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Abstract:
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In unobserved component models, trends, seasonal terms, cycles, and other components are modeled as stochastic processes and can be estimated using the Kalman filter, provided the model is linear. In many economic series, the components combine multiplicatively so the Kalman filter applies with a trivial logarithmic transformation, but more complicated setups. For instance, a model with both additive and multiplicative components, are problematic. In this paper, we will estimate nonlinear UC models with some classical nonlinear state estimation methods, like extended Kalman filtering. Specifically, we will analyze the performance in a model which combines a multiplicative trend and seasonal component with additive noise. As an empirical illustration, we fit a number of U.S. macro-economic time series.
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