78
Originally published by Ipea in July 1998 as
number 575 of the series Texto para Discussão.
AN ADAPTIVE RESAMPLING SCHEME
FOR CYCLE ESTIMATION
Alexandra Mello Schmidt
Dani Gamerman
Ajax R. B. Moreira
78
DISCUSSION PAPER
Originally published by Ipea in July 1998 as
number 575 of the series Texto para Discussão.
Brasília, January 2015
AN ADAPTIVE RESAMPLING SCHEME
FOR CYCLE ESTIMATION
Alexandra Mello Schmidt1
Dani Gamerman2
Ajax R. B. Moreira3
1. Bolsista do PNPE na Diretoria de Pesquisa do Ipea.
2. Do IM-UFRJ.
3. Da Diretoria de Pesquisa do Ipea.
Federal Government of Brazil
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Minister Roberto Mangabeira Unger
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DISCUSSION PAPER
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© Institute for Applied Economic Research – ipea 2015
Discussion paper / Institute for Applied Economic
Research.- Brasília : Rio de Janeiro : Ipea, 1990ISSN 1415-4765
1. Brazil. 2. Economic Aspects. 3. Social Aspects.
I. Institute for Applied Economic Research.
CDD 330.908
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SUMÁRIO
RESUMO
ABSTRACT
1 - INTRODUCTION.................................................................................1
2 - BAYESIAN DYNAMIC LINEAR MODELS...........................................2
2.1 - General Bayesian Dynamic Linear Model and Hyperparameters ....2
2.2 - Classes of DLM................................................................................4
3 - METHODOLOGY................................................................................7
3.1 - Sampling Importance Resampling ...................................................7
3.2 - Samping Importance Resampling in Two Steps ..............................8
4 - APPLICATIONS................................................................................10
4.1 - Simulated Data ..............................................................................10
4.2 - Electroencephalogram Data...........................................................12
4.3 - Brazilian Industrial General Production..........................................14
5 - CONCLUSION ..................................................................................15
APPENDIX .............................................................................................17
BIBLIOGRAFIA ......................................................................................26
RESUMO
Os modelos lineares dinâmicos (MLD) West and Harrison (1997) constituem
instrumentos úteis para a previsão de curto prazo de séries de tempo porque são
flexíveis e também podem decompor a trajetória da série em fatores relevantes
que têm interpretação e dinâmica característica. Tais modelos, entretanto,
dependem de quantidades desconhecidas, constantes ao longo da amostra,
denominadas hiperparâmetros.
Neste artigo, um (MLD) com componentes auto-regressivas é utilizado para
descrever séries que têm componentes cíclicas. A distribuição marginal para os
parâmetros de estado pode ser obtida ponderando as distribuições condicionais
desses parâmetros pela distribuição marginal dos hiperparâmetros. Na maioria dos
casos, a distribuição conjunta dos hiperparâmetros pode ser obtida analiticamente,
mas não a distribuição marginal dos componentes, o que requer integração
numérica. Propomos obter amostras de hiperparâmetros utilizando uma variante
do método de amostragem e reamostragem por importância (SIR). Apresentamos
uma aplicação com dados simulados e duas com dados reais.
ABSTRACT
Bayesian dynamic linear models (DLM) are useful in time series modelling
because of the flexibility that they present in obtaining a good forecast. They are
based on a decomposition of the relevant factors which explain the behavior of the
series through a series of state parameters. Nevertheless the DLM as developed in
West & Harrison (1997) depend on additional quantities, such as the variance of
the system disturbances, which, in practice, are unknown. These are refered as
hyperparameters of the model.
In this paper, DLM with auto-regressive components are used to describe time
series showing cyclic behavior. The marginal posterior distribution for state
parameters can be obtained by weighing the conditional distribution of state
parameters by the marginal distribution of hyperparameters. In most cases the
joint distribution of the hyperparameters can be obtained analytically but the
marginal distributions of the components can not, thus requiring numerical
integration. We propose to obtain samples of the hyperparameters by a variant of
the Sampling Importance Resampling (SIR) method. A few applications are made
with simulated and real datasets.
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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AN ADAPTIVE RESAMPLING SCHEME FOR CYCLE ESTIMATION
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