Abstract
The construction of an importance density for partially non-Gaussian state space models is crucial when simulation methods are used for likelihood evaluation, signal extraction, and forecasting. The method of efficient importance sampling is successful in this respect, but we show that it can be implemented in a computationally more efficient manner using standard Kalman filter and smoothing methods. Efficient importance sampling is generally applicable for a wide range of models, but it is typically a custom-built procedure. For the class of partially non-Gaussian state space models, we present a general method for efficient importance sampling. Our novel method makes the efficient importance sampling methodology more accessible because it does not require the computation of a (possibly) complicated density kernel that needs to be tracked for each time period. The new method is illustrated for a stochastic volatility model with a Student's t distribution.
| Original language | English |
|---|---|
| Pages (from-to) | 44-62 |
| Number of pages | 19 |
| Journal | Statistica Neerlandica |
| Volume | 73 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 2019 |
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Keywords
- efficient importance sampling
- Kalman filter
- Monte Carlo maximum likelihood
- non-Gaussian dynamic models
- simulation smoothing
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Modified efficient importance sampling for partially non-Gaussian state space models. / Koopman, Siem Jan; Lit, Rutger; Nguyen, Thuy Minh.
In: Statistica Neerlandica, Vol. 73, No. 1, 01.02.2019, p. 44-62.Research output: Contribution to Journal › Article › Academic › peer-review
TY - JOUR
T1 - Modified efficient importance sampling for partially non-Gaussian state space models
AU - Koopman, Siem Jan
AU - Lit, Rutger
AU - Nguyen, Thuy Minh
PY - 2019/2/1
Y1 - 2019/2/1
N2 - The construction of an importance density for partially non-Gaussian state space models is crucial when simulation methods are used for likelihood evaluation, signal extraction, and forecasting. The method of efficient importance sampling is successful in this respect, but we show that it can be implemented in a computationally more efficient manner using standard Kalman filter and smoothing methods. Efficient importance sampling is generally applicable for a wide range of models, but it is typically a custom-built procedure. For the class of partially non-Gaussian state space models, we present a general method for efficient importance sampling. Our novel method makes the efficient importance sampling methodology more accessible because it does not require the computation of a (possibly) complicated density kernel that needs to be tracked for each time period. The new method is illustrated for a stochastic volatility model with a Student's t distribution.
AB - The construction of an importance density for partially non-Gaussian state space models is crucial when simulation methods are used for likelihood evaluation, signal extraction, and forecasting. The method of efficient importance sampling is successful in this respect, but we show that it can be implemented in a computationally more efficient manner using standard Kalman filter and smoothing methods. Efficient importance sampling is generally applicable for a wide range of models, but it is typically a custom-built procedure. For the class of partially non-Gaussian state space models, we present a general method for efficient importance sampling. Our novel method makes the efficient importance sampling methodology more accessible because it does not require the computation of a (possibly) complicated density kernel that needs to be tracked for each time period. The new method is illustrated for a stochastic volatility model with a Student's t distribution.
KW - efficient importance sampling
KW - Kalman filter
KW - Monte Carlo maximum likelihood
KW - non-Gaussian dynamic models
KW - simulation smoothing
UR - http://www.scopus.com/inward/record.url?scp=85058822110&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85058822110&partnerID=8YFLogxK
U2 - 10.1111/stan.12128
DO - 10.1111/stan.12128
M3 - Article
VL - 73
SP - 44
EP - 62
JO - Statistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research
JF - Statistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research
SN - 0039-0402
IS - 1
ER -