Tanizaki H. and Mariano R.S. (1998) Nonlinear and Non-Gaussian State-Space Modeling with Monte-Carlo Simulations. Journal of Econometrics, 83, 263-290.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....methods have been developed to generate realizations from the smoothing density. Earlier existing approaches include approximating the individual marginal smoothing distribution , either using the two filter formula [8] or forward filtering backward smoothing [6] 28] As an alternative, Tanizaki [29] has recently proposed methods for generating random draws from the joint distribution or . As with the methods of [6] and [28] these techniques require the simulation of expensive normalizing constants, and the focus is on marginal state distributions rather than joint distributions over time. ....

....using the Markovian assumptions of the model, we can write (8) with the modified weights (9) This revised particle distribution can now be used to generate states successively in the reverse time direction, conditioning on future states. It should be noted that in contrast with [6] 28] and [29], the method does not require the simulation of any additional normalizing constants since the modified weights are easily renormalized. Having performed a forward sweep of particle filtering, generating weighted particles , the smoothing algorithm proceeds as follows: Algorithm 2 Generic ....

H. Tanizaki, "Nonlinear and non-Gaussian state space modeling using sampling techniques," Ann. Inst. Statist. Math., vol. 53, no. 1, pp. 63--81, 2001.

....the smoothing density are recursively generated at each time and the random draws from the smoothing are based on those from the filtering density. In the case of smoothing, the resampling approach has the disadvantage that it takes an extremely long time computationally. Tanizaki (1996, 1999) Tanizaki and Mariano (1998) and Mariano and Tanizaki (2000) proposed nonlinear filter and smoother utilizing rejection sampling, where random draws from the filtering density and the smoothing density are recursively obtained as in the resampling procedure. When the acceptance probability is close to zero, rejection ....

Tanizaki, H. and Mariano, R.S., 1998, " Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Simulations, " Journal of Econometrics, Vol.83, No.1,2, pp.263 -- 290.

....random draws from prediction, filtering and smoothing densities. For generation of filtering and smoothing random draws, one step ahead prediction random draws are chosen with the corresponding probabilities. Programming is very easy compared with the above two approaches. Tanizaki (1996, 1999a) Tanizaki and Mariano (1998), Hurzeler and Kunsch (1998) Mariano and Tanizaki (2000) proposed an nonlinear and nonnormal filter and smoother using rejection sampling. For a solution to nonlinear and nonnormal state space model, we use the random draws to obtain filtering and smoothing estimates. By rejection sampling, a ....

....extremely large number of random draws are required for precision of the filtering and smoothing estimates. Furthermore, improving computation time on rejection sampling and convergence on the Gibbs sampler, we introduce quasi filter and quasi smoother using the Metropolis Hastings algorithm (see Tanizaki (1998)) As mentioned above, the rejection sampling procedure does not work when the acceptance probability is small and the Markov chain Monte Carlo procedure needs numerous numbers of random draws because of slow convergence of the Gibbs sampler. The quasi filter and quasi smoother improve both the ....

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Tanizaki, H. and Mariano, R.S., 1998, " Nonlinear and Non-Gaussian State-Space Modeling with MonteCarlo Simulations, " Journal of Econometrics, Vol.83, No.1-2, pp.263 -- 290.

....generation of filtering and smoothing random draws, one step ahead prediction random draws are chosen with the corresponding probabilities. Programming is very easy compared with the above two approaches. Tanizaki (1996, 1999a) Tanizaki and Mariano (1998) Hurzeler and Kunsch (1998) Mariano and Tanizaki (2000) proposed an nonlinear and nonnormal filter and smoother using rejection sampling. For a solution to nonlinear and nonnormal state space model, we use the random draws to obtain filtering and smoothing estimates. By rejection sampling, a recursive algorithm of the random draws are obtained. Thus, ....

....of # t . c t is observable while both c p t and c T t are unobservable, where c p t is regarded as the state variable to be estimated by the nonlinear filtering and smoothing technique. Thus, we can estimate permanent and transitory consumption separately. Tanizaki (1993a, 1996) and Mariano and Tanizaki (2000) consider the above example, where the utility function of the representative agent is assumed to be a constant relative risk aversion type of utility function. Also see Diebold and Nerlove (1989) for a concise survey of testing the permanent income hypothesis. 2.1.6 Markov Switching Model The ....

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Tanizaki, H., 2000, " Nonlinear and Non-Gaussian State Space Modeling Using Sampling Techniques, " Unpublished Manuscript (http:// ht.econ.kobe-u.ac.jp/ # tanizaki/ cv/ papers/ sfil.pdf).

....with importance sampling. Moreover, Carlin, Polson and Sto#er (1992) Carter and Kohn (1994, 1996) and Chib and Greenberg (1996) proposed the nonlinear smoothing by Gibbs sampling. The nonlinear filter with rejection sampling is introduced by Mariano and Tanizaki (1999) Tanizaki (1996, 1999) and Tanizaki and Mariano (1998), where random draws are directly generated from the filtering densities. Gordon, Salmond and Smith (1993) and Kitagawa (1996) applied the resampling procedure to the nonlinear filter and smoother. Thus, in the last decade, a large amount of research on filtering theory has been devoted to ....

Tanizaki, H. and Mariano, R.S., 1998, "Nonlinear and Non-Gaussian StateSpace Modeling with Monte-Carlo Stochastic Simulations," Journal of Econometrics, Vol.83, No.1, 2, pp.263 -- 290.

....the Markov chain Monte Carlo methods. Tanizaki and Mariano (1994) Mariano and Tanizaki (1995) and Tanizaki (1996, 1999b) applied Monte Carlo integration with importance sampling to derive nonlinear and non Gaussian state space models. Tanizaki (1996, 1999a) Mariano and Tanizaki (1999) and Tanizaki and Mariano (1998) utilized rejection sampling to generate random draws directly from filtering densities. Gordon, Salmond and Smith (1993) and Kitagawa (1996) Kitagawa and Gersch (1996) Tanizaki (1997) and Tanizaki and Mariano (1996) also obtained filtering means by random draws. As for nonlinear and ....

....case for KS as in Simulation 2. In addition, even in the linear and normal case (i.e. Simulation 1) the estimate of # is underestimated and less e#cient for all # = 0.5, 0.9, 1.0 while (A) performs better than any other estimator. 6 SUMMARY Using rejection sampling, Tanizaki (1996, 1999a) Tanizaki and Mariano (1998) and Mariano and Tanizaki (1999) proposed a nonlinear and non Gaussian filter, where random draws are recursively generated from the filtering density at each time. Rejection sampling is very e#cient to generate random draws from the target density function. However, it is well known that (i) ....

Tanizaki, H. and Mariano, R.S., 1998, " Nonlinear and Non-Gaussian StateSpace Modeling with Monte Carlo Simulations, " Journal of Econometrics, Vol.83, No.1,2, pp.263 -- 290.

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Tanizaki, H., 1999c, " Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Techniques: A Survey and Comparative Study, " in Handbook of Statistics, edited by Rao, C.R. and Shanbhag, D.N., 27 North-Holland, forthcoming (http://ht.econ.kobe-u.ac.jp/ # tanizaki/cv/ papers/survey.pdf).

....the two filter formula, where forward and backward filtering are performed and combined to obtain the smoothing density. The smoother based on the two filter formula is discussed in Appendix A. The RS filter and smoother have been developed by Tanizaki (1996, 1999) Hurzeler and Kunsch (1998) and Tanizaki and Mariano (1998). To implement RS for random number generation, we need to compute the supremum in the acceptance probability, which depends on the underlying functional form of the measurement and transition equations. RS cannot be applied in the case where the acceptance probability is equal to zero, i.e. when ....

....in this paper. However, for comparison with the other estimators, we have discussed the IR filter based on (3.2) in Section 3.1. The filter based on (3.3) and the smoothers with (3.4) 3.5) and (3. 7) are proposed in this paper, where the RS filters and smoothers proposed by Tanizaki (1996, 1999) Tanizaki and Mariano (1998) are substantially extended to much less computational estimators. Under the same number of random draws, it is easily expected that RS gives us the best estimates of the three sampling techniques while MH yields the worst estimates. The features of RS are that we can generate random numbers from ....

Tanizaki, H. and Mariano, R.S. (1998). Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Simulations, J. of Econometrics, 83, 263--290.

....of the state variables yields less computational smoothers. Thus, in this paper we propose the nonlinear non Gaussian filters and smoothers using the joint densities of the state variables. 2. Preliminaries 2. 1 State Space Model Kitagawa (1987) Harvey (1989) Kitagawa and Gersch (1996) and Tanizaki (1996, 2001) discuss the nonlinear non Gaussian state space models, which are described by the following two equations: Measurement equation) y t = h t (# t , # t ) 2.1) Transition equation) # t = f t (# t 1 , # t ) 2.2) 3 where y t represents the observed data at time t while # t denotes the state ....

.... # t , # t and # 0 are mutually independently distributed as: # t # N(0, 1) # t # N(0, 10) and # 0 # N(0, 10) This model is examined in Kitagawa (1987, 1996, 1998) and Carlin et al. 1992) where the Gibbs sampler suggested by Carlin et al. 1992) does not work at all (see, for example, Tanizaki (2001)) Simulation V (Structural Change) The data generating process is given by: y t = # t # t and # t = d t ## t 1 # t , but the estimated system is: y t = # t # t and # t = ## t 1 # t , where d t = 1 for t = 21, 22, 40, d t = 1 for t = 61, 62, 80 and d t = 0 otherwise. This ....

Tanizaki, H. (2001). Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Techniques: A Survey and Comparative Study, Handbook of Statistics (Stochastic Processes: Modeling and Simulation) (ed. C.R. Rao and D.N. Shanbhag), Elsevier Science B.V., Amsterdam, forthcoming.

No context found.

Tanizaki H. and Mariano R.S. (1998) Nonlinear and Non-Gaussian State-Space Modeling with Monte-Carlo Simulations. Journal of Econometrics, 83, 263-290.

No context found.

H. Tanizaki, "Nonlinear and Non-Gaussian State Space Modeling Using Sampling Techniques," Annals of the Institute of Statistical Mathematics, vol. 53, no. 1, pp. 63--81, 2001.

No context found.

H. Tanizaki, \Nonlinear and non-Gaussian state space modeling using sampling techniques," Annals of the Institute of Statistical Mathematics, vol. 53, no. 1, pp. 63-81, 2001.

No context found.

Tanizaki H. and Mariano R.S. (1998) Nonlinear and Non-Gaussian State-Space Modeling with Monte-Carlo Simulations. Journal of Econometrics, 83, 263-290.

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