10614-017-9777-2

**Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels.** / Khorunzhina, Natalia; Richard, Jean-Francois.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels

AU - Khorunzhina,Natalia

AU - Richard,Jean-Francois

PY - 2019/3

Y1 - 2019/3

N2 - The objective of the paper is that of constructing finite Gaussian mixture approximations to analytically intractable density kernels. The proposed method is adaptive in that terms are added one at the time and the mixture is fully re-optimized at each step using a distance measure that approximates the corresponding importance sampling variance. All functions of interest are evaluated under Gaussian product rules. Since product rules suffer from an obvious curse of dimensionality, the proposed algorithm as presented is only applicable to models whose non-linear and/or non-Gaussian subspace is of dimension up to three. Extensions to higher-dimensional applications would require the use of sparse grids, as discussed in the paper. Examples include a sequential (filtering) evaluation of the likelihood function of a stochastic volatility model where all relevant densities (filtering, predictive and likelihood) are closely approximated by mixtures.

AB - The objective of the paper is that of constructing finite Gaussian mixture approximations to analytically intractable density kernels. The proposed method is adaptive in that terms are added one at the time and the mixture is fully re-optimized at each step using a distance measure that approximates the corresponding importance sampling variance. All functions of interest are evaluated under Gaussian product rules. Since product rules suffer from an obvious curse of dimensionality, the proposed algorithm as presented is only applicable to models whose non-linear and/or non-Gaussian subspace is of dimension up to three. Extensions to higher-dimensional applications would require the use of sparse grids, as discussed in the paper. Examples include a sequential (filtering) evaluation of the likelihood function of a stochastic volatility model where all relevant densities (filtering, predictive and likelihood) are closely approximated by mixtures.

KW - Finite mixture

KW - Distance measure

KW - Gaussian quadrature

KW - Importance sampling

KW - Adaptive algorithm

KW - Stochastic volatility

KW - Density kernel

KW - Finite mixture

KW - Distance measure

KW - Gaussian quadrature

KW - Importance sampling

KW - Adaptive algorithm

KW - Stochastic volatility

KW - Density kernel

UR - https://sfx-45cbs.hosted.exlibrisgroup.com/45cbs?url_ver=Z39.88-2004&url_ctx_fmt=info:ofi/fmt:kev:mtx:ctx&ctx_enc=info:ofi/enc:UTF-8&ctx_ver=Z39.88-2004&rfr_id=info:sid/sfxit.com:azlist&sfx.ignore_date_threshold=1&rft.object_id=954927382296&rft.object_portfolio_id=&svc.holdings=yes&svc.fulltext=yes

U2 - 10.1007/s10614-017-9777-2

DO - 10.1007/s10614-017-9777-2

M3 - Journal article

VL - 53

SP - 991

EP - 1017

JO - Computational Economics

T2 - Computational Economics

JF - Computational Economics

SN - 0927-7099

IS - 3

ER -