... | ... | @@ -386,7 +386,7 @@ mean, the median and some empirical quantiles. |
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Use for instance the following instruction:
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```example
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estimation(datafile=extreme,order=2,mode_compute=0);
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estimation(datafile=extreme,order=2,mode_compute=0,particle_filter_options = ('pruning', true, ...),...);
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```
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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 |
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default) starting from the initial conditions, the likelihood being
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calculated with the nonlinear filter by default, namely the Bootstrap
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particle filter with systematic resampling using standard Kitagawa's
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approach and 5,000 particles.
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approach and 5,000 particles and using `pruning` for the particle
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filter-related simulations. The **particle_filter_options = (NAME, VALUE, ...)**
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syntax allows setting some fine-grained options.
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Contrarily to linear estimation, it is not possible to calculate
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accurately the *posterior* mode in the presence of resampling because
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... | ... | @@ -408,30 +410,31 @@ confirm his/her choice. |
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The following table summarizes the options included in **estimation**.
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| Option names | Values ([default]) |
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| ------ | ------ |
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| filter_algorithm | [sis], apf, nlkf, gf, gmf, cpf |
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| proposal_approximation | [cubature], unscented, montecarlo |
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| distribution_approximation | [cubature], unscented, montecarlo |
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| number_of_particles | [5000] |
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| resampling | [systematic], none, generic |
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| resampling_method | [kitagawa], residual |
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| mode_compute | 7, 8, 9 |
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| mh_replic | [20000], 0 |
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| online_particle_filter | |
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| Option names | Values ([default]) |
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| ------ | ------ |
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| filter_algorithm | [sis], apf, nlkf, gf, gmf, cpf |
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| proposal_approximation | [cubature], unscented, montecarlo |
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| distribution_approximation | [cubature], unscented, montecarlo |
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| number_of_particles | [5000] |
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| resampling | [systematic], none, generic |
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| resampling_method | [kitagawa], residual |
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| mode_compute | 7, 8, 9 |
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| mh_replic | [20000], 0 |
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| online_particle_filter | |
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| nonlinear_filter_initialization| [1],2,3 |
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First of all, the choice of the filter is operated with the keyword
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**filter_algorithm**. The sequential importance sampling (**sis**) is
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the filter by default but one can also choose the auxiliary particle
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filter (**apf**), the nonlinear Kalman filter (**nlkf**), the gaussian
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filter (**gf**), the gaussian-mixture filter (**gmf**), and the
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filter (**apf**), the nonlinear Kalman filter (**nlkf**), the Gaussian
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filter (**gf**), the Gaussian-mixture filter (**gmf**), and the
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conditional particle filter (**cpf**).
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Keyword **online_particle_filter** triggers the online estimation of
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the model, using the method developped by Liu and West. It works for
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the model, using the method developed by Liu and West. It works for
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**order=1** as well as
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**order>1**. **options_.particle.liu_west_delta** controls the value
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of the $`\delta`$ parameter (set equal to 0.9 by default).
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**order>1**. **particle_filter_options = ('liu_west_delta', VALUE, ...)** controls the value
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of the $`\delta`$ parameter (set equal to 0.99 by default).
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Some dependencies among other keywords should be clarified. They are
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summarized by the following table.
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... | ... | @@ -451,10 +454,7 @@ methods. One should notice that unscented transform is controled with |
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three parameters: $`\alpha`$ and $`\kappa`$ that determine the spread
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of the sigma-points and $`\beta`$ that characterizes the
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(non-gaussian) distribution. By default, we set $`\alpha =
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\kappa=1`$ and $`\beta=2`$. They can be modified by redefining
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**options_.particle.unscented.alpha**,
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**options_.particle.unscented.kappa** and
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**options_.particle.unscented.beta**.
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\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.
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- The number of particles can be chosen with the keyword
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**number_of_particles**.
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... | ... | @@ -498,16 +498,24 @@ of the sigma-points and $`\beta`$ that characterizes the |
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chosen with the keyword **resampling_method** when resampling is
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used.
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- **options_.particle.initialization** controls the initial states
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- **nonlinear_filter_initialization** controls the initial states
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distribution of the filter. Three possibilities are offered to the
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user. If **options_.particle.initialization=1** (the default), the
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user. If **nonlinear_filter_initialization=1** (the default), the
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initial state vector covariance is the ergodic variance associated
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to the first order Taylor-approximation of the model. If it equals
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to 2, the initial state vector covariance is a monte-carlo based
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estimate of the ergodic variance (consistent with a k-order
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Taylor-approximation of the model). At last, if it equals to 3, the
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covariance is a diagonal matrix, whose value is determined by
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**options_.particle.initial_state_prior_std**.
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covariance is a diagonal matrix, with diagonal values that can be set
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with **particle_filter_options = ('initial_state_prior_std', double, ...)**.
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- **particle_filter_options = ('pruning', true, ...)** allows to enable
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pruning for particle-filter related simulations.
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- **particle_filter_options = ('mixture_state_variables', Integer, 'mixture_structural_shocks', Integer,'mixture_measurement_shocks', Integer,... )** allows to set the number
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of mixture components for the states (default: 5), structural shocks (default: 1), and measurement
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errors (default: 1), respectively for the Gaussian-mixture filter (**gmf**).
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# References
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... | ... | @@ -541,7 +549,7 @@ Proceedings of the IEEE, 95(5), 899-924. |
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Economics and Finance, Econometric Reviews, 31(3), 245-296.
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**Del Moral P. (2004)**, Feynman Kac Formulae: Genealogical and
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Interacting Particle Systems with Applications, New-York Springer.
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Interacting Particle Systems with Applications, Springer, New-York.
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**Douc R., Cappé O. and Moulines E. (2005)**, Comparison of Resampling
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Schemes for Particle Filtering, 4th International Symposium on Image
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... | ... | @@ -563,7 +571,7 @@ Nonlinear filtering, Oxford University Press. |
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Journal of Applied Econometrics 20, 891-910.
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**Fernandez-Villaverde, J. and Rubio-Ramirez J.F. (2007)**, Estimating
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Macroeconomic Models: a Likelihood Approach, The Review of Economic
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Macroeconomic Models: a Likelihood Approach, Review of Economic
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Studies 74(4), 1059-1087.
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**Fernandez-Villaverde, J., Rubio-Ramirez J.F. and Schorfheide
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... | ... | @@ -575,7 +583,7 @@ Studies 74(4), 1059-1087. |
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Proceedings-F, 140, 107-113.
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**Herbst E. and Schorfheide F. (2015)**, Bayesian Estimation of DSGE
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Models, online version.
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Models, Princeton University Press, Princeton.
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**Julier S.J. and Uhlmann J.K. (1997)**, A New Extension of the Kalman
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Filter to Nonlinear Systems, Proceedings of AeroSense, the 11th Int.
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... | ... | @@ -621,6 +629,6 @@ Association, 94(446), 590-599. |
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Particle Filters for Sequential Probabilistic Inference in Dynamic
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State-Space Models, mimeo.
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**Winschel V. and Kraltzig M. (2010)**, Solving, Estimating, and
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**Winschel V. and Krätzig M. (2010)**, Solving, Estimating, and
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Selecting Nonlinear Dynamic Models without the Curse of
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Dimensionality, Econometrica, 78(2), 803-821. |