For **order=1**, Dynare estimates the linearized model using the
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@@ -396,7 +396,9 @@ will build the *posterior* distribution using 20,000 draws (by
default) starting from the initial conditions, the likelihood being
calculated with the nonlinear filter by default, namely the Bootstrap
particle filter with systematic resampling using standard Kitagawa's
approach and 5,000 particles.
approach and 5,000 particles and using `pruning` for the particle
filter-related simulations. The **particle_filter_options = (NAME, VALUE, ...)**
syntax allows setting some fine-grained options.
Contrarily to linear estimation, it is not possible to calculate
accurately the *posterior* mode in the presence of resampling because
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@@ -419,19 +421,20 @@ The following table summarizes the options included in **estimation**.
| mode_compute | 7, 8, 9 |
| mh_replic | [20000], 0 |
| online_particle_filter | |
| nonlinear_filter_initialization| [1],2,3 |
First of all, the choice of the filter is operated with the keyword
**filter_algorithm**. The sequential importance sampling (**sis**) is
the filter by default but one can also choose the auxiliary particle
filter (**apf**), the nonlinear Kalman filter (**nlkf**), the gaussian
filter (**gf**), the gaussian-mixture filter (**gmf**), and the
filter (**apf**), the nonlinear Kalman filter (**nlkf**), the Gaussian
filter (**gf**), the Gaussian-mixture filter (**gmf**), and the
conditional particle filter (**cpf**).
Keyword **online_particle_filter** triggers the online estimation of
the model, using the method developped by Liu and West. It works for
the model, using the method developed by Liu and West. It works for
**order=1** as well as
**order>1**. **options_.particle.liu_west_delta** controls the value
of the $`\delta`$ parameter (set equal to 0.9 by default).
**order>1**. **particle_filter_options = ('liu_west_delta', VALUE, ...)** controls the value
of the $`\delta`$ parameter (set equal to 0.99 by default).
Some dependencies among other keywords should be clarified. They are
summarized by the following table.
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@@ -451,10 +454,7 @@ methods. One should notice that unscented transform is controled with
three parameters: $`\alpha`$ and $`\kappa`$ that determine the spread
of the sigma-points and $`\beta`$ that characterizes the
(non-gaussian) distribution. By default, we set $`\alpha =
\kappa=1`$ and $`\beta=2`$. They can be modified by redefining
**options_.particle.unscented.alpha**,
**options_.particle.unscented.kappa** and
**options_.particle.unscented.beta**.
\kappa=1`$ and $`\beta=2`$. They can be modified by using the **particle_filter_options = ('unscented_alpha', VALUE, 'unscented_beta', VALUE,'unscented_kappa', VALUE, ...)** syntax.
- The number of particles can be chosen with the keyword
**number_of_particles**.
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@@ -498,16 +498,24 @@ of the sigma-points and $`\beta`$ that characterizes the
chosen with the keyword **resampling_method** when resampling is
used.
-**options_.particle.initialization** controls the initial states
-**nonlinear_filter_initialization** controls the initial states
distribution of the filter. Three possibilities are offered to the
user. If **options_.particle.initialization=1** (the default), the
user. If **nonlinear_filter_initialization=1** (the default), the
initial state vector covariance is the ergodic variance associated
to the first order Taylor-approximation of the model. If it equals
to 2, the initial state vector covariance is a monte-carlo based
estimate of the ergodic variance (consistent with a k-order
Taylor-approximation of the model). At last, if it equals to 3, the
covariance is a diagonal matrix, whose value is determined by
**options_.particle.initial_state_prior_std**.
covariance is a diagonal matrix, with diagonal values that can be set
with **particle_filter_options = ('initial_state_prior_std', double, ...)**.
-**particle_filter_options = ('pruning', true, ...)** allows to enable
pruning for particle-filter related simulations.
-**particle_filter_options = ('mixture_state_variables', Integer, 'mixture_structural_shocks', Integer,'mixture_measurement_shocks', Integer,... )** allows to set the number
of mixture components for the states (default: 5), structural shocks (default: 1), and measurement
errors (default: 1), respectively for the Gaussian-mixture filter (**gmf**).
# References
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@@ -541,7 +549,7 @@ Proceedings of the IEEE, 95(5), 899-924.
Economics and Finance, Econometric Reviews, 31(3), 245-296.
**Del Moral P. (2004)**, Feynman Kac Formulae: Genealogical and
Interacting Particle Systems with Applications, New-York Springer.
Interacting Particle Systems with Applications, Springer, New-York.
**Douc R., Cappé O. and Moulines E. (2005)**, Comparison of Resampling
Schemes for Particle Filtering, 4th International Symposium on Image
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@@ -563,7 +571,7 @@ Nonlinear filtering, Oxford University Press.
Journal of Applied Econometrics 20, 891-910.
**Fernandez-Villaverde, J. and Rubio-Ramirez J.F. (2007)**, Estimating
Macroeconomic Models: a Likelihood Approach, The Review of Economic
Macroeconomic Models: a Likelihood Approach, Review of Economic
Studies 74(4), 1059-1087.
**Fernandez-Villaverde, J., Rubio-Ramirez J.F. and Schorfheide
...
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@@ -575,7 +583,7 @@ Studies 74(4), 1059-1087.
Proceedings-F, 140, 107-113.
**Herbst E. and Schorfheide F. (2015)**, Bayesian Estimation of DSGE
Models, online version.
Models, Princeton University Press, Princeton.
**Julier S.J. and Uhlmann J.K. (1997)**, A New Extension of the Kalman
Filter to Nonlinear Systems, Proceedings of AeroSense, the 11th Int.
