Application of the Kalman filter to a Markov switching model.
Item
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Title
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Application of the Kalman filter to a Markov switching model.
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Identifier
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AAI9720122
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identifier
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9720122
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Creator
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Nishiyama, Kazume.
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Contributor
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Adviser: Salih N. Neftci
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Date
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1997
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Language
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English
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Publisher
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City University of New York.
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Subject
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Economics, General | Economics, Finance | Statistics
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Abstract
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This paper proposes a linear approximation in the form of Kalman filter for models with Markov regime shifts. James Hamilton (1989) developed the optimal nonlinear algorithm for this type of model in Econometrica. However, the nonlinear filter lacks a closed form solution. It involves highly complicated and time-consuming procedures and is difficult to implement. On the other hand, the optimal linear filter, the Kalman filter, has a closed form solution and is simple and easy to implement. This paper investigates how well the Kalman filter approximates the optimal filter in various situations.;In the first section of this paper, the Kalman filter formulae are derived for a model with hidden states following a first order Markov process. Next, we apply the Kalman filter to US real GNP series to establish business cycle dates. These dates are compared with those of Hamilton and the national Bureau of Economic Research. Finally, simulations are conducted to compare the two filters in more general contexts.;The results indicate that the optimal linear filter approximates the nonlinear filter remarkably well. When the Kalman filter is applied to US real GNP series, it yields business cycle dates which are very similar to those of NBER and Hamilton. Moreover, the results of simulations indicate that the larger the unexpected jumps or shifts in the series, the better the Kalman filter approximates the nonlinear filter. Further, for extremely large unexpected jumps and shifts, the Kalman filter actually outperforms the nonlinear filter.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
